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Call number: | SPRINGER-2014-9783642195983:ONLINE Show nearby items on shelf |
Title: | Basic Concepts in Physics [electronic resource] : From the Cosmos to Quarks |
Author(s): |
Masud Chaichian Hugo Perez Rojas Anca Tureanu |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Basic Concepts in Physics: From the Cosmos to Quarks is the outcome of the authors' long and varied teaching experience in different countries and for different audiences, and gives an accessible and eminently readableintroduction to all the main ide as of modern physics. The books fresh approach, using a novel combination of historical and conceptual viewpoints, makes it ideal complementary reading to more standard textbooks. The first fivechapters are devoted to classical physics, from planetary mot ion to special relativity, always keeping in mind its relevance to questions of contemporary interest. The next six chapters deal mainly with newer developments in physics,from quantum theory and general relativity to grand unified theories, and the book concludes by discussing the role of physics in living systems. A basic grounding in mathematics is required of the reader, but technicalities areavoided as far as possible thus complex calculations are omitted so long as the essential ideas remain clear. The book is addressed to undergraduate and graduate students in physics and will also be appreciated by many professionalphysicists. It will likewise beof interest to students, researchers and teachers of other natural sciences, as well as to engineers, h igh-school teachers and the curious general reader, who will come to understand what physics isabout and how it describes the different phenomena of Nature. Not only will readers of this book learn much about physics, they will also learn to love it. |
Contents: | Gravitation and Newton Laws |
Entropy, Statistical Physics and Information | |
Electromagnetism and Maxwell Equations | |
Electromagnetic Waves | |
The Special Theory of Relativity | |
The Atom and Quantum Theory | |
Quantum Electrodynamics | |
Fermi | |
Dirac and Bose | |
Einstein Statistics | |
The Four Fundamental Forces | |
General Relativity and Cosmology | |
Unification of the Forces of Nature | |
Physics and Life | |
Index | |
ISBN: | 9783642195983 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Undergraduate Lecture Notes in Physics, 2192-4791 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Biochemistry |
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Call number: | SPRINGER-2014-9783319082288:ONLINE Show nearby items on shelf |
Title: | Dynamical Systems Generated by Linear Maps [electronic resource] |
Author(s): |
emal B Dolianin Anatolij B Antonevich |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systemstheory. However, for the d ynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications. The considered problems are natural and look rather simple, but in reality in thecourse of investigation, they confront users with plenty of subtle questions, and their detailed analysis needs a substantial effort. The problems arising are related to linear algebra and dynamical systems theory, and therefore, thebook can be considered as a natural amplification, refinement and supple ment to linear algebra and dynamical systems theory textbooks |
Contents: | From the Contents: Introduction |
Vector trajectory | |
The Jordan basis and special subspaces | |
Representation of the vector trajectory | |
The structures related to the principal term of the vector Trajectory | |
The asymptotic behavior of vector trajectories and trajectories of one | |
dimensional subspaces | |
ISBN: | 9783319082288 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Engineering , Vibration |
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Call number: | SPRINGER-2014-9783319035635:ONLINE Show nearby items on shelf |
Title: | Mathematical and Numerical Methods for Partial Differential Equations [electronic resource] : Applications for Engineering Sciences |
Author(s): |
Jol Chaskalovic |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approachfirst summarizes and o utlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverseexercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing thematerial, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic |
Contents: | From the Contents: Introduction to functional analytical methods of partial differential equations |
The finite element method | |
Variational Formulations of elliptic boundary problems | |
Finite Elements and differential Introduction to functional analytical methods of partial differential equations | |
The finite element method | |
Variational Formulations of elliptic boundary problems | |
ISBN: | 9783319035635 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematical Engineering, 2192-4732 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Numerical analysis , Engineering mathematics , Materials |
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Call number: | SPRINGER-2014-9783034808439:ONLINE Show nearby items on shelf |
Title: | Condenser Capacities and Symmetrization in Geometric Function Theory [electronic resource] |
Author(s): |
Vladimir N Dubinin |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original the main part has not been covered by existing textbooks andmonographs. After an introduc tion to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others)is established, followed by various types of symmet rization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problemsare solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis andpotential theory |
Contents: | Preface |
1.Conformal capacity | |
2. Asymptotics of the condenser capacity when one of the plate degenerates | |
Special transformations | |
4. Symmetrization | |
5. Metric properties of sets and condensers | |
6. Problems of extremal decomposition | |
7. Univalent functions | |
8. Multivalent functions | |
Appendices: A1. Dirichlet principle | |
A2. Uniqueness theorem for contracting mapping | |
A3. On separating transformation of sets and condensers | |
A4. On conservation of reduced moduli under geometric trans | |
formation of domains | |
A5. Quadratic differentials | |
A6. Unsolved problems | |
Reference | |
ISBN: | 9783034808439 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2014-9781447153610:ONLINE Show nearby items on shelf |
Title: | Probability Theory [electronic resource] : A Comprehensive Course |
Author(s): |
Achim Klenke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineeringand computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To addressthese concepts, the title covers a wide variet y of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables martingales percolation Markov chains andelectrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integral and stochasticdifferential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts inprobability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulat ions and some difficult proofs have been made more accessible. A wealth ofexamples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathe matics and statistics in physics, computer science,economics and biology |
Contents: | Basic Measure Theory |
Independence | |
Generating Functions | |
The Integral | |
Moments and Laws of Large Numbers | |
Convergence Theorems | |
Lp | |
Spaces and the RadonNikodym Theorem | |
Conditional Expectations | |
Martingales | |
Optional Sampling Theorems | |
Martingale Convergence Theorems and Their Applications | |
Backwards Martingales and Exchangeability | |
Convergence of Measures | |
Probability Measures on Product Spaces | |
Characteristic Functions and the Central Limit Theorem | |
Infinitely Divisible Distributions | |
Markov Chains | |
Convergence of Markov Chains | |
Markov Chains and Electr | |
ISBN: | 9781447153610 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9780817684099:ONLINE Show nearby items on shelf |
Title: | A Probability Path [electronic resource] |
Author(s): |
Sidney I Resnick |
Date: | 2014 |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate studentsfrom a variety of disci plines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research instatistics, applied probability, biology, operations research, mathematical finance, and engineering. Aone-semester course is laid out in an efficient and readable manner covering the core material. The first three chaptersprovide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applicationsto statistics (quantile and distribution function estimation), and applied probability. Two subsequent cha pters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treatsconditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance. Like Adventures in Stochastic Processes, Resnicks related and very successful textbook, A Probability Path isrich in appropriate examples, illustrations, and problems, and is suitable for classroom use or self-study. The present uncorrected, softcover reprintis designed to make this classic textbookavailable to a wider audience. This book is different from the classical textbooks on probability theory in that it treats the measure theoreticbackground not as a prerequisite but as an integral part of probability theory. Th e result is that the reader gets a thorough and well-structured framewo |
ISBN: | 9780817684099 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Modern Birkhuser Classics, 2197-1803 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) , Mathematical statistics |
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Call number: | SPRINGER-2013-9783642349287:ONLINE Show nearby items on shelf |
Title: | Surveys in Differential-Algebraic Equations I [electronic resource] |
Author(s): |
Achim Ilchmann Timo Reis |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The need for a rigorous mathematical theory for Differential-Algebraic Equations (DAEs) has its roots in the widespread applications of controlled dynamical systems, especially in mechanical and electrical engineering. Due to thestrong relation to (o rdinary) differential equations, the literature for DAEs mainly started out from introductory textbooks. As such, the present monograph is new in the sense that it comprises survey articles on various fields ofDAEs, providing reviews, presentations of the current state of research and new concepts in - Controllability for linear DAEs - Port-Hamiltonian differential-algebraic systems - Robustness of DAEs - Solution concepts for DAEs- DAEs in circuit modeling. The results in the individual chapters are pres ented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basicprinciples of DAEs) for self-study |
Note: | Springer eBooks |
ISBN: | 9783642349287 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Differential-Algebraic Equations Forum |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Systems theory , Numerical analysis |
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Call number: | SPRINGER-2013-9783642312380:ONLINE Show nearby items on shelf |
Title: | Quantum Physics in the Nanoworld [electronic resource] : Schrdinger's Cat and the Dwarfs |
Author(s): |
Hans Lth |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book deals with all essential aspects of non-relativistic quantum physics up to the quantization of fields. In contrast to common textbooks of quantum mechanics, modern experiments are described both for the purpose offoundation of the theory and in relation to recent applications. In this respect applications to nano-electronics as well as the realization of quantum-bits are presented and discussed. Furthermore, links are made to other importantresearch fields and applications, such as elementar y particle physics, solid state physics and nuclear magnetic resonance tomography in medicine. Even though the representation of the topics is largely performed in terms of Diracsbra-ket notation and by use of commutator algebra, the concrete description of the physical basis and the corresponding theoretical concepts are emphasized. Because of little requirement of complex mathematics, the book is suitable asan introduction into quantum physics, not only for physicists but also for chemists, biologists, engineers, computer scientists and even for philosophers as far as they are interested in natural philosophy and epistomology |
Note: | Springer eBooks |
Contents: | Some Fundamental Experiments |
Particle | |
Wave Duality | |
Quantum States in Hilbert Space | |
Angular Momentum, Spin and Particle Categories | |
Approximate Solutions for Important Model Systems | |
Superposition, Entanglement and other Oddities | |
Fields and Quanta | |
ISBN: | 9783642312380 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Physics, 1868-4513 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Nanochemistry , Quantum theory , Engineering , Nanotechnology |
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Call number: | SPRINGER-2013-9781461457251:ONLINE Show nearby items on shelf |
Title: | Hidden HarmonyGeometric Fantasies [electronic resource] : The Rise of Complex Function Theory |
Author(s): |
Umberto Bottazzini Jeremy Gray |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Hidden HarmonyGeometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted tocomplex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subjectCauchy, Riemann, and Weierstrassit looks at thecontributions of great mathematicians from dAlembert to Po incar, and Laplace to Weyl. Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric functiontheory, and the early years of complex function theory in several variables. Unique em phasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages.This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture o f the broad cultural and social context in which the main players lived and worked by paying attention to the rise ofmathematical schools and of contrasting national traditions. This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professionalmathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory |
Note: | Springer eBooks |
Contents: | List of Figures |
Introduction | |
1. Elliptic Functions | |
2. From real to complex | |
3. Cauch | |
4. Elliptic integrals | |
5. Riemann | |
6. Weierstrass | |
7. Differential equations | |
8. Advanced topics | |
9. Several variables | |
10. Textbooks | |
ISBN: | 9781461457251 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Sources and Studies in the History of Mathematics and Physical Sciences |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Number theory |
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Call number: | SPRINGER-2012-9788847025387:ONLINE Show nearby items on shelf |
Title: | Financial Mathematics [electronic resource] : Theory and Problems for Multi-period Models |
Author(s): |
Andrea Pascucci Wolfgang J Runggaldier |
Date: | 2012 |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | With the Bologna Accords a bachelor-master-doctor curriculum has been introduced in various countries with the intention that students may enter the job market already at the bachelor level. Since financial Institutions providenon negligible job oppo rtunities also for mathematicians, and scientists in general, it appeared to be appropriate to have a financial mathematics course already at the bachelor level in mathematics. Most mathematical techniques in usein financial mathematics are related to con tinuous time models and require thus notions from stochastic analysis that bachelor students do in general not possess. Basic notions and methodologies in use in financial mathematics canhowever be transmitted to students also without the technicalities f rom stochastic analysis by using discrete time (multi-period) models for which general notions from Probability suffice and these are generally familiar to studentsnot only from science courses, but also from economics with quantitative curricula. There d o not exists many textbooks for multi-period models and the present volume is intended to fill in this gap. It deals with the basic topics infinancial mathematics and, for each topic, there is a theoretical section and a problem section. The latter includ es a great variety of possible problems with complete solution |
Note: | Springer eBooks |
Contents: | Pricing and hedging |
Portfolio optimization | |
American options | |
Interest rates | |
ISBN: | 9788847025387 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Unitext, 2038-5714 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Economics |
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Call number: | SPRINGER-2012-9783642255885:ONLINE Show nearby items on shelf |
Title: | Manfredo P. do Carmo Selected Papers [electronic resource] |
Author(s): |
Manfredo P do Carmo Keti Tenenblat |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards,the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the mainfocus of this selection, though it also co ntains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featuredpapers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of currentinterest to researchers, including a paper co-authored with Frank Warner on the convexity of hy persurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the authorand his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collecti on pays tribute to one of the most distinguished mathematicians |
Note: | Springer eBooks |
Contents: | Preface |
A Summary of the Scientific Activities of Manfredo P. do Carmo | |
Summary of thePapers in this Volume by Manfredo P. do Carmo | |
Contributions | |
Complete List of Publications of Manfredo P. do Carmo | |
List of D.Sc. Students of Manfredo P. do Carmo | |
ISBN: | 9783642255885 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2012-9781461438946:ONLINE Show nearby items on shelf |
Title: | Calculus on Normed Vector Spaces [electronic resource] |
Author(s): |
Rodney Coleman |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematicalmaturity. All the important t opology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book isone of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader |
Note: | Springer eBooks |
Contents: | Preface |
1 Normed Vector Spaces | |
2 Differentiation | |
3 Mean value theorems | |
4 Higher derivatives and differentials | |
5 Taylor theorems and applications | |
6 Hilbert spaces | |
7 Convex functions | |
8 The inverse and implicit mapping theorems | |
9 Vector fields | |
10 The flow of a vector field | |
11 The calculus of variations: an introduction | |
Bibliography | |
Index | |
ISBN: | 9781461438946 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Mathematical optimization |
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Call number: | SPRINGER-2012-9781461436881:ONLINE Show nearby items on shelf |
Title: | Problems in Probability [electronic resource] |
Author(s): |
Albert N Shiryaev |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Problems in Probability comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled the exercisesin this text over the cour se of many years while working on topics which interested him the most. A substantial number of the exercises resulted from diverse sources such as textbooks, lecture notes, exercise manuals, monographs,and discussions that took place during special semin ars for graduate and undergraduate students. Many problems contain helpful hints and other relevant comments and a portion of the material covers some important applications fromoptimal control and mathematical finance. Readers of diverse backgroundsfrom students to researcherswill find a great deal of value in this book and can treat the work as an exercise manual, a handbook, or as a supplementary textto a course in probability theory, control, and mathematical finance. The problems and exercises in thi s book vary in nature and degree of difficulty. Some problems are meant to test the readers basic understanding, others are ofmedium-to-high degrees of difficulty and require more creative thinking. Other problems are meant to develop additional theoretic al concepts and tools or to familiarize the reader with various facts that are not necessarily covered inmainstream texts. Additional problems are related to the passage from random walk to Brownian motions and Brownian bridges. The appendix contains a su mmary of the main results, notation and terminology that are used throughout thebook. It also contains additional material from combinatorics, potential theory and Markov chainssubjects that are not covered in the book, but are nevertheless needed for man y of the exercises included here |
Note: | Springer eBooks |
Contents: | Preface |
1. Elementary Probability Theory | |
2. Mathematical Foundations of Probability Theory | |
3. Convergence of Probability Measures | |
4. Independent Random Variables | |
5. Stationary Random Sequences in Strict Sense | |
6. Stationary Random Sequences in Broad Sense | |
7. Martingales | |
8. Markov Chains | |
Appendix | |
References | |
ISBN: | 9781461436881 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Problem Books in Mathematics, 0941-3502 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Combinatorics , Distribution (Probability theory) |
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Call number: | SPRINGER-2012-9781461435822:ONLINE Show nearby items on shelf |
Title: | Introduction to the Mathematics of Finance [electronic resource] : Arbitrage and Option Pricing |
Author(s): |
Steven Roman |
Date: | 2012 |
Edition: | 2nd ed. 2012 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specificallywritten for advanced under graduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholesoption pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow muchmore smoothly. Several topics have been expanded such as the discussio ns of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewerchapters, and the material on the capital asset pricing model has been removed. The mathemati cs is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a smallamount of linear algebra is required. All necessary probability theory is developed throughout the book on a need-t o-know basis. No background in finance is required, since the book contains a chapter on options |
Note: | Springer eBooks |
Contents: | Preface |
Notation Key and Greek Alphabet | |
0 Introduction | |
Part 1 Options and Arbitrage | |
1 Background on Options | |
2 An Aperitif on Arbitrage | |
Part 2 Discrete | |
Time Pricing Models | |
3 Discrete Probability | |
4 Stochastic Processes, Filtrations and Martingales | |
5 Discrete | |
Time Pricing Models | |
6 The Binomial Model | |
7 Pricing Nonattainable Alternatives in an Incomplete Market | |
8 Optimal Stopping and American Options | |
Part 3 the Black | |
Scholes Option Pricing Formula | |
9 Continuous Probability | |
10 The Black | |
Scholes Option Pricing Formula | |
Appendix A: Convexity and the Separa | |
ISBN: | 9781461435822 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Distribution (Probability theory) |
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Call number: | SPRINGER-2012-9780817646622:ONLINE Show nearby items on shelf |
Title: | Self-adjoint Extensions in Quantum Mechanics [electronic resource] : General Theory and Applications to Schrdinger and Dirac Equations with Singular Potentials |
Author(s): |
D.M Gitman I.V Tyutin B.L Voronov |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis.Though a nave treatment exi sts for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded operators, resulting in paradoxes and inaccuracies. A propertreatment of these problems requires invoking certain nontrivial n otions and theorems from functional analysis concerning the theory of unbounded self-adjoint operators and the theory of self-adjoint extensions of symmetric operators.Self-adjoint Extensions in Quantum Mechanics begins by considering quantization problem s in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the nave treatment. The necessarymathematical background is then built by developing the theory of self-adjoint extensions. Through examination of v arious quantum-mechanical systems, the authors show how quantization problems associated with the correct definitionof observables and their spectral analysis can be treated consistently for comparatively simple quantum-mechanical systems. Systems that ar e examined include free particles on an interval, particles in a number of potential fieldsincluding delta-like potentials, the one-dimensional Calogero problem, the AharonovBohm problem, and the relativistic Coulomb problem. This well-organized text is m ost suitable for graduate students and postgraduates interested indeepening their understanding of mathematical problems in quantum mechanics beyond the scope of those treated in standard textbooks. The book may also serve as a useful resource for mathema ticians and researchers in mathematical andtheoretical physics |
Note: | Springer eBooks |
Contents: | Introduction |
Linear Operators in Hilbert Spaces | |
Basics of Theory of s.a. Extensions of Symmetric Operators | |
Differential Operators | |
Spectral Analysis of s.a. Operators | |
Free One | |
Dimensional Particle on an Interval | |
One | |
Dimensional Particle in Potential Fields | |
Schrdinger Operators with Exactly Solvable Potentials | |
Dirac Operator with Coulomb Field | |
Schrdinger and Dirac Operators with Aharonov | |
Bohm and Magnetic | |
Solenoid Fields | |
ISBN: | 9780817646622 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematical Physics : v62 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2011-9783642238994:ONLINE Show nearby items on shelf |
Title: | Newton Methods for Nonlinear Problems [electronic resource] : Affine Invariance and Adaptive Algorithms |
Author(s): |
Peter Deuflhard |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differentialequations). Its focus is on l ocal and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariantunder one out of four subclasses of affine transf ormations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the constructionof fully adaptive algorithms. Lots of numerical illustrations, compari son tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research |
Note: | Springer eBooks |
ISBN: | 9783642238994 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Series in Computational Mathematics, 0179-3632 : v35 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Differential Equations , Computer science Mathematics , Mathematical optimization , Engineering mathematics |
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Call number: | SPRINGER-2011-9780817681111:ONLINE Show nearby items on shelf |
Title: | A Friendly Guide to Wavelets [electronic resource] |
Author(s): |
Gerald Kaiser |
Date: | 2011 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers allthe fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoreticaldevelopments. I found Kaiser's straightforward end -of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should beessentially unbeatable for a long time. Proceedings of the IEEE It is well pr oduced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers inthat it presents a different approach to wavelet theory from the usual one. Computing Reviews I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternativesfor textbooks on wavelets. Physics Today This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation andcommon-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet th eory, Fourier analysis, and signal processing. SIAM Review The first half ofthe book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of el ectromagnetic wavelets...This theory promises to havemany other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes |
Note: | Springer eBooks |
Contents: | Preface |
Suggestions to the Reader | |
Symbols, Conventions, and Transforms | |
Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation | |
Windowed Fourier Transforms | |
Continuous Wavelet Transforms | |
Generalized Frames: Key to Analysis and Synthesis | |
Discrete Time | |
Frequency Analysis and Sampling | |
Discrete Time | |
Scale Analysis | |
Multiresolution Analysis | |
Daubechies Orthonormal Wavelet Bases | |
Part II: Physical Wavelets | |
Introduction to Wavelet Electromagnetics | |
Applications to Radar and Scattering | |
Wavelet Acoustics | |
References | |
Index | |
ISBN: | 9780817681111 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Mathematical physics |
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Call number: | SPRINGER-2010-9783642140372:ONLINE Show nearby items on shelf |
Title: | Classical Mechanics [electronic resource] : Hamiltonian and Lagrangian Formalism |
Author(s): |
Alexei Deriglazov |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, aswell as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyondthe traditional level adopted in the standar d textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described andexplained, so the book can be a good starting point for the undergradu ate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving thelevel of rigor that makes the book useful for the graduate students intending to work in one o f the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches oftheoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included |
Note: | Springer eBooks |
Contents: | Sketch of Lagrangian Formalism |
Hamiltonian Formalism | |
Canonical Transformations of Two | |
Dimensional Phase Space | |
Properties of Canonical Transformations | |
Integral Invariants | |
Potential Motion in a Geometric Setting | |
Transformations, Symmetries and Noether Theorem | |
Hamiltonian Formalism for Singular Theories | |
ISBN: | 9783642140372 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics , Mechanics , Engineering mathematics |
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Call number: | SPRINGER-2010-9783642053702:ONLINE Show nearby items on shelf |
Title: | Mechanics [electronic resource] : From Newton's Laws to Deterministic Chaos |
Author(s): |
Florian Scheck |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks toinclude dynamical system s and deterministic chaos in due detail. As compared to the previous editions the present fifth edition is updated and revised with more explanations, additional examples and sections on Noether's theorem.Symmetries and invariance principles, the basic ge ometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equationsof motion follow, to understand the importance of canonical mechanics an d of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches ofphysics. The book contains more than 120 problems with complete solutions, as well as some practica l examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook toaccompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics |
Note: | Springer eBooks |
Contents: | Elementary Newtonian Mechanics |
The Principles of Canonical Mechanics | |
The Mechanics of Rigid Bodies | |
Relativistic Mechanics | |
Geometric Aspects of Mechanics | |
Stability and Chaos | |
Continuous Systems | |
Exercises | |
Solution of Exercises | |
ISBN: | 9783642053702 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Physics, 1868-4513 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Differentiable dynamical systems , Mathematics , Mathematical physics , Mechanics , Mechanics, applied |
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Call number: | SPRINGER-2010-9781441963512:ONLINE Show nearby items on shelf |
Title: | Molecular Modeling and Simulation: An Interdisciplinary Guide [electronic resource] : An Interdisciplinary Guide |
Author(s): |
Tamar Schlick |
Date: | 2010 |
Edition: | Second |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Review of previous edition: I am often asked by physicists, mathematicians and engineers to recommend a book that would be useful to get them started in computational molecular biology. I am also often approached by mycolleagues in computational biol ogy to recommend a solid textbook for a graduate course in the area. Tamar Schlick has written the book that I will be recommending to both groups. Tamar has done an amazing job in writing a book that isboth suitably accessible for beginners, and suitably rigorous for experts. J. J. Collins, Boston University, USA. Molecular modeling is now an important branch of modern biochemistry. Schlick has brought her uniqueinterdisciplinary expertise to the subject. One of the most distinguished characteristics of the book is that it makes the reading really fun and the material accessible. a crystal clear logical presentation . Schlickhas added a unique title to the collection of mathematical biology textbooks . a valuable introduction to the field of compu tational molecular modeling. It is a unique textbook . Hong Qian, SIAM Review, 2005 |
Note: | Springer eBooks |
Contents: | Biomolecular Structure and Modeling: Historical Perspective |
Biomolecular Structure and Modeling: Problem and Application Perspective | |
Protein Structure Introduction | |
Protein Structure Hierarchy | |
Nucleic Acids Structure Minitutorial | |
Topics in Nucleic Acids Structure | |
Theoretical and Computational Approaches to Biomolecular Structure | |
Force Fields | |
Nonbonded Computations | |
Multivariate Minimization in Computational Chemistry | |
Monte Carlo Techniques | |
Molecular Dynamics: Basics | |
Molecular Dynamics: Further Topics | |
Similarity and Diversity in Chemical Design | |
Epilogue | |
ISBN: | 9781441963512 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Interdisciplinary Applied Mathematics, 0939-6047 : v21 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Biochemical engineering , Computer simulation , Biochemistry |
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Call number: | SPRINGER-2010-9781441957832:ONLINE Show nearby items on shelf |
Title: | The Theory of Differential Equations [electronic resource] Classical and Qualitative |
Author(s): |
Walter G Kelley Allan C Peterson |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the importanttopics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as a chapter on perturbation methods and a section in Chapter 3 that shows how to solvedifferential equations using Mathematica codes. In add ition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible withMathematica, version 7.0, and all Mathematica codes are in the book itself. Thi s new edition also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2concerning fundamental matrices, and many further enhancements to the first edition. This book can be u sed either for a second course in ordinary differential equations or as an introductory course for well-prepared students. Theprerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from lin ear algebra are introduced along with examples in the book. An undergraduate course in analysis is neededfor the more theoretical subjects covered in the final two chapters |
Note: | Springer eBooks |
Contents: | First |
Order Differential Equations | |
Linear Systems | |
Autonomous Systems | |
Perturbation Methods | |
The Self | |
Adjoint Second | |
Order Differential Equation | |
Linear Differential Equations of Order n | |
BVPs for Nonlinear Second | |
Order DEs | |
Existence and Uniqueness Theorems | |
ISBN: | 9781441957832 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext : v0 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential Equations |
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Call number: | SPRINGER-2010-9780817649876:ONLINE Show nearby items on shelf |
Title: | Probability and Statistical Models [electronic resource] : Foundations for Problems in Reliability and Financial Mathematics |
Author(s): |
Arjun K Gupta Wei-Bin Zeng Yanhong Wu |
Date: | 2010 |
Edition: | First |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. These models form the basis ofwell-known parametric l ifetime distributions such as exponential, Weibull, and gamma distributions, as well as change-point and mixture models. The authors also consider more general notions of non-parametric lifetime distributionclasses. In particular, emphasis is placed onlay ing the foundation for solving problems in reliability, insurance, finance, and credit risk. Exercises and solutions to selected problems accompany each chapter in order toallowstudents to explore these foundations. The key subjects covered include: * Exp onential distributions and the Poisson process * Parametric lifetime distributions * Non-parametric lifetime distribution classes * Multivariate exponentialextensions * Association and dependence * Renewal theory * Problems in reliability, insurance, fina nce, and credit risk Thiswork differs from traditional probability textbooks in a number of ways. Since no measure theory knowledge isnecessary to understand the material and coverage of the central limit theorem and normal theory related topics has been omitted,the work may be used as a single-semester senior undergraduate or first-year graduate textbook as wellas in a second course on probability modeling. Many of the chapters that examine central topics in applied probability can be read independently, allowing both instructors and readers extra flexibility in their use of the book.Probability and Statistical Models is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathemati cs, statistics, engineering, and economics |
Note: | Springer eBooks |
Contents: | Preface |
Preliminaries | |
Exponential Distribution | |
Poisson Process | |
Parametric Families | |
Lifetime Distribution Classes | |
Multivariate Lifetime Distributions | |
Association and Dependence | |
Renewal Theory | |
Risk Theory | |
Asset Pricing Theory | |
Credit Risk Modeling | |
Bibliographical Notes | |
Bibliography | |
Answers and Solutions to Selected Problems | |
Index | |
ISBN: | 9780817649876 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Distribution (Probability theory) , Economics Statistics , Engineering mathematics |
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Call number: | SPRINGER-2010-9780817649746:ONLINE Show nearby items on shelf |
Title: | The Versatile Soliton [electronic resource] |
Author(s): |
Alexandre T Filippov |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves. In this classic book, the concept of thesoliton is traced from t he beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology. The Versatile Soliton is anappropriate title indeed. There is much new histo rical information in the bookThe book is written in a lively language and the physics presented in a clear, pedagogical style. Most of the chapters require only knowledge of fairlyelementary mathematics and the main ideas of soliton physics are well expla ined without mathematics at allYet it contains valuable information and offers a historical review of soliton physics that cannot be found elsewhere.Centaurus In summary, this book is a good elementary treatment of solitons and the related history of phys ics and mathematics, even for readers with little knowledge of advanced mathematics. For readers with the latter knowledge, itis still a good introduction to the physical ideas required for the understanding of solitons prior to the study of more mathemat ical treatments from other sources. Mathematical Reviews This engaging book is an excellentintroduction into the wonderful world of soliton mechanics. Zentralblatt Math No doubt, everyone can get new information from the book. First, the book is strongly recommended to young researchers. In a certain sense, the bookis unique and definitely will find a niche among numerous textbooks on solitons. Physicala |
Note: | Springer eBooks |
Contents: | An Early History of the Soliton |
A Century and a Half Ago | |
The Great Solitary Wave of John Scott Russell | |
Relatives of the Soliton | |
Nonlinear Oscillations and Waves | |
A Portrait of the Pendulum | |
From Pendulum to Waves and Solitons | |
The Present and Future of the Soliton | |
Frenkels Solitons | |
Rebirth of the Soliton | |
Modern Solitons | |
ISBN: | 9780817649746 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Quantum theory |
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Call number: | SPRINGER-2010-9780817649685:ONLINE Show nearby items on shelf |
Title: | G.W. Stewart [electronic resource] : Selected Works with Commentaries |
Author(s): |
Misha E Kilmer Dianne P O'Leary |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. It is widely accepted that Stewart is the successor to JamesWilkinson, the first gi ant in the field, taking up the perturbation theory research that Wilkinson so ably began and using it as a foundation for algorithmic insights. Stewarts results on rounding error in numerical computationsprovided basic understanding of floating-point com putation. His results on perturbation of eigensystems, pseudo-inverses, least-squares problems, and matrix factorizations are fundamental to numerical practice today. His algorithms forthe singular value decomposition, updating and downdating matrix facto rizations, and the eigenproblem broke new ground and are still widely used in an increasing number of applications. Stewarts papers, widely cited, arecharacterized by elegance in theorems and algorithms and clear, concise, and beautiful exposition. His si x popular textbooks are excellent sources of knowledge and history. Stewart is a member of the National Academy of Engineering andhas received numerous additional honors, including the Bauer Prize. Key features of this volume include: * Forty-four of Stew arts most influential research papers in two subject areas: matrix algorithms and rounding and perturbationtheory * A biography of Stewart * A complete list of Stewarts publications, students, and honors * Selected photographs * Commentaries on Stewarts w orks in collaboration with leading experts in the field G.W. Stewart: SelectedWorks with Commentaries will appeal to graduate students, practitioners, and researchers in computational linear algebra and the history of mathematics |
Note: | Springer eBooks |
Contents: | Foreword |
Part I. G.W. Stewart | |
Biography of G.W. Stewart | |
Publications, Honors, and Students | |
Part II. Commentaries | |
Introduction to the Commentaries | |
Matrix Decompositions: LINPACK and Beyond | |
Updating and Downdating Matrix Decompositions | |
Least Squares, Projections, and Psuedo | |
Inverses | |
The Eigenproblem and Invariant Subspaces: Perturbation Theory | |
The SVD, Eigenproblem, and Invariant Subspaces: Algorithms | |
The Generalized Eigenproblem | |
Krylov Subspace Methods for the Eigenproblem | |
Other Contributions | |
References | |
Index | |
Part III. Reprints | |
Papers on Matrix | |
ISBN: | 9780817649685 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Contemporary Mathematicians |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Computer science Mathematics , Algorithms , Mathematics_$xHistory , Engineering mathematics |
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Call number: | SPRINGER-2010-9780817645526:ONLINE Show nearby items on shelf |
Title: | Partial Differential Equations [electronic resource] : Second Edition |
Author(s): |
Emmanuele DiBenedetto |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobiequations, elliptic equa tions with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions. Large parts of this revisedsecond edition have been streamlined and rew ritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics,physics, engineering, and the natural sciences, as well as an excellen t reference for applied mathematicians and mathematical physicists. The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinearelliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations. Reviews of the first edition: The author's intent is to presentan elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is p resented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation isclear and well organized. . . . The text is complemented by numerous exercises and hints to proofs. ---Mathematical Reviews This is a well-wri tten, self-contained, elementary introduction to linear, partial differential equations.---Zentralblatt MATH |
Note: | Springer eBooks |
Contents: | Preface to the Second Edition |
Preface to the First Edition | |
Preliminaries | |
Quasi | |
Linear Equations | |
The LaPlace Equation | |
Boundary Value Problems by Double Layer Potentials | |
Integral Equations and Eigenvalue Problems | |
The Heat Equation | |
The Wave Equation | |
Quasi | |
Linear Equations of First Order | |
Non | |
Linear Equations of First Order | |
References | |
Index | |
ISBN: | 9780817645526 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Fourier analysis , Integral equations , Differential equations, partial , Mathematical optimization , Mathematical physics |
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Call number: | SPRINGER-2010-9780387683614:ONLINE Show nearby items on shelf |
Title: | Additive Number Theory [electronic resource] : Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson |
Author(s): |
David Chudnovsky Gregory Chudnovsky |
Date: | 2010 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. Nathanson's numerous results have been widely published in top notchjournals and in a nu mber of excellent graduate textbooks (GTM Springer) and reference works. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate studentsand researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research |
Note: | Springer eBooks |
Contents: | |
Preface | |
Sum | |
product theorems and applications (Bourgain) | |
Can you hear the shape of a Beatty sequence? (Graham, OBryant) | |
Variance of signals and their finite Fourier transforms (Chudnovsky, Chudnovsky, Morgan) | |
Sparse sets in time and frequency related to diophantine problems and integrable systems (Chudnovsky, Chudnovsky, Morgan) | |
Addition theorems in acyclic semigroups (Cilleruelo, Hamidoune, Serra) | |
Small sumsets in free products of Z/2Z (Eliahou, Lecouvey) | |
A combinatorial approach to sums of two squares and related problems (Elsholtz) | |
A note on Elkins improvement of Behrend | |
ISBN: | 9780387683614 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Logic, Symbolic and mathematical , Number theory |
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Call number: | SPRINGER-2009-9789048123315:ONLINE Show nearby items on shelf |
Title: | Nonlinear Solid Mechanics [electronic resource] |
Author(s): |
Adnan Ibrahimbegovic |
Date: | 2009 |
Publisher: | Dordrecht : Springer Netherlands |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume provides insight into modelling and ultimate limit computation of complex structures, with their components represented by solid deformable bodies. The book examines practically all the important questions of currentinterests for nonlinea r solid mechanics: plasticity, damage, large deformations, contact, dynamics, instability, localisation and failure, discrete models, multi-scale, multi-physics and parallel computing, with special attention givento finite element solution methods. The pr esentation of topics is structured around different aspects of typical boundary value problems in nonlinear solid mechanics, which provides the best pedagogical approach while keeping the booksize reasonable despite its very broad contents. Other strong p oints are the exhaustive treatment of subjects, with each question studied from different angles of mechanics, mathematics and computation, as well as a successful mergerof scientific cultures and heritage from Europe and the USA. The book content and sty le is also the product of rich international experience in teaching Master and Doctoral level courses, as well as the courses organized forparticipants from industry (IPSI courses) in France, and similar courses in Germany and Italy. Every effort was made to make the contents accessible to non-specialists and users of computer programs. The original French editionpublished by Hermes Science - Lavoisier Paris in 2006 was nominated for the Roberval Award for University Textbooks in French |
Note: | Springer eBooks |
Contents: | Boundary value problem in linear and nonlinear elasticity |
Inelastic behavior at small strains | |
Large displacements and deformations | |
Changing boundary conditions: contact problems | |
Dynamics and time | |
integration schemes | |
Thermodynamics and solution methods for coupled problems | |
Geometric and material instabilities | |
Multi | |
scale modelling of inelastic behavior | |
ISBN: | 9789048123315 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Solid Mechanics and its Applications, 0925-0042 : v160 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Mathematical optimization , Engineering , Materials |
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Call number: | SPRINGER-2009-9780387849232:ONLINE Show nearby items on shelf |
Title: | Solving the Pell Equation [electronic resource] |
Author(s): |
Michael J Jacobson Hugh C Williams |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks andrecreational books conc erning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computationaltechniques, but in the process of deriving these i t will be necessary to develop the corresponding theory. One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the samelevel of preparedness to the delights of algebraic number theory through t he medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with someknowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography.The intended audience is number theorists, both professional and amateur, and students, but we wish to emphasize that thi s is not intended to be a textbook its focus is much too narrow for that. It could, however be used assupplementary reading for students enrolled in a second course in number theory |
Note: | Springer eBooks |
Contents: | Early History of the Pell Equation |
Continued Fractions | |
Quadratic Number Fields | |
Ideals and Continued Fractions | |
Some Special Pell Equations | |
The Ideal Class Group | |
The Analytic Class Number Formula | |
Some Additional Analytic Results | |
Some Computational Techniques | |
(f, p) Representations of | |
ideals | |
Compact Representations | |
The Subexponential Method | |
Applications to Cryptography | |
Unconditional Verification of the Regulator and the Class Number | |
Principal Ideal Testing in | |
Conclusion | |
ISBN: | 9780387849232 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | CMS Books in Mathematics, 1613-5237 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Number theory |
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Call number: | SPRINGER-2009-9780387683249:ONLINE Show nearby items on shelf |
Title: | An Introduction to Homological Algebra [electronic resource] |
Author(s): |
Joseph J Rotman |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | With a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to Homological Algebra. The author provides a treatment of Homological Algebra whichapproaches the subject in ter ms of its origins in algebraic topology. In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added. Applicationsinclude the following: * to rings -- Lazard's theorem that flat modules are direct limits of free modules, Hilbert's Syzygy Theorem, Quillen-Suslin's solution of Serre's problem about projectives over polynomial rings,Serre-Auslander-Buchsbaum characterization of regular local rings (and a sketch of unique f actorization) * to groups -- Schur-Zassenhaus, Gaschutz's theorem on outer automorphisms of finite p-groups, Schur multiplier, cotorsiongroups * to sheaves -- sheaf cohomology, Cech cohomology, discussion of Riemann-Roch Theorem over compact Riemann surfa ces. Learning Homological Algebra is a two-stage affair. Firstly, one must learn the language of Ext and Tor, andwhat this describes. Secondly, one must be able to compute these things using a separate language: that of spectral sequences. The basic prope rties of spectral sequences are developed using exact couples. All is done in the context ofbicomplexes, for almost all applications of spectral sequences involve indices. Applications include Grothendieck spectral sequences, change of rings, Lyndon-Hochs child-Serre sequence, and theorems of Leray and Cartan computing sheafcohomology. Joseph Rotman is Professor Emeritus of Mathematics at the University of Illinois at Urbana-Champaign. He is the author of numerous successful textbooks, including Advanced M odern Algebra (Prentice-Hall 2002), Galois Theory,2nd Edition (Springer 1998) A First Course in Abstract Algebra (Prentice-Hall 1996), Introduction to the Theory of Groups, 4th Edition (Springer 1995) |
Note: | Springer eBooks |
Contents: | Preface to the second edition |
How to read this book | |
Introduction | |
Hom and tensor | |
Special modules | |
Specific rings | |
Setting the stage | |
Homology | |
Tor and ext | |
Homology and rings | |
Homology and groups | |
Spectral sequences | |
References | |
Special notation | |
Index | |
ISBN: | 9780387683249 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2008-9789491216350:ONLINE Show nearby items on shelf |
Title: | Topological Groups and Related Structures [electronic resource] |
Author(s): |
Alexander Arhangelskii Mikhail Tkachenko |
Date: | 2008 |
Publisher: | Paris : Atlantis Press |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, theobjects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groupsand semigroups, paratopological groups, etc. S pecial emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of theoperation. The main scope of the book, however, is outside of the loca lly compact structures, thus distinguishing the monograph from a series of more traditional textbooks. The book is unique in that it presents very importantmaterial, dispersed in hundreds of research articles, not covered by any monograph in existence. Th e reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the wayto the frontier of the knowledge is quite short almost every section of the book contains several intriguing open proble ms whose solutions can contribute significantly to the area |
Note: | Springer eBooks |
ISBN: | 9789491216350 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Atlantis Studies in Mathematics, 1875-7634 : v1 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Algebraic topology |
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Call number: | SPRINGER-2008-9783764387242:ONLINE Show nearby items on shelf |
Title: | A Natural Introduction to Probability Theory [electronic resource] |
Author(s): |
Ronald Meester |
Date: | 2008 |
Edition: | Second Edition |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book [is] an excellent new introductory text on probability. The classical way of teaching probability is based on measure theory. In this book discrete and continuous probability are studied with mathematical precision,within the realm of Rieman n integration and not using notions from measure theory. Numerous topics are discussed, such as: random walks, weak laws of large numbers, infinitely many repetitions, strong laws of large numbers,branching processes, weak convergence and [the] central li mit theorem. The theory is illustrated with many original and surprising examples and problems. Zentralblatt Math Most textbooks designed for a one-year course inmathematical statistics cover probability in the first few chapters as preparation for the st atistics to come. This book in some ways resembles the first part of such textbooks: it's all probability, no statistics. But it does theprobability more fully than usual, spending lots of time on motivation, explanation, and rigorous development of the m athematics. The exposition is usually clear and eloquent. Overall, this is a five-star book on probability thatcould be used as a textbook or as a supplement. MAA online |
Note: | Springer eBooks |
Contents: | Preface |
Experiments | |
Random Variables and Random Vectors | |
Random Walk | |
Limit Theorems | |
Intermezzo | |
Continuous Random Variables and Vectors | |
Infinitely Many Repetitions | |
The Poisson Process | |
Limit Theorems | |
Extending the Probabilities | |
Interpreting Probabilities | |
Further Reading | |
Answers to Selected Exercises | |
Index | |
ISBN: | 9783764387242 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2008-9783764374785:ONLINE Show nearby items on shelf |
Title: | Analysis II [electronic resource] |
Author(s): |
Herbert Amann Joachim Escher |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and cleardevelopment that started in Volume I (3-7643-7153-6) continues. In this way a sustainable basis will be created which allows to deal with interesting applications that sometimes go considerably beyond the material that is representedin traditional textbooks. This applies, for ins tance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations. Another exampleis the presentation of the local theory of submanifolds of Rn |
Note: | Springer eBooks |
Contents: | Preface |
VI. Integral Calculus in One Variable | |
1. Step Continuous Functions | |
2. Continuous Extensions | |
3. The Cauchy | |
Riemann Integral | |
4. Properties of the Integral | |
5. The Technology of Integration | |
6. Sums and Integrals | |
7. Fourier Series | |
8. Improper Integrals | |
9. The Gamma Function | |
VII. Differential Calculus in Several Variables | |
1. Continuous Linear Mappings | |
2. Differentiability | |
3. Calculation Rules | |
4. Multilinear Mappings | |
5. Higher Derivatives | |
6. Nemytski Operators and Calculus of Variations | |
7. Inverse Mappings | |
8. Implicit Functions | |
9. Manifolds | |
10. Tang | |
ISBN: | 9783764374785 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2008-9783540683490:ONLINE Show nearby items on shelf |
Title: | Interpolation Processes [electronic resource] : Basic Theory and Applications |
Author(s): |
Giuseppe Mastroianni Gradimir V Milovanovi |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs,recent results on conver gent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In thisspecial, but fundamental and important field of r eal analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthogonal polynomials, moduli ofsmoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. Beside the basic propertiesof the classical orthogonal polynomials the book provides new results on nonclassical ortho gonal polynomials including methods for their numerical construction |
Note: | Springer eBooks |
Contents: | 1. Constructive Elements and Approaches in Approximation Theory |
1.1 Introduction to Approximation Theory | |
1.2 Basic Facts on Trigonometric Approximation | |
1.3 Chebyshev Systems and Interpolation | |
1.4 Interpolation by Algebraic Polynomials | |
2. Orthogonal Polynomials and Weighted Polynomial Approximation | |
2.1 Orthogonal Systems and Polynomials | |
2.2 Orthogonal Polynomials on the Real Line | |
2.3 Classical Orthogonal Polynomials | |
2.4 Nonclassical Orthogonal Polynomials | |
2.5 Weighted Polynomial Approximation | |
3. Trigonometric Approximation | |
3.1 Approximating Properties of Oper | |
ISBN: | 9783540683490 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Integral equations , Sequences (Mathematics) , Functions, special |
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Call number: | SPRINGER-2008-9781848000483:ONLINE Show nearby items on shelf |
Title: | Probability Theory [electronic resource] : A Comprehensive Course |
Author(s): |
Achim Klenke |
Date: | 2008 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils ofrandom developments on the financial markets, and they guide us in constructing more efficient algorithms. This text is a comprehensive course in modern probability theory and its measure-theoretical foundations. Aimed primarily atgraduate students and researchers, the book cov ers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables martingales percolation Markov chainsand electrical networks construction of stochastic processes Poisson poi nt processes and infinite divisibility large deviation principles and statistical physics Brownian motion and stochastic integral and stochastic differentialequations. The theory is developed rigorously and in a self-contained way, with the chapters on me asure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world ofprobability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation |
Note: | Springer eBooks |
Contents: | Basic Measure Theory |
Independence | |
Generating Functions | |
The Integral | |
Moments and Laws of Large Numbers | |
Convergence Theorems | |
Lp | |
Spaces and the Radon | |
Nikodym Theorem | |
Conditional Expectations | |
Martingales | |
Optional Sampling Theorems | |
Martingale Convergence Theorems and Their Applications | |
Backwards Martingales and Exchangeability | |
Convergence of Measures | |
Probability Measures on Product Spaces | |
Characteristic Functions and the Central Limit Theorem | |
Infinitely Divisible Distributions | |
Markov Chains | |
Convergence of Markov Chains | |
Markov Chains and Electric | |
ISBN: | 9781848000483 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) , Mathematical statistics |
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Call number: | SPRINGER-2008-9781846289729:ONLINE Show nearby items on shelf |
Title: | Sturm-Liouville Theory and its Applications [electronic resource] |
Author(s): |
M. A Al-Gwaiz |
Date: | 2008 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Undergraduate textbooks on Fourier series which follow a pointwise approach to convergence miss the rich geometric content which comes with treating the subject within the inner product space L2. This book, developed from acourse taught to senior und ergraduates, provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The basic results of this theory, namely the orthogonality and completeness ofits eigenfunctions, are established in Chapter 2 the remaining chapters present examples and applications. The last two chapters, on Fourier and Laplace transformations, while not part of the Sturm-Liouville theory, extend the Fourierseries method for representing functions to integral representations . The treatment relies heavily on the convergence properties of sequences and series of numbers as well as functions, and assumes a solid background in advancedcalculus and an acquaintance with ordinary differential equations and linear algebra. Familiari ty with the relevant theorems of real analysis, such as the AscoliArzel theorem, is also useful for following the proofs. Thepresentation follows a clear and rigorous mathematical style that is both readable and well motivated, with many examples and appl ications used to illustrate the theory. Although addressed primarily to undergraduate students ofmathematics, the book will also be of interest to students in related disciplines, such as physics and engineering, where Fourier analysis and special functio ns are used extensively for solving linear differential equations |
Note: | Springer eBooks |
Contents: | Inner Product Space |
The SturmLiouville Theory | |
Fourier Series | |
Orthogonal Polynomials | |
Bessel Functions | |
The Fourier Transformation | |
The Laplace Transformation | |
ISBN: | 9781846289729 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Differential Equations , Functions, special , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2008-9780387789019:ONLINE Show nearby items on shelf |
Title: | Lattices and Ordered Sets [electronic resource] |
Author(s): |
Steven Roman |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study.Prerequisites are ke pt to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on wellordering and ordinal numbers, which is not u sually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises. Topic coverage includes: modular, semimodular anddistributive lattices, boolean algebras, representation of distr ibutive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more. Steven Roman is the author of manysuccessful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), F ield Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004) |
Note: | Springer eBooks |
Contents: | Preface |
Partially Ordered Sets | |
Well | |
Ordered Sets | |
Lattices | |
Modular and Distributive Lattices | |
Boolean Algebras | |
The Representation of Distributive Lattices | |
Algebraic Lattices | |
Prime and Maximal Ideals: Separation Theorems | |
Congruence Relations on Lattices | |
Duality for Distributive Lattices: The Priestley Topology | |
Free Lattices | |
Fixed | |
Point Theorems | |
Appendix A: A Bit of Topology | |
Appendix B: A Bit of Category Theory | |
References | |
Index of Symbols | |
Index | |
ISBN: | 9780387789019 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2008-9780387754819:ONLINE Show nearby items on shelf |
Title: | History of Mathematics [electronic resource] : A Supplement |
Author(s): |
Craig Smoryski |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book attempts to fill two gaps which exist in the standard textbooks on the History of Mathematics. One is to provide students with material that could encourage more critical thinking. General textbooks, attempting to coverthree thousand years of mathematical history, must necessarily oversimplify almost everything, the practice of which can scarcely promote a critical approach to the subject. For this reason, Craig Smorynski chooses a more narrow butdeeper coverage of a few select topics. The second aim of this book is to include the proofs of important results which are typically neglected in the modern history of mathematics curriculum. The most obvious of these is the oft-citednecessity of introducing complex numbers in applying the algebra ic solution of cubic equations. This solution, though it is now relegated to courses in the History of Mathematics, was a major occurrence in the history of mathematics.It was the first substantial piece of mathematics in Europe that was not a mere extens ion of what the Greeks had done and thus signified the coming of age of European mathematics. The fact that the solution, in the case of threedistinct real roots to a cubic, necessarily involved complex numbers both made inevitable the acceptance and stud y of these numbers and provided a stimulus for the development of numerical approximation methods. Other unique featuresinclude: * a prefatory essay on the ways in which sources may be unreliable, followed by an annotated bibliography * a modern recountin g of a Chinese word problem from the 13th century, illustrating the need for consulting multiplesources when the primary source is unavailable * the solution of the cubic equation, including multiple proofs that the algebraic solution uses complex numbers whenever the cubic equation has three distinct real solutions * acritical reappraisal of Horner's Method The final chapter contains lighter material, including a critical look at North Korea's stam |
Note: | Springer eBooks |
Contents: | Introduction |
Annotated Bibliography | |
Foundations of Geometry | |
The Construction Problems of Antiquity | |
A Chinese Problem | |
The Cubic Equation | |
Horners Method | |
Some Lighter Material | |
Appendix A: Small Projects | |
Index | |
ISBN: | 9780387754819 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry , Mathematics_$xHistory |
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Call number: | SPRINGER-2008-9780387724881:ONLINE Show nearby items on shelf |
Title: | Algebra [electronic resource] : Fields with Structure, Algebras and Advanced Topics |
Author(s): |
Falko Lorenz |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by afirst course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions andalgebraic geometry. The main focus of the seco nd volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of afield, the calculus of Witt vectors, the Schur group of a field, a nd local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the Germanversion: This is a charming textbook, introducing the reader to the classical parts of algebr a. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at leastin the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews |
Note: | Springer eBooks |
Contents: | Ordered Fields and Real Fields |
Hilbert's Seventeenth Problem and the Real Nullstellensatz | |
Orders and Quadratic Forms | |
Absolute Values on Fields | |
Residue Class Degree and Ramification Index | |
Local Fields | |
Witt Vectors | |
The Tsen Rank of a Field | |
Fundamentals of Modules | |
Wedderburn Theory | |
Crossed Products | |
The Brauer Group of a Local Field | |
Local Class Field Theory | |
Semisimple Representations of Finite Groups | |
The Schur Group of a Field | |
ISBN: | 9780387724881 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Field theory (Physics) , Matrix theory , Number theory |
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Call number: | SPRINGER-2008-9780387718132:ONLINE Show nearby items on shelf |
Title: | Design and Analysis of Simulation Experiments [electronic resource] |
Author(s): |
Jack P.C Kleijnen |
Date: | 2008 |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This is an advanced expository book on statistical methods for the Design and Analysis of Simulation Experiments (DASE). Though the book focuses on DASE for discrete-event simulation (such as queuing and inventory simulations),it also discusses DASE for deterministic simulation (such as engineering and physics simulations). The text presents both classic and modern statistical designs. Classic designs (e.g., fractional factorials) assume only a few factorswith a few values per factor. The resulting i nput/output data of the simulation experiment are analyzed through low-order polynomials, which are linear regression (meta)models. Modern designs allow many more factors, possible with manyvalues per factor. These designs include group screening (e.g., S equential Bifurcation, SB) and space filling designs (e.g., Latin Hypercube Sampling, LHS). The data resulting from these modern designs may be analyzed through low-orderpolynomials for group screening and various metamodel types (e.g., Kriging) for LHS. In this way, the book provides relatively simple solutions for the problem of which scenarios to simulate and how to analyze the resulting data. Thebook also includes methods for computationally expensive simulations. It discusses only those tactical issu es that are closely related to strategic issues i.e., the text briefly discusses run-length and variance reduction techniques.The leading textbooks on discrete-event simulation pay little attention to the strategic issues of simulation. The author has bee n working on strategic issues for approximately forty years, in various scientific disciples--such asoperations research, management science, industrial engineering, mathematical statistics, economics, nuclear engineering, computer science, and informatio n systems. The intended audience is comprised of researchers, graduate students,and mature practitioners in the simulation area. They are assumed to have a basic knowledge of simulation and mathematica |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Black Box Metamodels | |
Low | |
Order Polynomial Regression | |
Metamodels and Designs: A Single Factor | |
Low | |
Order Polynomial Models and Designs: Multiple Factors | |
Low | |
Order Polynomial Models and Screening Designs: Hundreds of Factors | |
Kriging Metamodels | |
Latin Hypercube Sampling (LHS) and other Space | |
Filling Designs | |
Cross | |
Validation of Metamodels | |
Conclusions and Further Research | |
ISBN: | 9780387718132 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | International Series in Operations Research & Management Science, 0884-8289 : v111 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) , Mathematical statistics , Engineering design , Industrial engineering |
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Call number: | SPRINGER-2007-9783540715849:ONLINE Show nearby items on shelf |
Title: | Numerical Treatment of Partial Differential Equations [electronic resource] : Translated and revised by Martin Stynes |
Author(s): |
Christian Grossmann Hans-Gorg Roos Martin Stynes |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book deals with discretization techniques for elliptic, parabolic and hyperbolic partial differential equations. It provides an introduction to the main principles of discretizations and presents to the reader the ideas andanalysis of advanced n umerical methods in this area. It is the authors' aim to give mathematically-inclined students, scientists and engineers a textbook that contains all the basic discretization techniques for the three fundamentaltypes of partial differential equations and in which the reader can find analytical tools, properties of discretizations, and some advice on algorithmic aspects. The book also covers recent research developments: for instance,introductions are given to a posteriori error estimation, discontinuous G alerkin methods, and optimal control for partial differential equations---these topics of current interest are rarely considered in other textbooks. While finiteelement methods are the main focus of the book, finite difference methods and finite volume te chniques are also presented. Furthermore, the book provides the basic tools needed to solve the discrete problems generated, while chapterson singularly perturbed problems, variational inequalities and optimal control illuminate special topics that reflec t the research interests of the authors |
Note: | Springer eBooks |
Contents: | Notation |
1 Basics | |
2 Finite Difference Methods | |
3 Weak Solutions | |
4 The Finite Element Method | |
5 Finite Element Methods for Unsteady Problems | |
6 Singularly Perturbed Boundary Value Problems | |
7 Variational Inequalities, Optimal Control | |
8 Numerical Methods for Discretized Problems | |
Bibliography: Textbooks and Monographs | |
Bibliography:Original Papers | |
Index | |
ISBN: | 9783540715849 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Numerical analysis |
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Call number: | SPRINGER-2007-9781402057960:ONLINE Show nearby items on shelf |
Title: | Factorization Method in Quantum Mechanics [electronic resource] |
Author(s): |
Shi-Hai Dong |
Date: | 2007 |
Publisher: | Dordrecht : Springer Netherlands |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantumcontrol at the Reader s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existingquantum mechanics textbooks. Related to this cl assic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestoneof these approaches. In fact the Authors driving force has been his d esire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since theliterature is inundated with scattered articles in this field, and to pave the Readers way into this territory as rapidly as possible. The result: clear and understandable derivations with the necessary mathematical steps includedso that the intelligent reader should be able to follow the text with relative ease, in particular when mathematically diffic ult material is presented. Audience: Researchers and students of physics, mathematics, chemistry andelectrical engineering |
Note: | Springer eBooks |
ISBN: | 9781402057960 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fundamental Theories of Physics : v150 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2007-9780817645861:ONLINE Show nearby items on shelf |
Title: | Dynamical Systems with Applications using Mathematica [electronic resource] |
Author(s): |
Stephen Lynch |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Dynamical Systems with Applications using Mathematica provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes thereader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics,and neural networks. Mathematicas symbolic, numeri cal, and graphical capabilities make it ideal for the study of nonlinear dynamical systems. An introductory chapter provides complete tutorials on how to use Mathematicastext-based input commands and palettes, enabling new users to become familiar with th e program, while providing a good reference source for experts. Working Mathematica notebooks will be available athttp://library.wolfram.com/infocenter/Books/AppliedMathematics/. Throughout the book, the author has focused on breadth of coverage rather th an fine detail, with theorems and proofs being kept to a minimum. The first part of the bookdeals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems. Some of the mater ial presented is at the postgraduate level and has been influenced bythe authors own research interests. Exercises are included at the end of every chapter. A comprehensive bibliography including textbooks and research papers rounds out the work. The book is intended for senior undergraduate andgraduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many chapters of the book are especially useful as reference material for senior undergraduate independ ent project work.Also by the author: Dynamical Systems with Applications using MATLAB, ISBN 978-0-8176-4321-8 Dynamical Systems with Applications using Maple, ISBN 978-0-8176-4150-4 |
Note: | Springer eBooks |
Contents: | Preface |
A Tutorial Introduction to Mathematica | |
Differential Equations | |
Planar Systems | |
Interacting Species | |
Limit Cycles | |
Hamiltonian Systems, Lyapunov Functions, and Stability | |
Bifurcation Theory | |
Three | |
Dimensional Autonomous Systems and Chaos | |
Poincar Maps and Nonautonomous Systems in the Plane | |
Local and Global Bifurcations | |
The Second Part of David Hilbert's Sixteenth Problem | |
Linear Discrete Dynamical Systems | |
Nonlinear Discrete Dynamical Systems | |
Complex Iterative Maps | |
Electromagnetic Waves and Optical Resonators | |
Fractals and Multifractals | |
Chaos C | |
ISBN: | 9780817645861 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Engineering mathematics , Engineering |
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Call number: | SPRINGER-2007-9780387692005:ONLINE Show nearby items on shelf |
Title: | Einstein's General Theory of Relativity [electronic resource] : With Modern Applications in Cosmology |
Author(s): |
yvind Grn Sigbjrn Hervik |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Many of us have experienced the same fallen and broken something. Yet supposedly, gravity is the weakest of the fundamental forces it is claimed to be 10-15 times weaker than electromagnetism. Still, every one of us has more orless had a personal rel ationship with gravity. Einsteins General Theory of Relativity: With Modern Applications in Cosmology by Oyvind Gron and Sigbjorn Hervik is about gravity and the concept of gravity as Albert Einstein saw it-curved spaces, four-dimensional manifolds and ge odesics. The book starts with the 1st principals of relativity and an introduction to Einsteins field equations. Next up are the three classical tests of the relativity theory and anintroduction to black holes. The book contains several topics not found i n other textbooks, such as Kaluza-Klein theory, anisotropic models of the universe, and new developments involving brane cosmology. Gron and Hervik have includeda part in the book called Advanced Topics. These topics range from the very edge of research t o older, accepted ideas. In particular, the last two chapters deal with Einstein gravity in five dimensions, which has been a hot topicof research in recent years. On one final note, cosmology has also proven to be a very important testing arena for the g eneral theory of relativity and a large part of the book is therefore devoted to this subject |
Note: | Springer eBooks |
Contents: | Newtonian Physics and Special Relativity |
Relativity Principals and Gravitation | |
The Special Theory of Relativity | |
The Mathematics of the General Theory of Relativity | |
Vectors, Tensors, and Forms | |
Basis Vector Fields and Metric Tensor | |
Non | |
inertial Reference Frames | |
Differentiation, Connections and Integration | |
Curvature | |
Einstein's Field Equations | |
Einstein's Field Equations | |
The Linear Field Approximation | |
The Schwarzschild Solution and Black Holes | |
Cosmology | |
Homogeneous and Isotropic Universe Models | |
Universe Models with Vacuum Energy | |
An Anisotropic Univers | |
ISBN: | 9780387692005 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2007-9780387681207:ONLINE Show nearby items on shelf |
Title: | A Topological Picturebook [electronic resource] |
Author(s): |
George K Francis |
Date: | 2007 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Praise for George Francis's A Topological Picturebook: Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the newgeneration what ``han ds on'' really means. - John Stillwell, University of San Francisco The Topological Picturebook has taught a whole generation of mathematicians to draw, to see, and to think. - Tony Robbin, artist and author ofShadows of Reality: The Fourth Dimension in R elativity, Cubism, and Modern Thought The classic reference for how to present topological information visually, full of amazing hand-drawn pictures of complicated surfaces. - John Sullivan,Technische Universitat Berlin A Topological Picturebook lets stud ents see topology as the original discoverers conceived it: concrete and visual, free of the formalism that burdens conventional textbooks. - Jeffrey Weeks, author of TheShape of Space A Topological Picturebook is a visual feast for anyone concerned with mathematical images. Francis provides exquisite examples to build one's visualization muscles. At the same time, he explains the underlyingprinciples and design techniques for readers to create their own lucid drawings. - George W. Hart, Stony Brook Unive rsity In this collection of narrative gems and intriguing hand-drawn pictures, George Francis demonstrates thechicken-and-egg relationship, in mathematics, of image and text. Since the book was first published, the case for pictures in mathematics has bee n won, and now it is time to reflect on their meaning. A Topological Picturebook remainsindispensable. - Marjorie Senechal, Smith College and co-editor of the Mathematical Intelligencer |
Note: | Springer eBooks |
Contents: | 1 Descriptive Topology |
2 Methods and Media | |
3 Pictures in Perspective | |
4 The Impossible Tribar | |
5 Shadows from Higher Dimension | |
6 Sphere Eversions | |
7 Group Pictures | |
8 The Figure Eight Knot | |
Postscript | |
ISBN: | 9780387681207 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry , Topology |
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Call number: | SPRINGER-2007-9780387489469:ONLINE Show nearby items on shelf |
Title: | The Geometry of an Art [electronic resource] The History of the Mathematical Theory of Perspective from Alberti to Monge |
Author(s): |
Kirsti Andersen |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph describes how the understanding of the geometry behind perspective evolved between the years 1435 and 1800 and how new insights within the mathematical theory of perspective influenced the way the discipline waspresented in textbooks. In order to throw light on these issues, the author has chosen to focus on a number of key questions, including: What were the essential innovations in the mathematical theory of perspective? Was thereany interplay between the developments of the mathem atical theory of perspective and other branches of geometry? What were the driving forces behind working out an advanced mathematical theory of perspective? Were thereregional differences in the mathematical approach to perspective? And if so, how did t hey relate to local applications of perspective? How did mathematicians and practitioners of perspective interact? In fact, the last issue istouched upon so often that a considerable part of this book could be seen as a case study of the difficulties in bridging the gap between those with mathematical knowledge and the mathematically untrained practitioners who wish to usethis knowledge. The author has based her work on more than 200 books, booklets, and pamphlets on perspective. She starts with the firs t treatise known to deal with geometrical perspective, Leon Alberti Battistas De pictura, and endsaround 1800, when the theory of mathematical perspective as an independent discipline was absorbed first into descriptive geometry and later into projective geometry. The prominent protagonists are Guidobaldo del Monte, Simon Stevin,Willem sGravesande, Brook Taylor, and Johann Heinrich Lambert. As far as data were available, the author has provided brief biographies of all the writers on perspective whose wor k she studied. The book also contains an extensivebibliography divided into two parts, one for primary sources on perspective, and the second for all other literature. Kirsti Anders |
Note: | Springer eBooks |
Contents: | Introduction |
Acknowledgements | |
Notes to the reader | |
The birth of perspective | |
Alberti and Piero della Francesca | |
Leonardo da Vinci | |
Italy in cinquecento | |
North of the Alps before sixteen hundred | |
The birth of the mathematical theory of perspective: Guidobaldo and Stevin | |
The Dutch development after Stevin | |
Italy after Guidobaldo | |
France and the Southern Netherlands after 1600 | |
Britain | |
The German speaking areas after 1600 | |
Lambert | |
Monge closing a circle | |
Summing up | |
Appendix: On ancient roots of perspective | |
Appendix: The Appearance of a rectangle la Le | |
ISBN: | 9780387489469 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Sources and Studies in the History of Mathematics and Physical Sciences |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry , Mathematics_$xHistory |
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Call number: | SPRINGER-2007-9780387488998:ONLINE Show nearby items on shelf |
Title: | Exercises in Modules and Rings [electronic resource] |
Author(s): |
T. Y Lam |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | For the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flatmodules, homological and uniform dimensions, noncommutative localizations and Goldies theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Moritas classical theory of category dualities andequivalences. Each of the nineteen sections begins with a n introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail many are accompanied by pertinenthistorical and bibliographical information, or a commentary on possible improveme nts, generalizations, and latent connections to other problems. This volume is designed as a problem book for the authors Lectures on Modules and Rings(Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as asource for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of theauthors lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classica l Ring Theory (Springer, 2003) offer to the mathematics community the fullest andmost comprehensive reference to date for problem solving in the theory of modules and rings |
Note: | Springer eBooks |
Contents: | Free Modules |
Projective and Injective Modules | |
Flat Modules and Homological Dimensions | |
More Theory of Modules | |
Rings of Quotients | |
More Rings of Quotients | |
robenius and Quasi | |
Frobenius Rings | |
Matrix Rings, Categories of Modules, and Morita Theory | |
ISBN: | 9780387488998 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Problem Books in Mathematics, 0941-3502 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2006-9783540348061:ONLINE Show nearby items on shelf |
Title: | The Wulff Crystal in Ising and Percolation Models [electronic resource] Ecole d'Et de Probabilits de Saint-Flour XXXIV - 2004 |
Author(s): |
Raphal Cerf Jean Picard |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can befound only in research pa pers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted |
Note: | Springer eBooks |
Contents: | Phase coexistence and subadditivity |
Ising models | |
Bernoulli percolation | |
FK or random cluster model | |
The Wulff crystal | |
Large deviation theory | |
Surface large deviation principles | |
Volume large deviations | |
Coarse graining | |
Decoupling | |
Surface tension | |
Interface estimate | |
Sets of finite perimeter | |
Surface energy | |
The Wulff theorem | |
LDP for the cluster shapes | |
Enhanced upper bound | |
LDP for FK percolation | |
LDP for ising | |
ISBN: | 9783540348061 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1878 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematical optimization , Distribution (Probability theory) , Mathematical physics |
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Call number: | SPRINGER-2006-9783540330677:ONLINE Show nearby items on shelf |
Title: | Compact Riemann Surfaces [electronic resource] : An Introduction to Contemporary Mathematics |
Author(s): |
Jrgen Jost |
Date: | 2006 |
Edition: | Third Edition |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporarymathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in includingan introduction to Teichmller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation |
Note: | Springer eBooks |
Contents: | Topological Foundations |
Differential Geometry of Riemann Surfaces | |
Harmonic Maps | |
Teichmller Spaces | |
Geometric Structures on Riemann Surfaces | |
Erratum to: Characterizing Programming Systems Allowing Program Self | |
reference | |
ISBN: | 9783540330677 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry |
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Call number: | SPRINGER-2006-9783540294719:ONLINE Show nearby items on shelf |
Title: | Radiation Physics for Medical Physicists [electronic resource] |
Author(s): |
Ervin B Podgorak |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book summarizes the radiation physics knowledge that professionals working in medical physics need to master for efficient and safe dealings with ionizing radiation. It contains eight chapters, each chapter covering aspecific group of subjects r elated to radiation physics and is intended as a textbook for a course in radiation physics in medical-physics graduate programs. However, the book may also be of interest to the large number ofprofessionals, not only medical physicists, who in their dail y occupations deal with various aspects of medical physics and find a need to improve their understanding of radiation physics. The main target audience for this book isgraduate students studying for M.Sc. and Ph.D. degrees in medical physics, who have to possess the necessary physics and mathematics background knowledge to be able to follow and master the complete textbook. Medical residents,technology students and biomedical engineering students may find certain sections too challenging or esoteric, yet they will find many sections interesting and useful in their studies. Candidates preparing for professionalcertification exams in any of the medical physics subspecialties should find the material useful, and some of the material would also help candidat es preparing for certification examinations in medical dosimetry or radiation-relatedmedical specialties. Numerous textbooks are available covering the various subspecialties of medical physics but they generally make a transition from the elementary basi c physics directly into the intricacies of the given medicalphysics subspecialty. The intent of this textbook is to provide the missing link between the elementary physics on the one hand and the physics of the subspecialties on the other hand |
Note: | Springer eBooks |
Contents: | Introduction to Modern Physics |
Rutherford | |
Bohr Atomic Model | |
Production of X | |
rays | |
Two | |
Particle Collisions | |
Charged Particle Stopping Powers | |
Interactions of Neutrons with Matter | |
Photon Interactions with Matter | |
Radioactivity | |
ISBN: | 9783540294719 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Biological and Medical Physics, Biomedical Engineering, 1618-7210 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Radiology, Medical , Nuclear medicine , Particle acceleration , Biomedical engineering |
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Call number: | SPRINGER-2006-9783540291565:ONLINE Show nearby items on shelf |
Title: | Introduction to Wave Scattering, Localization and Mesoscopic Phenomena [electronic resource] |
Author(s): |
Sheng Ping |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Waves represent a classic topic of study in physics, mathematics, and engineering. Many modern technologies are based on our understanding of waves and their interaction with matter. In the past thirty years there have been somerevolutionary developm ents in the study of waves. The present volume is the only available source which details these developments in a systematic manner, with the aim of reaching a broad audience of non-experts. It is an importantresource book for those interested in understa nding the physics underlying nanotechnology and mesoscopic phenomena, as well as for bridging the gap between the textbooks and research frontiers in any wave related topic. A specialfeature of this volume is the treatment of classical and quantum mechani cal waves within a unified framework, thus facilitating an understanding of similarities and differences between the two |
Note: | Springer eBooks |
Contents: | Introduction |
Quantum and classical waves | |
Wave scattering and the coherent potential approximation | |
Coherent waves and effective media | |
Diffusive waves | |
The coherent backscattering effect | |
Renormalized diffusion | |
The scaling theory of localization | |
Localized states and the approach to localization | |
Localization phenomena in electronic systems | |
Mesoscopic phenomena | |
ISBN: | 9783540291565 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Series in MATERIALS SCIENCE, 0933-033X : v88 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Nanotechnology |
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Call number: | SPRINGER-2006-9780387472898:ONLINE Show nearby items on shelf |
Title: | Spinning Flight [electronic resource] : Dynamics of Frisbees, Boomerangs, Samaras, and Skipping Stones |
Author(s): |
Ralph D Lorenz |
Date: | 2006 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | More frisbees are sold each year than baseballs, basketballs, and footballs combined. Yet these familiar flying objects have subtle and clever aerodynamic and gyrodynamic properties which are only recently being documented bywind tunnel and other stu dies. In common with other rotating bodies discussed in this readily accessible book, they are typically not treated in textbooks of aeronautics and the literature is scattered in a variety of places. This bookdevelops the theme of disc-wings and spinning aerospace vehicles in parallel. Many readers will have enjoyed these vehicles and their dynamics in recreational settings, so this book will be of wide interest. In addition to spinningobjects of various shapes, several exotic manned aircraft with disc p latforms have been proposed and prototypes built - these include a Nazi secret weapon and the De Havilland Avrocar, also discussed in the book. Boomerangsrepresent another category of spinning aerodynamic body whose behavior can only be understood by coup ling aerodynamics with gyrodynamics. The narrative, supported by equations and graphs, explains how the shape and throw of a boomerangrelates to its trajectory. The natural world presents still other examples, namely the samaras or seed-wings of many tree species, which autorotate during their descent, like a helicopter whose engine has failed. In short, thisbook discusses a range of familiar, connected, but largely undeveloped, topics in an accessible, but complete manner. Toys familiar to all of us are covered as well as high-tech products of the aerospace industry. Spinning Flightincludes not only the latest published results but also describes Lorenzs own experiments with how-to instructions on how readers can do their own experiments |
Note: | Springer eBooks |
Contents: | Aerodynamics of Balls |
Bouncing Balls, Airbags, and Tumbleweeds | |
Spinning Bullets, Bombs, and Rockets | |
Satellites and Spin | |
Encountering Asteroids and Comets | |
Planetary Probes and Spinning Parachutes | |
Frisbees | |
Spinning Cylinders and Rings | |
Spinning Aircraft and Nonspinning Disc Aircraft | |
The Boomerang | |
Samaras | |
Skipping Stones and Bouncing Bombs | |
Conclusions | |
ISBN: | 9780387472898 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mechanics , Astrophysics |
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Call number: | SPRINGER-2006-9780387342412:ONLINE Show nearby items on shelf |
Title: | A Concise Introduction to Mathematical Logic [electronic resource] |
Author(s): |
Wolfgang Rautenberg |
Date: | 2006 |
Edition: | 2 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create alogistic foundation for m athematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there arealready several well-known textbooks on mathematical logic, this book is unique in that it is more concise than most others the material is treated in a streamlined fashion. This allows the lecturer to select the material for aone-semester course on a topic more easily. Although the book is intended for us e as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover justthe material for an introductory course on mathematical logic combined with the necessary material from set theory. Chapter 3 is partly of a descriptive nature, providing a view towards decision problems, automated theorem proving,non-standard models and related subjects. The other chapters contain material on logic programming for computer scientists, mod el theory, recursion theory, Gdel's Incompleteness Theorems, and applications of mathematical logic.Philosophical and foundational problems of mathematics are discussed where appropriate. The author has provided exercises for each section, as well as hint s or even complete solutions to most exercises at the end of the book. From theforeword, written by Lev Beklemishev: a well-written introduction to this beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Gdels incompleteness theorems,as well as some topics motivated by applications, such as a chapter on logic programming. The author has taken great care to make the expositi |
Note: | Springer eBooks |
Contents: | Foreword |
Preface | |
Introduction | |
Notation | |
Propositional Logic | |
Predicate Logic | |
Gdels Completeness Theorem | |
The Foundations of Logic Programming | |
Elements of Model Theory | |
Incompleteness and Undecidability | |
On the Theory of Self | |
Reference | |
Hints to the Exercises | |
Literature | |
Index of Terms and Names | |
Index of Symbols | |
ISBN: | 9780387342412 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Logic, Symbolic and mathematical |
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Call number: | SPRINGER-2006-9780387316086:ONLINE Show nearby items on shelf |
Title: | Algebra [electronic resource] : Fields and Galois Theory |
Author(s): |
Falko Lorenz |
Date: | 2006 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by afirst course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions andalgebraic geometry. The main focus of the seco nd volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, diophantinedimensions of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews ofthe German version: This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are,at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews |
Note: | Springer eBooks |
Contents: | Constructibility with Ruler and Compass |
Algebraic Extensions | |
Simple Extensions | |
Fundamentals of Divisibility | |
Prime Factorization in Polynomial Rings. Gausss Theorem | |
Polynomial Splitting Fields | |
Separable Extensions | |
Galois Extensions | |
Finite Fields, Cyclic Groups and Roots of Unity | |
Group Actions | |
Applications of Galois Theory to Cyclotomic Fields | |
Further Steps into Galois Theory | |
Norm and Trace | |
Binomial Equations | |
Solvability of Equations | |
Integral Ring Extensions with Applications to Galois Theory | |
The Transcendence of ? | |
Fundamentals of Transcenden | |
ISBN: | 9780387316086 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Field theory (Physics) , Number theory |
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Call number: | SPRINGER-2006-9780387277318:ONLINE Show nearby items on shelf |
Title: | Probability Theory with Applications [electronic resource] |
Author(s): |
M. M Rao R. J Swift |
Date: | 2006 |
Edition: | Second Edition |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Probability Theory and Applications is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including someimportant applications. This n ew edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentationare better highlighted with several (small and large) alterations made to each chapter. Key features of the book include: indicating the need for abstract theory even in applications and showing the inadequacy of existing resultsfor certain apparently simple real-world problems attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject providing a treatment of conditionalexpectations and of conditional probabilities that is more complete than in other existing textbooks. Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key resultsare given multiple proofs when each argument has something to contribute. Audience This book is intended for graduate students and re searchers interested in probability theory |
Note: | Springer eBooks |
Contents: | Part I. Foundations |
1. Background Material and Preliminaries | |
2. Independence and Strong Convergence | |
3. Conditioning and some Dependence Classes | |
Part II. Analytical Theory | |
4. Probability Distributions and Characteristic Functions | |
5. Weak Limit Laws | |
Part III. Applications | |
6. Stopping Times, Martingales, and Convergences | |
7. Limit Laws for some Dependent Sequences | |
8. A Glimpse of Stochastic Processes | |
References | |
Author Index | |
Subject Index | |
ISBN: | 9780387277318 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Its Applications : v582 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2005-9783764373238:ONLINE Show nearby items on shelf |
Title: | Analysis I [electronic resource] |
Author(s): |
Herbert Amann Joachim Escher |
Date: | 2005 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is the first of a three volume introduction to analysis. It is distinguished by its modern and clear presentation, concentrating always on the essential concepts. In contrast to most other textbooks, there is noartificial separation between the theories of one variable and that of many variables. Emphasis is placed on the early development of a solid foundation in topology. As well, the basics of complex analysis are covered. This book isdirected primarily to the students and instructors of beginning courses in analysis. But, with the many examples, exercises and the supplementary material, it is also suitable for self-study, as preparation for advanced study, and as abasis for other research in mathematics and physics. This textbook provid es an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential.'' Zeitschrift fr Analysisund ihre Anwendung 18, No. 4 (G. Berger, review of the first German edition) One advantage of this p resentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications.'' W. Grlz, reviewof the first German edition |
Note: | Springer eBooks |
Contents: | Preface |
I. Basics | |
II.Convergence | |
III. Continuous Functions | |
IV. Calculus in One Variable | |
V. Sequences of Functions | |
Bibliography | |
Index | |
ISBN: | 9783764373238 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2005-9783540299264:ONLINE Show nearby items on shelf |
Title: | Analysis II [electronic resource] : Differential and Integral Calculus, Fourier Series, Holomorphic Functions |
Author(s): |
Roger Godement |
Date: | 2005 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences atParis VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches tothe main results, in order to initiate the read er to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas overcalculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first twovolumes are now available in English |
Note: | Springer eBooks |
Contents: | Differential and Integral Calculus |
The Riemann Integral | |
Integrability Conditions | |
The Fundamental Theorem (FT) | |
Integration by parts | |
Taylors Formula | |
The change of variable formula | |
Generalised Riemann integrals | |
Approximation Theorems | |
Radon measures in ? or ? | |
Schwartz distributions | |
Asymptotic Analysis | |
Truncated expansions | |
Summation formulae | |
Harmonic Analysis and Holomorphic Functions | |
Analysis on the unit circle | |
Elementary theorems on Fourier series | |
Dirichlets method | |
Analytic and holomorphic functions | |
Harmonic functions and Fourie | |
ISBN: | 9783540299264 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2005-9780387276021:ONLINE Show nearby items on shelf |
Title: | An Introduction to Difference Equations [electronic resource] |
Author(s): |
Saber Elaydi |
Date: | 2005 |
Edition: | Third Edition |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate andbeginning graduate s tudents. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, along with recentresults on local and global stability of o ne-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model. SaberElaydi is Professor of Mathematics at Trinity University. He is also the author of Discrete Chaos (1999), and the Editor-In-Chief of the Journal of Difference Equations and Applications. About the Second Edition: The book is a valuablereference for anyone who models discrete systems. Dynamicists have the long-awaited disc rete counterpart to standard textbooks such as Hirsch and Smale ('Differential Equations, Dynamical Systems, and Linear Algebra'). It is so wellwritten and well designed, and the contents are so interesting to me, that I had a difficult time putting it do wn. - Shandelle Henson, Journal of Difference Equations and Applications Among the few introductory texts to differenceequations this book is one of the very best ones. It has many features that the other texts don't have, e.g., stability theory, the Z-tr ansform method (including a study of Volterra systems), and asymptotic behavior of solutions ofdifference equations (including Levinson's lemma) are studied extensively. It also contains very nice examples that primarily arise in applications in a variety of disciplines, including neural networks, feedback control, biology,Markov chains, economics, and heat transfer... -Martin Bohner, University of Missouri, Rolla |
Note: | Springer eBooks |
Contents: | Preface |
List of Symbols | |
Dynamics of First | |
Order Difference Equations | |
Linear Difference Equations of Higher Order | |
Systems of Linear Difference Equations | |
Stability Theory | |
Higher Order Scalar Difference Equations | |
The Z | |
Transform Method and Volterra Difference Equations | |
Oscillation Theory | |
Asymptotic Behavior of Difference Equations | |
Applications to Continued Fractions and Orthogonal Polynomials | |
Control Theory | |
Answers and Hints to Selected Problems | |
Appendix A: Stability of Nonhyperbolic Fixed Points of Maps on the Real Line | |
Vandermonde Matrix | |
Stability of | |
ISBN: | 9780387276021 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional equations |
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Call number: | SPRINGER-2001-9781489928498:ONLINE Show nearby items on shelf |
Title: | Dynamical Systems with Applications using MAPLE |
Author(s): |
Stephen Lynch |
Date: | 2001 |
Size: | 1 online resource (399 p.) |
Note: | 10.1007/978-1-4899-2849-8 |
Contents: | 0 A Tutorial Introduction to Maple -- 1 Differential Equations -- 2 Linear Systems in the Plane -- 3 Nonlinear Systems in the Plane -- 4 Interacting Species -- 5 Limit Cycles -- 6 Hamiltonian Systems, Lyapunov Functions, and Stability |
-- 7 Bifurcation Theory -- 8 Three-Dimensional Autonomous Systems and Chaos -- 9 Poincaré Maps and Nonautonomous Systems in the Plane -- 10 Local and Global Bifurcations -- 11 The Second Part of David Hilbert’s Sixteenth Problem -- 12 | |
Limit Cycles of Liénard Systems -- 13 Linear Discrete Dynamical Systems -- 14 Nonlinear Discrete Dynamical Systems -- 15 Complex Iterative Maps -- 16 Electromagnetic Waves and Optical Resonators -- 17 Analysis of Nonlinear Optical | |
Resonators -- 18 Fractals -- 19 Multifractals -- 20 Controlling Chaos -- 21 Examination-Type Questions -- 22 Solutions to Exercises -- References -- Textbooks -- Research Papers | |
ISBN: | 9781489928498 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Differential equations , Applied mathematics , Engineering mathematics , Computer mathematics , Mathematical models , Complexity, Computational , Physics , Theoretical, Mathematical and Computational Physics , Computational Mathematics and Numerical Analysis , Mathematical Modeling and Industrial Mathematics , Applications of Mathematics , Ordinary Differential Equations , Complexity |
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Call number: | SPRINGER-1996-9783034891738:ONLINE Show nearby items on shelf |
Title: | Mathematics of the 19th Century Geometry, Analytic Function Theory |
Author(s): | |
Date: | 1996 |
Size: | 1 online resource (291 p.) |
Note: | 10.1007/978-3-0348-9173-8 |
Contents: | 1. Geometry -- 1. Analytic and Differential Geometry -- 2. Projective Geometry -- 3. Algebraic Geometry and Geometric Algebra -- 4. Non-Euclidean Geometry -- 5. Multi-Dimensional Geometry -- 6. Topology -- 7. Geometric Transformations |
-- Conclusion -- 2. Analytic Function -- Results Achieved in Analytic Function Theory in the Eighteenth Century -- Development of the Concept of a Complex Number -- Complex Integration -- The Cauchy Integral Theorem. Residues -- | |
Elliptic Functions in the Work of Gauss -- Hypergeometric Functions -- The First Approach to Modular Functions -- Power Series. The Method of Majorants -- Elliptic Functions in the Work of Abel -- C.G.J. Jacobi. Fundamenta nova | |
functionum ellipticarum -- The Jacobi Theta Functions -- Elliptic Functions in the Work of Eisenstein and Liouville. The First Textbooks -- Abelian Integrals. Abel’s Theorem -- Quadruply Periodic Functions -- Summary of the Development | |
of Analytic Function Theory over the First Half of the Nineteenth Century -- V. Puiseux. Algebraic Functions -- Bernhard Riemann -- Riemann’s Doctoral Dissertation. The Dirichlet Principle -- Conformal Mappings -- Karl Weierstrass -- | |
Analytic Function Theory in Russia. Yu.V. Sokhotski? and the Sokhotski?-Casorati-Weierstrass Theorem -- Entire and Meromorphic Functions. Picard’s Theorem -- Abelian Functions -- Abelian Functions (Continuation) -- Automorphic | |
Functions. Uniformization -- Sequences and Series of Analytic Functions -- Conclusion -- Literature -- (F. A. Medvedev) -- General Works -- Collected Works and Other Original Sources -- Auxiliary Literature to Chapter 1 -- Auxiliary | |
Literature to Chapter 2 -- Index of Names (A. F. Lapko) | |
ISBN: | 9783034891738 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Geometry , History , Mathematics , History of Mathematical Sciences , Geometry , Analysis |
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Call number: | SPRINGER-1995-9789401584807:ONLINE Show nearby items on shelf |
Title: | Numerical Methods for the Solution of Ill-Posed Problems |
Author(s): |
A. N Tikhonov |
Date: | 1995 |
Size: | 1 online resource (254 p.) |
Note: | 10.1007/978-94-015-8480-7 |
Contents: | 1. Regularization methods -- 2. Numerical methods for the approximate solution of ill-posed problems on compact sets -- 3. Algorithms for the approximate solution of ill-posed problems on special sets -- 4. Algorithms and programs for |
solving linear ill-posed problems -- Appendix: Program listings -- I. Program for solving Fredholm integral equations of the first kind, using Tikhonov’s method with transformation of the Euler equation to tridiagonal form -- II. | |
Program for solving Fredholm integral equations of the first kind by Tikhonov’s method, using the conjugate gradient method -- III. Program for solving Fredholm integral equations of the first kind on the set of nonnegative functions, | |
using the regularization method -- IV. Program for solving one-dimensional integral equations of convolution type -- V. Program for solving two-dimensional integral equations of convolution type -- VI. Program for solving Fredholm | |
integral equations of the first kind on the sets of monotone and (or) convex functions. The method of the conditional gradient -- VII. Program for solving Fredholm integral equations of the first kind on the sets of monotone and (or) | |
convex functions. The method of projection of conjugate gradients -- VIII. Program for solving Fredholm integral equations of the first kind on the sets of monotone and (or) convex functions. The method of projection of conjugate | |
gradients onto the set of vectors with nonnegative coordinates -- IX. General programs -- Postscript -- 1. Variational methods -- 2. Iterative methods -- 3. Statistical methods -- 4. Textbooks -- 5. Handbooks and Conference Proceedings | |
ISBN: | 9789401584807 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 328 |
Keywords: | Mathematics , Integral equations , Operator theory , Computer mathematics , Algorithms , Mathematical optimization , Mathematics , Computational Mathematics and Numerical Analysis , Integral Equations , Operator Theory , Optimization , Algorithms |
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Call number: | SPRINGER-1994-9781461202516:ONLINE Show nearby items on shelf |
Title: | Prime Numbers and Computer Methods for Factorization |
Author(s): |
Hans Riesel |
Date: | 1994 |
Edition: | Second Edition |
Size: | 1 online resource (464 p.) |
Note: | 10.1007/978-1-4612-0251-6 |
Contents: | 1. The Number of Primes Below a Given Limit -- 2. The Primes Viewed at Large -- 3. Subtleties in the Distribution of Primes -- 4. The Recognition of Primes -- 5. Classical Methods of Factorization -- 6. Modem Factorization Methods -- |
7. Prime Numbers and Cryptography -- Appendix 1. Basic Concepts in Higher Algebra -- Modules -- Euclid’s Algorithm -- The Labor Involved in Euclid’s Algorithm -- A Definition Taken from the Theory of Algorithms -- A Computer Program | |
for Euclid’s Algorithm -- Reducing the Labor -- Binary Form of Euclid’s Algorithm -- Groups -- Lagrange’s Theorem. Cosets -- Abstract Groups. Isomorphic Groups -- The Direct Product of Two Given Groups -- Cyclic Groups -- Rings -- Zero | |
Divisors -- Fields -- Mappings. Isomorphisms and Homomorphisms -- Group Characters -- The Conjugate or Inverse Character -- Homomorphisms and Group Characters -- Appendix 2. Basic Concepts in Higher Arithmetic -- Divisors. Common | |
Divisors -- The Fundamental Theorem of Arithmetic -- Congruences -- Linear Congruences -- Linear Congruences and Euclid’s Algorithm -- Systems of Linear Congruences -- Carmichael’s Function -- Carmichael’s Theorem -- Appendix 3. | |
Quadratic Residues -- Legendre’s Symbol -- Arithmetic Rules for Residues and Non-Residues -- The Law of Quadratic Reciprocity -- Jacobi’s Symbol -- Appendix 4. The Arithmetic of Quadratic Fields -- Appendix 5. Higher Algebraic Number | |
Fields -- Algebraic Numbers -- Appendix 6. Algebraic Factors -- Factorization of Polynomials -- The Cyclotomic Polynomials -- Aurifeuillian Factorizations -- Factorization Formulas -- The Algebraic Structure of Aurifeuillian Numbers -- | |
Appendix 7. Elliptic Curves -- Cubics -- Rational Points on Rational Cubics -- Homogeneous Coordinates -- Elliptic Curves -- Rational Points on Elliptic Curves -- Appendix 8. Continued Fractions -- What Is a Continued Fraction? -- | |
Regular Continued Fractions. Expansions -- Evaluating a Continued Fraction -- Continued Fractions as Approximations -- Euclid’s Algorithm and Continued Fractions -- Linear Diophantine Equations and Continued Fractions -- A Computer | |
Program -- Continued Fraction Expansions of Square Roots -- Proof of Periodicity -- The Maximal Period-Length -- Short Periods -- Continued Fractions and Quadratic Residues -- Appendix 9. Multiple-Precision Arithmetic -- Various | |
Objectives for a Multiple-Precision Package -- How to Store Multi-Precise Integers -- Addition and Subtraction of Multi-Precise Integers -- Reduction in Length of Multi-Precise Integers -- Multiplication of Multi-Precise Integers -- | |
Division of Multi-Precise Integers -- Input and Output of Multi-Precise Integers -- A Complete Package for Multiple-Precision Arithmetic -- A Computer Program for Pollard’s rho Method -- Appendix 10. Fast Multiplication of Large | |
Integers -- The Ordinary Multiplication Algorithm -- Double Length Multiplication -- Recursive Use of Double Length Multiplication Formula -- A Recursive Procedure for Squaring Large Integers -- Fractal Structure of Recursive Squaring | |
-- Large Mersenne Primes -- Appendix 11. The Stieltjes Integral -- Functions With Jump Discontinuities -- The Riemann Integral -- Definition of the Stieltjes Integral -- Rules of Integration for Stieltjes Integrals -- Integration by | |
Parts of Stieltjes Integrals -- The Mean Value Theorem -- Applications -- Tables. For Contents -- List of Textbooks | |
ISBN: | 9781461202516 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 126 |
Keywords: | Mathematics , Computer mathematics , Number theory , Mathematics , Number Theory , Computational Mathematics and Numerical Analysis |
Availability: | Click here to see Library holdings or inquire at
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Location: | ONLINE |
Call number: | SPRINGER-1991-9781461209393:ONLINE Show nearby items on shelf |
Title: | Theory of Complex Functions |
Author(s): |
Reinhold Remmert |
Date: | 1991 |
Size: | 1 online resource (458 p.) |
Note: | 10.1007/978-1-4612-0939-3 |
Contents: | Historical Introduction -- Chronological Table -- A. Elements of Function Theory -- 0. Complex Numbers and Continuous Functions -- 1. Complex-Differential Calculus -- 2. Holomorphy and Conformality. Biholomorphic Mappings.. -- 3. |
Modes of Convergence in Function Theory -- 4. Power Series -- 5. Elementary Transcendental Functions -- B. The Cauchy Theory -- 6. Complex Integral Calculus -- 7. The Integral Theorem, Integral Formula and Power Series Development -- | |
C. Cauchy-Weierstrass-Riemann Function Theory -- 8. Fundamental Theorems about Holomorphic Functions -- 9. Miscellany -- 10. Isolated Singularities. Meromorphic Functions -- 11. Convergent Series of Meromorphic Functions -- 12. Laurent | |
Series and Fourier Series -- 13. The Residue Calculus -- 14. Definite Integrals and the Residue Calculus -- Short Biographies o/Abel, Cauchy, Eisenstein, Euler, Riemann and Weierstrass -- Photograph of Riemann’s gravestone -- | |
Literature -- Classical Literature on Function Theory — Textbooks on Function Theory — Literature on the History of Function Theory and of Mathematics Symbol Index -- Name Index -- Portraits of famous mathematicians 3 | |
ISBN: | 9781461209393 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate in Texts Mathematics, Readings in Mathematics: 122 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis |
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Call number: | SPRINGER-1985-9781461251163:ONLINE Show nearby items on shelf |
Title: | New Directions in Two-Year College Mathematics Proceedings of the Sloan Foundation Conference on Two-Year College Mathematics, held July 11–14 at Menlo College in Atherton, California |
Author(s): | |
Date: | 1985 |
Size: | 1 online resource (491p p.) |
Note: | 10.1007/978-1-4612-5116-3 |
Contents: | 1. A Case for Curriculum Change -- Mathematics In Today’s Community College -- Let’s Keep the “College” In Our Community Colleges: Mathematics for College Transfer -- A New Start for Mathematics Curriculum -- Mathematics as a Course |
of Problem Solving- Then and Now -- 2. Technical Mathematics -- Technical Mathematics: A Dilemma -- Occupational Education and Mathematics: Ownership Makes the Difference -- Technical Mathematics in Two-Year College Programs -- 3. | |
Endangered Curriculum Elements -- Reflections on Basic Mathematics Programs in the Two-Year College -- Liberal Arts Mathematics—Cornerstone or Dinosaur? -- Statistics in the Two-Year College Curriculum -- 4. New Curricula and New Tools | |
-- It’s Going to Happen Anyway… -- Discrete Topics in the Undergraduate Curriculum: How Big a Step Should We Take? -- Calculators Do More than Compute -- The Lessons of Williamstown -- Style Versus Content: Forces Shaping the Evolution | |
of Textbooks -- 5. The Learning of Mathematics -- Research in the Learning of Mathematics: Some Genuinely New Directions -- Knowledge Transmission and Acquisition: Cognitive and Affective Considerations -- 6. Faculty Renewal and | |
Professionalism -- Relevancy and Revitalization: Retaining Quality and Vitality in Two-Year College Mathematics Faculty -- The Academic Training of Two-Year College Mathematics Faculty -- Current Continuing Education Needs of Two-Year | |
College Faculty Must be Met! -- 7. Coordinating Curriculum Change -- Coordinating Curriculum in Two-Year Colleges with Baccalaureate Institutions -- Some Reflections on the Interaction of Mathematics Programs at Two- and Four-Year | |
Colleges -- Mathematics Programs in High Schools and Two-Year Colleges | |
ISBN: | 9781461251163 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematics , Mathematics, general |
Availability: | Click here to see Library holdings or inquire at
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Location: | ONLINE |
Call number: | QC20.B35::2006 Show nearby items on shelf |
Title: | Mathematical Methods in Science and Engineering |
Author(s): |
S. Selcuk Bayin 1951- |
Date: | 2006 |
Publisher: | Wiley-Interscience |
ISBN: | 0470041420 |
Keywords: | Mathematical Physics, Textbooks , Engineering Mathematics, Textbooks |
Availability: | Click
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Location: | MAIN |
Call number: | QC173.59.M3P65::2014 Show nearby items on shelf |
Title: | Gravity: Newtonian, post-Newtonian, relativistic |
Author(s): |
Eric Poisson Clifford M. Will |
Date: | 2014 |
Publisher: | Cambridge: Cambridge University Press |
Size: | 780 p. |
Contents: | 1. Foundations of Newtonian gravity, 2. Structure of self-gravitating bodies, 3. Newtonian orbital dynamics, 4. Minkowski spacetime, 5. Curved spacetime, 6. Post-Minkowskian theory: formulation, 7. Post-Minkowskian theory: implementation, 8. Post-Newt onian theory: fundamentals, 9. Post-Newtonian theory: system of isolated bodies, 10. Post-Newtonian celestial mechanics, astrometry and navigation, 11. Gravitational waves, 12. Radiative losses and radiation reaction, 13. Alternative theories of gravity |
ISBN: | 9781107032866 |
Keywords: | General relativity (Physics) Mathematics Textbooks , Gravity Mathematics Textbooks. , SCIENCE / Cosmology |
Availability: | Click
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Location: | SUGGESTIONS (email library@fnal.gov if you would like this title added to the Library collection.) |
Call number: | QA39.A7413::2014 Show nearby items on shelf |
Title: | Mathematical understanding of nature: Essays on amazing physical phenomena and their understanding by mathematicians |
Author(s): |
Vladimir Igorevich Arnold |
Date: | 2014 |
Publisher: | Providence, Rhode Island: AMS, American Mathematical Society |
Size: | 167 p |
ISBN: | 9781470417017 |
Keywords: | Mathematics Popular works. , Mechanics of particles and systems -- Instructional exposition (textbooks, tutor , Fluid mechanics -- Instructional exposition (textbooks, tutorial papers, etc.) , Optics, electromagnetic theory -- Instructional exposition (textbooks, tutorial |
Availability: | Click
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Call number: | QA37.2.B63::2006 Show nearby items on shelf |
Title: | Mathematical Methods in the Physical Sciences |
Author(s): |
Mary L. Boas |
Date: | 2006 |
Publisher: | Wiley |
Note: | 3rd ed. |
Contents: | Infinite Series, Power Series |
Complex Numbers | |
Linear Algebra | |
Partial Differentiation | |
Multiple Integrals | |
Vector Analysis | |
Fourier Series and Transforms | |
Ordinary Differential Equations | |
Calculus of Variations | |
Tensor Analysis | |
Special Functions | |
Legendre, Bessel, Hermite, and Laguerre Functions | |
Partial Differential Equations | |
Functions of a Complex Variable | |
Probability and Statistics | |
ISBN: | 0471198269 |
Keywords: | Mathematics - Textbooks |
Availability: | Click
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Location: | MAIN |
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