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Call number: | SPRINGER-2016-9783319335070:ONLINE Show nearby items on shelf |
Title: | Monte Carlo and Quasi-Monte Carlo Methods MCQMC, Leuven, Belgium, April 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (57 p.) |
Note: | 10.1007/978-3-319-33507-0 |
Contents: | Part I Invited papers -- Multilevel Monte Carlo Implementation for SDEs driven by Truncated Stable Processes -- Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo -- Vandermonde Nets and Vandermonde Sequences -- Path Space Markov Chain Monte Carlo Methods in Computer Graphics -- Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC -- Some Results on the Complexity of Numerical Integration -- Approximate Bayesian Computation: A Survey on Recent Results -- Part II Contributed papers -- Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier–Stokes Equations -- Unbiased Simulation of Distributions with Explicitly Known Integral Transforms -- Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting -- Comparison between LS-Sequences and β -adic van der Corput Sequences -- Computational Higher Order Quasi-Monte Carlo Integration -- Numerical |
Computation of Multivariate Normal Probabilities using Bivariate Conditioning -- Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations -- On ANOVA Decompositions of Kernels and Gaussian Random Field Paths -- The Mean Square Quasi-Mont e Carlo Error for Digitally Shifted Digital Nets -- Uncertainty and Robustness in Weather Derivative Models -- Reliable Adaptive Cubature Using Digital Sequences -- Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives -- Adaptive Multidimensional Integration Based on Rank-1 Lattices -- Path Space Filtering -- Tractability of Multivariate Integration in Hybrid Function Spaces -- Derivative-based Global Sensitivity Measures and Their Link with S obol’ Sensitivity Indices -- Bernstein Numbers and Lower Bounds for the Monte Carlo Error -- A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes -- A Strategy for Parallel | |
Implementations of Stochastic Lagrangian Simulation -- A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets -- Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve -- Uniform Weak Tractability of Weighted Integration -- Incremental Greedy Algorithm and Its Applications in Numerical Integration -- On “Upper Error Bounds for Quadrature Formulas on Function Classes” by K K Frolov -- Tractability of Function Approxi mation With Product Kernels -- Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratiﬁed Inputs -- List of Participants -- Index | |
ISBN: | 9783319335070 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 163 |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Computer mathematics , Mathematics , Computational Mathematics and Numerical Analysis , Applications of Mathematics |
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Call number: | SPRINGER-2016-9783319287393:ONLINE Show nearby items on shelf |
Title: | Nonlocal Diffusion and Applications |
Author(s): |
Claudia Bucur |
Date: | 2016 |
Size: | 1 online resource (23 p.) |
Note: | 10.1007/978-3-319-28739-3 |
Contents: | Introduction -- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps -- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions -- 2.2 Fractional Sobolev Inequality and Generalized Coarea F ormula -- 2.3 Maximum Principle and Harnack Inequality -- 2.4 An s-harmonic function -- 2.5 All functions are locally s-harmonic up to a small error -- 2.6 A function with constant fractional Laplacian on the ball -- 3 Extension problems -- 3.1 Water wave model -- 3.2 Crystal dislocation -- 3.3 An approach to the extension problem via the Fourier transform -- 4 Nonlocal phase transitions -- 4.1 The fractional Allen-Cahn equation -- 4.2 A nonlocal version of a conjecture by De Giorgi -- 5 Nonlocal minimal surfaces -- 5.1 Graphs and s-minimal surfaces -- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity -- 6 A nonlocal nonlinear stationary Schrödinger type equation -- 6.1 From the nonlocal Uncertainty Principle to a |
fractional weighted inequality -- Alternative proofs of some results -- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3 -- References | |
ISBN: | 9783319287393 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes of the Unione Matematica Italiana: 20 |
Keywords: | Mathematics , Functional analysis , Integral transforms , Operational calculus , Partial differential equations , Calculus of variations , Mathematics , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization , Integral Transforms, Operational Calculus , Functional Analysis |
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Call number: | SPRINGER-2016-9783319278070:ONLINE Show nearby items on shelf |
Title: | Advanced Calculus of a Single Variable |
Author(s): |
Tunc Geveci |
Date: | 2016 |
Size: | 1 online resource (77 p.) |
Note: | 10.1007/978-3-319-27807-0 |
Contents: | Preface -- Real Numbers, Sequences and Limits -- Limits and Continuity of Functions -- The Derivative -- The Riemann Integral -- Infinite Series -- Sequences and Series of Functions. Index. |
ISBN: | 9783319278070 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Integral transforms , Operational calculus , Mathematics , Integral Transforms, Operational Calculus , Functional Analysis |
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Call number: | SPRINGER-2016-9783034809641:ONLINE Show nearby items on shelf |
Title: | Application of Holomorphic Functions in Two and Higher Dimensions |
Author(s): |
Klaus Gürlebeck |
Date: | 2016 |
Size: | 1 online resource (3 p.) |
Note: | 10.1007/978-3-0348-0964-1 |
Contents: | 1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index |
ISBN: | 9783034809641 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Mathematics , Integral Transforms, Operational Calculus , Functions of a Complex Variable , Partial Differential Equations , Functional Analysis |
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Call number: | SPRINGER-2016-9781493930289:ONLINE Show nearby items on shelf |
Title: | Linear Canonical Transforms Theory and Applications |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (26 p.) |
Note: | 10.1007/978-1-4939-3028-9 |
Contents: | Foreward -- PART I : Fundamentals -- Development of linear canonical transforms – a historical sketch -- The linear canonical transformation: definition and properties -- Eigenfunctions of the linear canonical transform -- Uncertainty |
principles and the linear canonical transform -- The linear canonical transformations in classical optics -- Optical Implementation of Linear Canonical Transforms -- PART II : Discretization and Computation -- Linear canonical domains | |
and degrees of freedom of signals and systems -- Sampling and discrete linear canonical transforms -- Self-imaging and discrete paraxial optics -- Fast algorithms for digital computation of linear canonical transforms -- PART III : | |
Applications -- Deterministic phase retrieval using the LCT -- Analyzing digital holographic systems with the LCT -- Double random phase encoding based optical encryption systems using some linear canonical transforms: weaknesses and | |
countermeasures -- Complex valued ABCD Matrices -- Linear canonical transforms on quantum states of light | |
ISBN: | 9781493930289 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Series in Optical Sciences: 198 |
Keywords: | Physics , Integral transforms , Operational calculus , Optics , Electrodynamics , Microwaves , Optical engineering , Physics , Optics and Electrodynamics , Microwaves, RF and Optical Engineering , Integral Transforms, Operational Calculus , Numerical and Computational Physics |
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Call number: | SPRINGER-2014-9783642541247:ONLINE Show nearby items on shelf |
Title: | Mathematics for Physicists and Engineers [electronic resource] : Fundamentals and Interactive Study Guide |
Author(s): |
Klaus Weltner Sebastian John Wolfgang J Weber Peter Schuster Jean Grosjean |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This textbook offers an accessible and highly approved approach which is characterized by the combination of the textbook with a detailed study guide available online at our repository extras.springer.com. This study guide dividesthe whole learning t ask into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and to return to the study guide afterwards. Working with thestudy guide his or her learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degree of difficulties is slowlyrising the students gain confidence and experience their own prog ress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties he or she is given supplementary explanations and in case ofindividual needs supplementary exercises and applications. So the sequence of the studies i s individualized according to the individual performance and needs and can be regarded as full tutorial course. The study guide satisfies twoobjectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offer s advice on the improvement of study skills. Empirical studies have shown that the student's competence for using writteninformation has improved significantly by using this study guide. The new edition includes a new chapter on Fourier integrals and Four ier transforms, numerous sections had been updated, 30 new problems with solutions had been added.The interactive study guide has seen a substantial update |
Contents: | From the Contents: Vector Algebra I: Scalars and Vectors |
Vector Algebra II: Scalar and Vector Products | |
Functions | |
Exponential, Logarithmic and Hyperbolic Functions | |
Differential Calculus | |
Integral Calculus | |
Applications of Integration | |
Taylor Series and Power Series | |
Complex Numbers | |
Differential Equations | |
Laplace Transforms | |
Functions of Several Variables Partial Differentiation and Total Differentiation | |
Multiple Integrals Coordinate Systems | |
Transformation of Coordinates Matrices | |
Sets of Linear Equations Determinanats | |
Eigenvalues and Eigenvectors of R | |
ISBN: | 9783642541247 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2014-9781447163954:ONLINE Show nearby items on shelf |
Title: | An Introduction to Laplace Transforms and Fourier Series [electronic resource] |
Author(s): |
Phil Dyke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative.Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis onapplication with the necessary mathematical g rounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Onlyknowledge of elementary trigonometry and calculus are required as prereq uisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics ormathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems |
Contents: | The Laplace Transform |
Further Properties of the Laplace Transform | |
Convolution and the Solution of Ordinary Differential Equations | |
Fourier Series | |
Partial Differential Equations | |
Fourier Transforms | |
Wavelets and Signal Processing | |
Complex Variables and Laplace Transforms | |
ISBN: | 9781447163954 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functions of complex variables , Integral Transforms , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9783034805728:ONLINE Show nearby items on shelf |
Title: | Offbeat Integral Geometry on Symmetric Spaces [electronic resource] |
Author(s): |
Valery V Volchkov Vitaly V Volchkov |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces ofarbitrary ranks as we ll as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for variousclasses of functions, far-reaching generalizatio ns of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful invarious fields of contemporary mathematics. The proofs given are mini mal in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historicalperspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and theHeisenberg group, integral equations, special functions, and transmutation operators theory |
Note: | Springer eBooks |
Contents: | Preface |
Part 1. Analysis on Symmetric Spaces. 1 Preliminaries | |
2 The Euclidean case | |
3 Symmetric spaces of the non | |
compact type | |
4 Analogies for compact two | |
point homogeneous Spaces | |
5 The phase space associated to the Heisenberg group | |
Part 2. Offbeat Integral Geometry | |
1 Functions with zero ball means on Euclidean space | |
2 Two | |
radii theorems in symmetric spaces | |
3 The problem of finding a function from its ball means | |
4 Sets with the Pompeiu property | |
5 Functions with zero integrals over polytopes | |
6 Ellipsoidal means | |
7 The Pompeiu property on a sphere | |
8 The Pompeiu | |
ISBN: | 9783034805728 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Integral Transforms , Functions, special , Global differential geometry |
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Call number: | SPRINGER-2013-9781461472971:ONLINE Show nearby items on shelf |
Title: | Differential Equations [electronic resource] : A Primer for Scientists and Engineers |
Author(s): |
Christian Constanda |
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: | Differential Equations: A Primer for Scientists and Engineers is a textbook designed with the needs of todays student in mind. It is the ideal textbook for a first course in elementary differential equations for futureengineers and scientists, includ ing mathematicians. This book is accessible to anyone who has a basic knowledge of precalculus algebra and differential and integral calculus. Its carefully crafted text adopts a concise, simple,no-frills approach to differential equations, which helps st udents acquire a solid experience in many classical solution techniques. With a lighter accent on the physical interpretation of the results, a more manageable page count thancomparable texts, a highly readable style, and over 800 exercises designed to be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct yet fully rigorous fashion. Thebook formally splits the pure and applied parts of the contents by placing the discussion of selecte d mathematical models in separate chapters. At the end of most of the 230 worked examples, the author provides theMathematica commands for verifying the results. The book can be used independently by the average student to learn the fundamentals of the su bject, while those interested in pursuing more advanced material can regard it as an easilytaken first step on the way to the next level. Additionally, practitioners who encounter differential equations in their professional work will find this text to be a convenient source of reference. Other Springer publications byChristian Constanda: Dude, Can you Count? ISBN: 978-1-84882-538-3 Stationary Oscillations of Elastic Plates, ISBN: 978-0-8176-8340-8. Christian Constanda, MS, PhD, DSc, is the holder of the Charles W. Oliphant Endowed Chair inMathematical Sciences at the University of Tulsa, USA. He is also the Chairman of the International Consortium on Integral Methods in Science and Engineerin |
Note: | Springer eBooks |
Contents: | 1. Introduction |
2. First Order Equations | |
3. Mathematical Models with First | |
Order Equations | |
4. Linear Second | |
Order Equations | |
4. Higher | |
Order Equations | |
5. Mathematical Models with Second | |
Order Equations | |
6. Higher | |
Order Linear Equations | |
7. Systems of Differential Equations | |
8. The Laplace Transformation | |
9. Series Solutions | |
A. Algebra Techniques | |
B. Calculus Techniques | |
C. Table of Laplace Transforms | |
D. The Greek Alphabet | |
ISBN: | 9781461472971 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Texts in Mathematics and Technology, 1867-5506 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations |
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Call number: | SPRINGER-2013-9781461460121:ONLINE Show nearby items on shelf |
Title: | Linear Integral Equations [electronic resource] : Theory & Technique |
Author(s): |
Ram P Kanwal |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematicalphysics.Thisuncorrectedso ftcover reprint of the second edition places the emphasis onapplications and presents a variety of techniques with extensive examples. Originally published in1971,Linear Integral Equationsis idealas atext for a beginning graduate level course. Its treatme nt of boundary value problemsalso makesthe bookuseful to researchersin many applied fields |
Note: | Springer eBooks |
Contents: | Introduction |
Integral Equations with Separable Kernels | |
Method Of Successive Approximations | |
Classical Fredholm Theory | |
Applications of Ordinary Differential Equations | |
Applications of Partial Differential Equations | |
Symmetric Kernels | |
Singular Integral Equations | |
Integral Transformation Methods | |
Applications to Mixed Boundary Value Problems | |
Integral Equations Perturbation Methods | |
Appendix | |
Bibliography | |
Index | |
ISBN: | 9781461460121 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Integral Transforms , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461440819:ONLINE Show nearby items on shelf |
Title: | Ramanujan's Lost Notebook [electronic resource] : Part IV |
Author(s): |
George E Andrews Bruce C Berndt |
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: | In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pagesin the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, Ramanujan's lost notebook. Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume isthefourthof fivevolumes thatthe authors plan to write on Ramanujans lost notebook. In contrast to thefirst three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series. Most of the entriesexamined in this volume fall under the purviews of number theory and classical analysis. Se veral incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are ondiophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguingentries are connected with the classical, unsolved circle and divisor problems. Reviewfrom the second volume: Fans of Ramanujan's mathematics are sur e to be delighted by this book. While some of the content is taken directly frompublished papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubte dly be inspiring research for decades to come. The nextinstallment in this series is eagerly awaited. - MathSciNet Review from the first volume: Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to a n understanding of the work ofthe genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complet |
Note: | Springer eBooks |
Contents: | Preface |
1 Introduction | |
2 Double Series of Bessel Functions and the Circle and Divisor Problems | |
3 Koshliakov's Formula and Guinand's Formula | |
4 Theorems Featuring the Gamma Function | |
5 Hypergeometric Series | |
6 Euler's Constant | |
7 Problems in Diophantine Approximation | |
8 Number Theory | |
9 Divisor Sums | |
10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions | |
11 Two Partial Unpublished Manuscripts on Sums Involving Primes | |
12 Infinite Series | |
13 A Partial Manuscript on Fourier and Laplace Transforms | |
14 Integral Analogues of Theta Functions adn | |
ISBN: | 9781461440819 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Fourier analysis , Functions, special , Number theory |
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Call number: | SPRINGER-2012-9788847019478:ONLINE Show nearby items on shelf |
Title: | The Mathematical Legacy of Leon Ehrenpreis [electronic resource] |
Author(s): |
Irene Sabadini Daniele C Struppa |
Date: | 2012 |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his mostimportant contribution, t he Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, andoffered new insights in integral geometry. Leon Ehr enpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which (Farkas, Kawai,Kuchment, Quinto) were hiscollaborators |
Note: | Springer eBooks |
Contents: | Analyticity on Curves by M. Agranovsky, L. Zalcman |
On local injectivity for generalized Radon transforms by J. Boman | |
Deconvolution for the Pompeiu problem on the Heisenberg group by Der | |
Chen Chang, W. Eby, E. Grinberg | |
Theta Functions Wronskians and Weierstrass Points for Linear Spaces of Meromorphic Functions by H.M. Farkas | |
The admissibility theorem for the spatial X | |
ray transform over the two element field by E.L. Grinberg | |
Microlocal analysis of fixed singularities of WKB solutions of a Schroedinger equation by S. Kamimoto, T. Kawai, Y. Takei | |
Geometric Properties of Boundary | |
ISBN: | 9788847019478 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics, 2190-5614 : v16 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential equations, partial |
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Call number: | SPRINGER-2012-9783642312144:ONLINE Show nearby items on shelf |
Title: | Analytically Tractable Stochastic Stock Price Models [electronic resource] |
Author(s): |
Archil Gulisashvili |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in acelebrated Black-Sch oles model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatilityprocess is a geometric Brownian motion, the St ein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of theauthor's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author alsoestablishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financialmathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, s tochastic analysis and probability theory |
Note: | Springer eBooks |
Contents: | Preface |
Aknowledgements | |
1.Volatility Processes | |
2.Stock Price Models with Stochastic Volatility | |
3.Realized Volatility and Mixing Distributions | |
4.Integral Transforms of Distribution Densities | |
5.Asymptotic Analysis of Mixing Distributions | |
6.Asymptotic Analysis of Stock Price Distributions | |
7.Regularly Varying Functions and Pareto Type Distributions | |
8.Asymptotic Analysis of Option Pricing Functions | |
9.Asymptotic Analysis of Implied Volatility | |
10.More Formulas for Implied Volatility | |
11.Implied Volatility in Models Without Moment Explosions | |
Bibliography | |
Index | |
ISBN: | 9783642312144 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Finance, 1616-0533 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Finance , Distribution (Probability theory) |
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Call number: | SPRINGER-2012-9783642308987:ONLINE Show nearby items on shelf |
Title: | q -Fractional Calculus and Equations [electronic resource] |
Author(s): |
Mahmoud H Annaby Zeinab S Mansour |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9783642308987 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional equations , Functions of complex variables , Integral equations , Integral Transforms , Mathematical physics |
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Call number: | SPRINGER-2012-9783034804288:ONLINE Show nearby items on shelf |
Title: | Interpolation, Schur Functions and Moment Problems II [electronic resource] |
Author(s): |
Daniel Alpay Bernd Kirstein |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parametersequences. Schur ana lysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricialgeneralizations. These problems include interpolation a nd moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics relatedto matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number ofrecent developments in orthogonal rational matrix functions, matrix-valued Carathodory functions a nd maximal weight solutions for particular matricial moment problems on the unit circle |
Note: | Springer eBooks |
ISBN: | 9783034804288 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v226 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Integral Transforms , Operator theory |
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Call number: | SPRINGER-2011-9783034800877:ONLINE Show nearby items on shelf |
Title: | Vector-valued Laplace Transforms and Cauchy Problems [electronic resource] : Second Edition |
Author(s): |
Wolfgang Arendt Charles J.K Batty Matthias Hieber Frank Neubrander |
Date: | 2011 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operatorsis developed completel y in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations aregiven. The book contains an introduction to t he Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, andfunctional analysis. The authors have succeeded admirably in bringing toge ther a wealth of recent material, much of which appears in book form for the first time. This authoritative work is likely to become a standard reference on boththe Laplace transform and its applications to the abstract Cauchy problem. The book is an exc ellent textbook as well. Proofs are always transparent and complete, and many topics that could have been considered as backgroundmaterial are covered as well. All this makes the text very accessible and self-contained. Applications to concrete differenti al operators are given throughout the text. Each chapter ends with historical and bibliographical comments. In summary, this book will be of interest to a wide audience of (functional) analysts and it should have a place in every mathematics library. Warm ly recommended! Jan van Neerven, Nieuw Archief voor Wiskunde, No. 3, 2003 |
Note: | Springer eBooks |
Contents: | Preface to the First Edition |
Preface to the Second Edition | |
I Laplace Transforms and Well | |
Posedness of Cauchy Problems | |
1 The Laplace Integral | |
2 The Laplace Transform | |
3 Cauchy Problems | |
II Tauberian Theorems and Cauchy Problems | |
4 Asymptotics of Laplace Transforms | |
5 Asymptotics of Solutions of Cauchy Problems | |
III Applications and Examples | |
6 The Heat Equation | |
7 The Wave Equation | |
8 Translation Invariant Operators on Lp(Rn) | |
A Vector | |
valued Holomorphic Functions | |
B Closed Operators | |
C Ordered Banach Spaces | |
D Banach Spaces which Contain c0 | |
E Distribution | |
ISBN: | 9783034800877 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monographs in Mathematics : v96 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2011-9781461405894:ONLINE Show nearby items on shelf |
Title: | Approximation by Multivariate Singular Integrals [electronic resource] |
Author(s): |
George A Anastassiou |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the generalmultivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly.This book studies the rate of convergence of these o perators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theoremfor functions of two variables. Relevant background information and mot ivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply tomany areas of pure and applied mathematics, such a mathematical analysis, probability, statisti cs and partial differential equations. This book is appropriate for researchers and selected seminars at the graduate level |
Note: | Springer eBooks |
ISBN: | 9781461405894 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral Transforms , Differential equations, partial , Distribution (Probability theory) |
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Call number: | SPRINGER-2011-9781441960559:ONLINE Show nearby items on shelf |
Title: | Integral Geometry and Radon Transforms [electronic resource] |
Author(s): |
Sigurdur Helgason |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In this text, integral geometry deals with Radons problem of representing a function on a manifold in terms of its integrals over certain submanifoldshence the term the Radon transform. Examples and far-reachinggeneralizations lead to fundamental pro blems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial differential equations and group representations). For the case ofthe plane, the inversion theorem and the support theorem ha ve had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroomuse or self-study. A number of exercises point to further results with document ation. From the reviews: Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. The contents of the book isconcentrated around the duality and double fibration, which is realized through the masterful treatment of a variety of examples. The book is written by an expert, who has made fundamental contributions to the area. Boris Rubin,Louisiana State University |
Note: | Springer eBooks |
Contents: | The Radon Transformon Rn |
A Duality in Integral Geometry | |
The Radon Transform on Two | |
Point Homogeneous Spaces | |
The X | |
Ray Transform on a Symmetric Space | |
Orbital Integrals | |
The Mean | |
Value Operator | |
Fourier Transforms and Distribution: A Rapid Course | |
Lie Transformation Groups and Differential Operators | |
Bibliography | |
Notational Conventions | |
Index | |
ISBN: | 9781441960559 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Integral Transforms , Global differential geometry |
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Call number: | SPRINGER-2010-9783034604086:ONLINE Show nearby items on shelf |
Title: | Introduction to Hyperfunctions and Their Integral Transforms [electronic resource] : An Applied and Computational Approach |
Author(s): |
Urs Graf |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook presents an elementary introduction to generalized functions by using Sato's approach of hyperfunctions which is based on complex function theory. This very intuitive and appealing approach has particularly greatcomputational power. Th e concept of hyperfunctions and their analytic properties is introduced and discussed in detail in the first two chapters of the book. Thereafter the focus lies on generalizing the (classical) Laplace,Fourier, Hilbert, Mellin, and Hankel transformations t o hyperfunctions. Applications to integral and differential equations and a rich variety of concrete examples accompany the text throughout the book. Requiring only standardknowledge of the theory of complex variables, the material is easily accessible f or advanced undergraduate or graduate students. It serves as well as a reference for researchers in pure and applied mathematics, engineering and physics. |
Note: | Springer eBooks |
Contents: | Preface |
1 Introduction to Hyperfunctions | |
2 Analytic Properties | |
3 Laplace Transforms | |
4 Fourier Transforms | |
5 Hilbert Transforms | |
6 Mellin Transforms | |
7 Hankel Transforms | |
A Complements | |
B Tables | |
List of Symbols | |
Bibliography. Index | |
ISBN: | 9783034604086 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Integral Transforms , Functions, special , Computer science |
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Call number: | SPRINGER-2010-9780387927121:ONLINE Show nearby items on shelf |
Title: | The Mathematics of Medical Imaging [electronic resource] A Beginners Guide |
Author(s): |
Timothy G Feeman |
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: | A Beginner's Guide to the Mathematics of Medical Imaging presents the basic mathematics of computerized tomography the CT scan for an audience of undergraduates in mathematics and engineering. Assuming no prior backgroundin advanced mathematical an alysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magneticresonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. The text is self-contained with a range of practical exercises, topics forfurther study, and an ample bibliography, making it ideal for use in an undergrad uate course in applied or engineering mathematics, or by practitioners in radiology who want to know more about the mathematical foundations of theirfield |
Note: | Springer eBooks |
Contents: | Preface |
X | |
Rays | |
Lines and Line Integrals | |
The Radon Transform | |
Back Projection | |
Complex Numbers | |
The Fourier Transform | |
Two Big Theorems | |
Filters and Convolution | |
Discrete Image Reconstruction | |
Sampling | |
Algebraic Reconstruction Techniques | |
ISBN: | 9780387927121 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Texts in Mathematics and Technology, 1867-5506 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Radiology, Medical , Computer science , Computer vision , Functional analysis , Integral Transforms , Biomedical engineering |
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Call number: | SPRINGER-2010-9780387789637:ONLINE Show nearby items on shelf |
Title: | Topics in Hyperplane Arrangements, Polytopes and Box-Splines [electronic resource] |
Author(s): |
Corrado De Concini Claudio Procesi |
Date: | 2010 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Several mathematical areas that have been developed independently over the last 30 years are brought together revolving around the computation of the number of integral points in suitable families of polytopes. The problem isformulated here in terms of partition functions and multivariate splines. In its simplest form, the problem is to compute the number of ways a given nonnegative integer can be expressed as the sum of h fixed positive integers. Thisgoes back to ancient times and was investigated b y Euler, Sylvester among others in more recent times also in the higher dimensional case of vectors. The book treats several topics in a non-systematic way to show and compare a varietyof approaches to the subject. No book on the material is available in the existing literature. Key topics and features include: - Numerical analysis treatments relating this problem to the theory of box splines - Study of regularfunctions on hyperplane and toric arrangements via D-modules - Residue formulae for partition fu nctions and multivariate splines - Wonderful completion of the complement of hyperplane arrangements - Theory and properties of the Tuttepolynomial of a matroid and of zonotopes Graduate students as well as researchers in algebra, combinatorics and numeri cal analysis, will benefit from Topics in Hyperplane Arrangements, Polytopes, and Box Splines |
Note: | Springer eBooks |
Contents: | Introduction |
I Preliminaries. 1 Polytopes. 2 Hyperplane Arrangements. 3 Fourier and Laplace Transforms. 4 Modules Over the Weyl Algebra. 5 Differential and Difference Equations. 6 Approximation Theory I | |
II The Differentiable Case. 7 Splines. 8 Rx as a D | |
Module. 9 The function Tx. 10 Cohomology. 11 Differential Equations | |
III The Discrete Case. 12 Partition Functions. 13 Toric Arrangements. 14 Cohomology of Toric Arrangements. 15 Difference Equations. 16 Applications. 17 Approximation Theory II | |
IV The Wonderful Model. 18 Minimal Models | |
ISBN: | 9780387789637 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Topological Groups , Differential Equations , Cell aggregation Mathematics |
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Call number: | SPRINGER-2009-9789491216244:ONLINE Show nearby items on shelf |
Title: | The Wavelet Transform [electronic resource] |
Author(s): |
Ram Shankar Pathak |
Date: | 2009 |
Publisher: | Paris : Atlantis Press |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book contains many important new results on the theory of wavelet transform, such as its relations with Hilbert transform and other fractional integral operators, convolution for wavelet transform. Wavelet transforms oncertain distribution space s, on spaces of type S and type W, and on generalized Sobolev space have been studied. Asymptotic expansions of the wavelet transform when translation or dilation parameter is large/small have been obtained.So far, these results are not published in book form. The results well-illustrated by means of specific examples and relevant figures will find applications in approximation theory, signal processing and in the study of partialdifferential equations. An overview of the various topics covered in the b ook facilitates easy reference. Research workers, interested in these topics, will find many open problems being treated in this book |
Note: | Springer eBooks |
ISBN: | 9789491216244 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Atlantis Studies in Mathematics for Engineering and Science, 1875-7642 : v4 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Numerical analysis |
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Call number: | SPRINGER-2009-9783642001734:ONLINE Show nearby items on shelf |
Title: | Mathematics for Physicists and Engineers [electronic resource] : Fundamentals and Interactive Study Guide |
Author(s): |
Klaus Weltner Wolfgang J Weber Jean Grosjean Peter Schuster |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Mathematics is the basic language in physics and engineering. It is an essential tool which first and second year students have to master as soon as possible. A lack of competence in mathematics is the main reason for failure anddrop out in the begin ning periods of study. This textbook offers an accessible and highly approved approach which is characterized by the combination of the textbook with a detailed study guide available online at extras.springer.com.This study guide divides the whole learnin g task into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and to return to the study guideafterwards. Working with the study guide his or her learning resul ts are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degreeof difficulties is slowly rising the students gain confidence and experience their own p rogress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties he or she is given supplementaryexplanations and in case of individual needs supplementary exercises and applications. So the sequence of the studie s is individualised according to the individual performance and needs and can be regarded as full tutorial course. Morethan that the study guide aims to satisfy two objectives simultaneously: firstly it enables students to make effective use of the textbo ok and secondly it offers advice on the improvement of study skills. Empirical studies have shownthat the student's competence for using written information has improved significantly by using this study guide |
Note: | Springer eBooks |
Contents: | Vector Algebra I: Scalars and Vectors |
Vector Algebra II: Scalar and Vector Products | |
Functions | |
Exponential, Logarithmic and Hyperbolic Functions | |
Differential Calculus | |
Integral Calculus | |
Applications of Integration | |
Taylor Series and Power Series | |
Complex Numbers | |
Differential Equations | |
Laplace Transforms | |
Functions of Several Variables Partial Differentiation and Total Differentiation | |
Multiple Integrals Coordinate Systems | |
Transformation of Coordinates Matrices | |
Sets of Linear Equations Determinants | |
Eigenvalues and Eigenvectors of Real Matrices | |
Vect | |
ISBN: | 9783642001734 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2009-9783211994320:ONLINE Show nearby items on shelf |
Title: | Maple and Mathematica [electronic resource] : A Problem Solving Approach for Mathematics |
Author(s): |
Inna K Shingareva Carlos Lizrraga-Celaya |
Date: | 2009 |
Publisher: | Vienna : Springer Vienna |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The first book to compare the main two computer algebra systems (CAS), Maple and Mathematica used by students, mathematicians, scientists, and engineers. Both systems are presented in parallel so that Mathematica users can learnMaple quickly by findi ng the Maple equivalent to Mathematica functions, and vice versa. This student reference handbook consists of core material for incorporating Maple and Mathematica as a working tool into different undergraduatemathematical courses (abstract and linear alg ebra, geometry, calculus and analysis, complex functions, special functions, integral and discrete transforms, algebraic and transcendental equations, ordinary and partial differentialequations, integral equations, numerical analysis and scientific comput ing). The book also contains applications from various areas of mathematics, physics, and music theory and can be useful for graduate students, professors, andresearchers in science and engineering. One of the goals of this book is to develop problem-solv ing skills (that are most useful for solving sophisticated research problems) finding solutions with Maple and Mathematica and not todepend on a specific version of both systems (Maple 12 and Mathematica 6 and 7 are considered). Part I, describes the foun dations of Maple and Mathematica (with equivalent problems and solutions). Part II, describes Mathematics withMaple and Mathematica by using equivalent problems. Finally, this book is ideal for scientists who want to corroborate their Maple and Mathematic a work with independent verification provided by another CAS. J. Carter, SIAM Review 50:149-152 (2008). |
Note: | Springer eBooks |
Contents: | From the contents Preface |
Foundations of Maple and Mathematica: Maple Mathematica | |
Mathematics: Maple and Mathematica: Graphics Algebra Linear Algebra Geometry Calculus and Analysis Complex Functions Special Functions and Orthogonal Polynomials Integral and Discrete Transforms MathematicalEquations Numerical Analysis and Sci entific Computing | |
References | |
General Index | |
Maple Index | |
Mathematica Index | |
CD | |
ROM Contents | |
ISBN: | 9783211994320 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Computer science Mathematics , Computer software , Engineering |
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Call number: | SPRINGER-2009-9781848825338:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group [electronic resource] |
Author(s): |
Valery V Volchkov Vitaly V Volchkov |
Date: | 2009 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book presents the first systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces. This area has its classical roots in the beginning of the twentieth century and is now a very activeresearch area, having cl ose connections to harmonic analysis, complex analysis, integral geometry, and analysis on symmetric spaces. The main purpose of this book is the study of local aspects of spectral analysis and spectralsynthesis on Euclidean spaces, Riemannian symmetric s paces of an arbitrary rank and Heisenberg groups. The subject can be viewed as arising from three classical topics: John's support theorem, Schwartz's fundamental principle, andDelsarte's two-radii theorem. Highly topical, the book contains most of the si gnificant recent results in this area with complete and detailed proofs. In order to make this book accessible to a wide audience, the authors have includedan introductory section that develops analysis on symmetric spaces without the use of Lie theory. C hallenging open problems are described and explained, and promising new research directions are indicated. Designed for both experts andbeginners in the field, the book is rich in methods for a wide variety of problems in many areas of mathematics |
Note: | Springer eBooks |
ISBN: | 9781848825338 |
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 , Integral Transforms , Functions, special |
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Call number: | SPRINGER-2009-9780817646639:ONLINE Show nearby items on shelf |
Title: | Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics [electronic resource] |
Author(s): |
Claudio Bartocci Ugo Bruzzo Daniel Hernndez Ruiprez |
Date: | 2009 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry,category theory, gauge theory , and string theory has been closely related to generalizations of integral transforms of a more geometric character. FourierMukai and Nahm Transforms in Geometry and Mathematical Physics examines thealgebro-geometric approach (FourierMukai functors) as w ell as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organizedinto a monograph. Key features: * Basic constructions and definitions are presen ted in preliminary background chapters * Presentation explores applications and suggests several open questions * Extensive bibliography and index Thisself-contained monograph provides an introduction to current research in geometry and mathematical physi cs and is intended for graduate students and researchers just entering this field |
Note: | Springer eBooks |
Contents: | Integral functors |
Fourier | |
Mukai functors | |
Fourier | |
Mukai on Abelian varieties | |
Fourier | |
Mukai on K3 surfaces | |
Nahm transforms | |
Relative Fourier | |
Mukai functors | |
Fourier | |
Mukai partners and birational geometry | |
Derived and triangulated categories | |
Lattices | |
Miscellaneous results | |
Stability conditions for derived categories | |
ISBN: | 9780817646639 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v276 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial , Global differential geometry , Mathematical physics |
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Call number: | SPRINGER-2009-9780387981284:ONLINE Show nearby items on shelf |
Title: | Fractional Differentiation Inequalities [electronic resource] |
Author(s): |
George A Anastassiou |
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: | Fractional differentiation inequalities are by themselves an important area of research. They have many applications in pure and applied mathematics and many other applied sciences. One of the most important applications is inestablishing the uniquen ess of a solution in fractional differential equations and systems and in fractional partial differential equations. They also provide upper bounds to the solutions of the above equations. In this book theauthor presents the Opial, Poincar, Sobolev, Hilbe rt, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati,Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. E ach chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is alsoexamined. This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathema ticians, engineers, and other applied scientists will also find this book useful |
Note: | Springer eBooks |
Contents: | OpialType Inequalities for Functions and Their Ordinary and Canavati Fractional Derivatives |
Canavati Fractional OpialType Inequalities and Fractional Differential Equations | |
RiemannLiouville Opialtype Inequalities for Fractional Derivatives | |
Opialtype Inequalities for RiemannLiouville Fractional Derivatives | |
OpialType Inequalities Involving Canavati Fractional Derivatives of Two Functions and Applications | |
OpialType Inequalities for RiemannLiouville Fractional Derivatives of Two Functions with Applications | |
Canavati Fractional OpialType Inequalitie | |
ISBN: | 9780387981284 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Integral Transforms , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2009-9780387684178:ONLINE Show nearby items on shelf |
Title: | Inequalities for Differential Forms [electronic resource] |
Author(s): |
Ravi P Agarwal Shusen Ding Craig Nolder |
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: | During the recent years, differential forms have played an important role in many fields. In particular, the forms satisfying the A-harmonic equations, have found wide applications in fields such as general relativity, theory ofelasticity, quasiconfo rmal analysis, differential geometry, and nonlinear differential equations in domains on manifolds. This monograph is the first one to systematically present a series of local and global estimates and inequalitiesfor differential forms. The presentation c oncentrates on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator,and the gradient operator are also covered. Additionally, some r elated topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance ofbibliographical references and historical material supplement the text throughout. This rigo rous text requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluablereference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields |
Note: | Springer eBooks |
Contents: | HardyLittlewood inequalities |
Norm comparison theorems | |
Poincar | |
type inequalities | |
Caccioppoli inequalities | |
Imbedding theorems | |
Reverse Hlder inequalities | |
Inequalities for operators | |
Estimates for Jacobians | |
Lipschitz and norms | |
ISBN: | 9780387684178 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Integral Transforms , Operator theory , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2009-9780387095042:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods [electronic resource] : For Students of Physics and Related Fields |
Author(s): |
Sadri Hassani |
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: | Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid,and relevant examples fr om the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential andintegral calculus, the book continues with infi nite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Diracdelta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section onProbability and plenty of new material on tensors and integral transforms. Some praise for the p revious edition: The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often,the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of pa rticular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, adiscussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches li ke this are not isolated cases the book includes a large number of notes on people andideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities. --Physics Today Very well written (i.e., extremely read able), very well targeted (mainly to an average student ofphysics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's w |
Note: | Springer eBooks |
Contents: | Coordinates and Calculus |
Coordinate Systems and Vectors | |
Differentiation | |
Integration: Formalism | |
Integration: Applications | |
Dirac Delta Function | |
Algebra of Vectors | |
Planar and Spatial Vectors | |
Finite | |
Dimensional Vector Spaces | |
Vectors in Relativity | |
Infinite Series | |
Infinite Series | |
Application of Common Series | |
Integrals and Series as Functions | |
Analysis of Vectors | |
Vectors and Derivatives | |
Flux and Divergence | |
Line Integral and Curl | |
Applied Vector Analysis | |
Curvilinear Vector Analysis | |
Tensor Analysis | |
Complex Analysis | |
Complex Arithmetic | |
Co | |
ISBN: | 9780387095042 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2008-9788847008762:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis I [electronic resource] |
Author(s): |
Claudio Canuto Anita Tabacco |
Date: | 2008 |
Publisher: | Milano : Springer Milan |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organisedto appeal especially t o Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variableare presented in a manner that elicits criti cal reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices whenplanning an introductory lecture course. The book may in fact be e mployed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding keytechniques. Proofs to the main results befit the intermediate level, together with several remark s and complementary notes enhancing the treatise. The last, and farthest-reaching, level consists of links to online material, whichenable the strongly motivated reader to explore further into the subject. Definitions and properties are furnished with sub stantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least halfof which guide the reader to the solution |
Note: | Springer eBooks |
ISBN: | 9788847008762 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Integral equations , Integral Transforms , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2008-9784431732402:ONLINE Show nearby items on shelf |
Title: | Algebraic Analysis of Differential Equations [electronic resource] : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai |
Author(s): |
Takashi Aoki Hideyuki Majima Yoshitsugu Takei Nobuyuki Tose |
Date: | 2008 |
Publisher: | Tokyo : Springer Japan |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9784431732402 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral Transforms , Differential Equations , Differential equations, partial , Functions, special |
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Call number: | SPRINGER-2008-9783764387518:ONLINE Show nearby items on shelf |
Title: | Approximation of Additive Convolution-Like Operators [electronic resource] : Real C*-Algebra Approach |
Author(s): |
Victor D Didenko Bernd Silbermann |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation,double layer potential equ ation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The listof the methods considered includes spline Gale rkin, spline collocation, qualocation, and quadrature methods |
Note: | Springer eBooks |
Contents: | Preface |
1. Complex and Real Algebras | |
2. Integral Operators. Smooth Curves | |
3. Riemann | |
Hilbert Problem | |
4. Piecewise Smooth and Open Contours | |
5. Muskhelishvili Equation | |
6. Numerical Examples | |
Bibliography | |
ISBN: | 9783764387518 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Integral Transforms , Operator theory , Differential equations, partial , Numerical analysis |
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Call number: | SPRINGER-2008-9783764382728:ONLINE Show nearby items on shelf |
Title: | Holomorphic Functions in the Plane and n-dimensional Space [electronic resource] |
Author(s): |
Klaus Grlebeck Klaus Habetha Wolfgang Sprig |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-calledquaternionic and Clifford or h ypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensionalresults based on a uniform notion of holomorphy. Hi storical remarks, lots of examples, figures and exercises accompany each chapter |
Note: | Springer eBooks |
Contents: | Introduction |
I. Numbers | |
Complex Numbers | |
Quaternions | |
Clifford numbers | |
II. Functions | |
Topological Aspects | |
Holomorphic Functions | |
Power Functions and Mbius Transformations | |
III. Integration und Integral Theorems | |
Integral Theorems and | |
formulas | |
Teodorescu Transformation | |
IV. Series and Local Properties | |
Power Series | |
Orthogonal Series | |
Elementary Functions | |
Local Structure of Holomorphic Functions | |
Special Functions | |
Appendices | |
Bibliography | |
Index | |
ISBN: | 9783764382728 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functions of complex variables , Integral Transforms , Potential theory (Mathematics) |
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Call number: | SPRINGER-2008-9780817646790:ONLINE Show nearby items on shelf |
Title: | Geometric Integration Theory [electronic resource] |
Author(s): |
Steven Krantz Harold Parks |
Date: | 2008 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook introduces geometric measure theory through the notion of currents. Currentscontinuous linear functionals on spaces of differential formsare a natural language in which to formulate various types of extremalproblems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem,the area and coarea formulas, the compactness the orem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, andmany other parts of mathematics * Provides considerable background materi al for the student Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for use in the classroom andfor self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for graduate students and researchers |
Note: | Springer eBooks |
Contents: | Preface |
Basics | |
Carathodorys Construction and Lower | |
Dimensional Measures | |
Invariant Meaures and the Construction of Haar Meaure | |
Covering Theorems and the Differentiation of Integrals | |
Analytical Tools: the Area Formula, the Coarea Formula, and Poincar Inequalities | |
The Calculus of Differential Forms and Stokess Theorem | |
Introduction to Currents | |
Currents and the Calculus of Variations | |
Regularity of Mass | |
Minimizing Currents | |
Appendix | |
References | |
Index of Notation | |
Index | |
ISBN: | 9780817646790 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Integral Transforms , Geometry , Discrete groups , Global differential geometry |
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Call number: | SPRINGER-2007-9783540446972:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Engineers and Scientists 3 [electronic resource] : Fourier Analysis, Partial Differential Equations and Variational Methods |
Author(s): |
Kwong-Tin Tang |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis,integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problemsets with answers are used to enhance stu dents' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses |
Note: | Springer eBooks |
Contents: | 1. Fourier series |
2. Fourier transforms | |
3. Orthogonal functions and Sturm | |
Liouville problems | |
4. Bessel and Legendre functions | |
5. Partial differential equations in Cartesian coordinates | |
6. Partial differential equations with curved boundaries | |
7. Calculus of variation | |
ISBN: | 9783540446972 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Engineering mathematics |
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Call number: | SPRINGER-2007-9783540302742:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Engineers and Scientists 1 [electronic resource] : Complex Analysis, Determinants and Matrices |
Author(s): |
Kwong-Tin Tang |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis,integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problemsets with answers are used to enhance stu dents' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses |
Note: | Springer eBooks |
Contents: | Complex numbers |
Complex functions | |
Complex series and theory of resudues | |
Determinants | |
Matrix algebra | |
Eigenvalue problems of matrices | |
ISBN: | 9783540302742 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Engineering mathematics |
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Call number: | SPRINGER-2007-9783540302704:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Engineers and Scientists 2 [electronic resource] : Vector Analysis, Ordinary Differential Equations and Laplace Transforms |
Author(s): |
Kwong-Tin Tang |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis,integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problemsets with answers are used to enhance stu dents' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses |
Note: | Springer eBooks |
Contents: | 1. Vectors |
2. Vector calculus | |
3. Curved coordinates | |
4. Vector transformation and Cartesian Tensors | |
5. Ordinary dioeerential equations | |
6. Laplace transforms | |
ISBN: | 9783540302704 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Engineering mathematics |
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Call number: | SPRINGER-2007-9783211732656:ONLINE Show nearby items on shelf |
Title: | Maple and Mathematica [electronic resource] : A Problem Solving Approach for Mathematics |
Author(s): |
Inna Shingareva Carlos Lizrraga-Celaya |
Date: | 2007 |
Publisher: | Vienna : Springer Vienna |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book compares the two computer algebra programs, Maple and Mathematica used by students, mathematicians, scientists, and engineers. Structured by presenting both systems in parallel, Mathematicas users can learn Maplequickly by finding the Maple equivalent to Mathematica functions, and vice versa. This student reference handbook consists of core material for incorporating Maple and Mathematica as a working tool into different undergraduatemathematical courses (algebra, geometry, calculus, comple x functions, special functions, integral transforms, mathematical equations). Part I describes the foundations of Maple and Mathematica (with equivalent problems and solutions).Part II describes Mathematics with Maple and Mathematica by using equivalent p roblems |
Note: | Springer eBooks |
Contents: | From the contents: Preface |
Foundations of Maple and Mathematica: Maple Mathematica | |
Mathematics: Maple and Mathematica: Graphics Algebra Geometry Calculus Complex Functions Special Functions Integral and Discrete Transforms Mathematical Equations: | |
References | |
General Index | |
Maple Index | |
Mathematica Index | |
ISBN: | 9783211732656 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science Mathematics , Computer science , Computer software |
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Call number: | SPRINGER-2007-9780387688558:ONLINE Show nearby items on shelf |
Title: | Numerical Methods for Laplace Transform Inversion [electronic resource] |
Author(s): |
Alan M Cohen |
Date: | 2007 |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Operational methods have been used for over a century to solve many problemsfor example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be verydemanding to determine the inv erse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult toevaluate in order to get an answer at a particular time v alue. The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material onthe theory of Laplace transforms together with a comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplacetransforms. Audience This book is intended for engineers, scientists, mathematicians, statisticians and fina ncial planners |
Note: | Springer eBooks |
Contents: | Preface |
Acknowledgments | |
Notation | |
Basic Results | |
Inversion Formulae and Practical Results | |
The Method of Series Expansion | |
Quadrature Methods | |
Rational Approximation Methods | |
The Method of Talbot | |
Methods Based on the Post | |
Widder Inversion Formula | |
The Method of Regularization | |
Survey Results | |
Applications | |
Appendix | |
Index | |
ISBN: | 9780387688558 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Numerical Methods and Algorithms, 1571-5698 : v5 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral Transforms , Engineering mathematics |
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Call number: | SPRINGER-2006-9783764375751:ONLINE Show nearby items on shelf |
Title: | Symplectic Geometry and Quantum Mechanics [electronic resource] |
Author(s): |
Maurice Gosson |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a rigorous presentation of the basics of symplecticgeometry and of its mul tiply-oriented extension. Further chapters concentrate on Lagrangian manifolds, Weyl operators and the Wigner-Moyal transform as well as on metaplectic groups and Maslov indices. Thus the keys for themathematical description of quantum mechanics in phase space are discussed. They are followed by a rigorous geometrical treatment of the uncertainty principle. Then Hilbert-Schmidt and trace-class operators are exposed in order totreat density matrices. In the last chapter the Weyl pseudo-differential calculu s is extended to phase space in order to derive a Schrdinger equation in phase space whose solutions are related to those of the usual Schrdingerequation by a wave-packet transform. The text is essentially self-contained and can be used as basis for gradu ate courses. Many topics are of genuine interest for pure mathematicians working in geometry and topology |
Note: | Springer eBooks |
Contents: | Preface |
Notation | |
I. Symplectic Geometry | |
1. Symplectic Spaces and Lagrangian Planes | |
2. The Symplectic Group | |
3. Multi | |
Oriented Symplectic Geometry | |
4. Intersection Indices | |
II. Heisenberg Group, Weyl Calculus, and Metaplectic Representation | |
5. Lagrangian Manifolds and Quantization | |
6. Heisenberg Group and Weyl Operators | |
7. The Metaplectic Group | |
III. Quantum Mechanics in Phase Space | |
8. The Uncertainty Principle | |
9. The Density Operator | |
10. A Phase Space Weyl Calculus | |
Appendices | |
Bibliography | |
Index | |
ISBN: | 9783764375751 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v166 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Integral Transforms , Operator theory , Differential equations, partial , Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2006-9783764375140:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators and Related Topics [electronic resource] |
Author(s): |
Paolo Boggiatto Luigi Rodino Joachim Toft M. W Wong |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume consists of sixteen peer-reviewed articles based on the invited talks at the International Conference on Pseudo-Differential Operators and Related Topics held at Vxj University in Sweden from June 22 to June 25,2004. The objective is to l ook at pseudo-differential operators and related topics and to report recent advances in a broad spectrum of topics such as partial differential equations, quantization, Wigner transforms, Weyl transforms onLie groups, mathematical physics, time-frequency analysis, frames, and stochastic processes. The book should be of great interest to graduate students and researchers in analysis, mathematical physics and mathematical sciences. It is avaluable complement to the volume Advances in Pseudo-Differential Op erators published in the same series in 2004 |
Note: | Springer eBooks |
ISBN: | 9783764375140 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v164 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2006-9783764374532:ONLINE Show nearby items on shelf |
Title: | Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems [electronic resource] |
Author(s): |
Karl-Heinz Frster Peter Jonas Heinz Langer |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume contains 16 original research papers written by participants of the 3rd Workshop on Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems, which was held at the Technische Universitt Berlin, Germany,December 1214, 2003. They d eal with spectral and perturbation theory of linear operators in indefinite inner product spaces and their applications. The topics include extension theory of symmetric operators, normal operators,realization theory and models of generalized Nevanlinna f unctions, interpolation problems, reproducing kernel spaces, matrix and operator pencils, locally definitizable functions, and semigroups |
Note: | Springer eBooks |
ISBN: | 9783764374532 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v162 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Integral Transforms , Operator theory , Mathematical physics |
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Call number: | SPRINGER-2006-9780387288154:ONLINE Show nearby items on shelf |
Title: | The Mathematica GuideBook for Symbolics [electronic resource] |
Author(s): |
Michael Trott |
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: | Mathematica is today's most advanced technical computing system. It features a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematicalfunctions using state-of- the-art algorithms. Combined with a user-friendly interface, and a complete mathematical typesetting system, Mathematica offers an intuitive easy-to-handle environment of great power and utility. TheMathematica GuideBook for Symbolics (code and text fully tailored for Mathematica 5.1) deals with Mathematica's symbolic mathematical capabilities. Structural and mathematical operations on single and systems of polynomials arefundamental to many symbolic calculations and they are covered in considerable detai l. The solution of equations and differential equations, as well as the classical calculus operations (differentiation, integration, summation, seriesexpansion, limits) are exhaustively treated. Generalized functions and their uses are discussed. In addit ion, this volume discusses and employs the classical orthogonal polynomials and special functions of mathematical physics. Todemonstrate the symbolic mathematics power, a large variety of problems from mathematics and phyics are discussed |
Note: | Springer eBooks |
Contents: | Introduction and Orientation |
I. Symbolic computations: Remarks | |
Manipulation of polynomials | |
Manipulations of rational functions of polynomials | |
Manipulations of trigonometric expressions | |
Systems of linear and nonlinear equations | |
Classical analysis | |
Differential equations | |
Integral transforms and generalized functions | |
Three applications | |
Overview | |
II Classical orthogonal polynomials: Remarks | |
General properties of orthogonal polynomials | |
Hermite polynomials | |
Jacobi polynomials | |
Gegenbauer polynomials | |
Laguerre polynomials | |
Legendre polynomials | |
Chebyshev | |
ISBN: | 9780387288154 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra Data processing , Algorithms , Computer science , Computer software |
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Call number: | SPRINGER-2005-9782287281990:ONLINE Show nearby items on shelf |
Title: | Introduction aux mthodes numriques [electronic resource] |
Author(s): |
Franck Jedrzejewski |
Date: | 2005 |
Edition: | Deuxime dition |
Publisher: | Paris : Springer Paris |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Au cours de lhistoire, les mthodes de calcul ont t lexpression de pratiques sans cesse renouveles. Le dveloppement de linformatique a largement contribu une rapide progression de lensemble destechniques numriques. En moins de cinquante ans, le paysa ge algorithmique a t compltement transform. Aujourdhui, la plupart des logiciels que nous employons font appel des mthodes de plus en plus efficaces. Dans lessimulations, comme dans les modlisations, lanalyse numrique occupe une place centrale. Composant s essentiels de la vie scientifique, les mthodes et algorithmes qui sont prsents ici, illustrs par de nombreux exemples,sont mis la porte de tous. De lapproximation polynomiale la rsolution dquations aux drives partielles par des mthodes de diffrences, de volumes et dlments finis, ce livre offre un large panorama desmthodes numriques actuelles. Il sappuie sur une exprience dune dizaine dannes denseignement et sadresse un public trs vari: tudiants en sciences, lves dcoles dingnieur ou de classesprparato ires qui souhaiteraient acqurir rapidement les bases des mthodes numriques. Cette seconde dition offre des complments danalyse matricielle et un nouveau chapitre sur les quations de la physique mathmatique,qui sont au cur des proccupations daujourdhui |
Note: | Springer eBooks |
Contents: | Problmes numriques |
Approximation et interpolation | |
Rsolution dquations | |
Intgration numrique | |
Systmes linaires | |
Valeurs et vecteurs propres | |
quations et systmes dquations diffrentielles | |
quations aux drives partielles | |
quations elliptiques | |
quations paraboliques | |
quations hyperboliques | |
Mthode des lments finis | |
quations de physique | |
ISBN: | 9782287281990 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Fourier analysis , Functional analysis , Integral Transforms , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2005-9781846281204:ONLINE Show nearby items on shelf |
Title: | Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes [electronic resource] |
Author(s): |
Igor Chudinovich Christian Constanda |
Date: | 2005 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematicalinvestigation of the model , which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potentialrepresentations, and the solution of the latter in Sobolev sp aces. The analysis, performed in spaces of distributions, is applicable to a wide variety of data with less smoothness than that required in the corresponding classicalproblems, and is very useful for constructing error estimates in numerical computations . The presentation is detailed and clear, yet reasonably concise. This illustrative model was chosen because of its practical importance and someunusual mathematical features, but the solution technique developed in the book can easily be adapted to many other hyperbolic systems of partial differential equations arising in continuum mechanics |
Note: | Springer eBooks |
Contents: | Formulation of the Problems and their Nonstationary Boundary Integral Equations |
Problems with Dirichlet Boundary Conditions | |
Problems with Neumann Boundary Conditions | |
Boundary Integral Equations for Problems with Dirichlet and Neumann Boundary Conditions | |
Transmission Problems and Multiply Connected Plates | |
Plate Weakened by a Crack | |
Initial | |
Boundary Value Problems with Other Types of Boundary Conditions | |
Plate on a Generalized Elastic Foundation | |
Problems with Nonhomogeneous Equations and Nonhomogeneous Initial Conditions | |
Appendix A: The Fourier and Laplace Transforms of | |
ISBN: | 9781846281204 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Integral equations , Materials |
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Call number: | SPRINGER-2005-9780817644277:ONLINE Show nearby items on shelf |
Title: | Computer Algebra Recipes for Mathematical Physics [electronic resource] |
Author(s): |
Richard H Enns |
Date: | 2005 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Over two hundred novel and innovative computer algebra worksheets or recipes will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in theirmathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditionalmathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computeralgebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed the relevant MAPLE commands are introduced on aneed-to-know basis * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is u sed, accompanied with amusing or thought-provoking quotations This is a self-contained and standalone text, similarin style and format to Computer Algebra Recipes: A Gourmet's Guide to Mathematical Models of Science (ISBN 0-387-95148-2), Springer New York 2001 and Computer Algebra Recipes for Classical Mechanics (ISBN 0-8176-4291-9), Birkhuser2003. Computer Algebra Recipes for Mathematical Physics may be used in the classroom, for self-study, as a reference, or as a text for an online course |
Note: | Springer eBooks |
Contents: | The Appetizers |
Linear ODEs of Physics | |
Applications of Series | |
Vectors and Matrices | |
The Entrees | |
Linear PDEs of Physics | |
Complex Variables | |
Integral Transforms | |
Calculus of Variations | |
The Desserts | |
NLODEs & PDEs of Physics | |
Numerical Methods | |
ISBN: | 9780817644277 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Computer software , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2005-9780387242330:ONLINE Show nearby items on shelf |
Title: | Theory and Applications of Special Functions [electronic resource] : A Volume Dedicated to Mizan Rahman |
Author(s): |
Mourad E.H Ismail Erik Koelink |
Date: | 2005 |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. Also, it includes an article by Askey, Ismail, and Koelink on Rahmans mathematicalcontributions and how they influenced the recent upsurge in the subject. Audience This book is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups, and integrable systems |
Note: | Springer eBooks |
Contents: | Preface |
Dedication | |
Mizan Rahman, His Mathematics and Literary Writings | |
q | |
Bessel Functions | |
a | |
Gaussian Polynomials | |
On a Generalized Gamma Convolution Related to the q | |
Calculus | |
Ramanujan and Cranks | |
The Saalschtz Chain Reactions and Multiple q | |
Series Transformations | |
Painlev Equations and Associated Polynomials | |
Zeta Functions of Heisenberg Graphs over Finite Rings | |
q | |
Analogues of Some Multivariable Biorthogonal Polynomials | |
Multivariable Askey | |
Wilson Polynomials | |
Continuous Hahn Functions | |
Series and Integrals | |
Little q | |
Jacobi Functions | |
A Second Addition | |
ISBN: | 9780387242330 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, 1389-2177 : v13 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral Transforms , Functions, special |
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Call number: | SPRINGER-2004-9783764378042:ONLINE Show nearby items on shelf |
Title: | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
Author(s): |
Rolf Sören Krausshar |
Date: | 2004 |
Size: | 1 online resource (168 p.) |
Note: | 10.1007/b95203 |
Contents: | Introduction -- 1. Function Theory in Hypercomplex Spaces -- 2. Clifford-analytic Eisenstein Series Associated to Translation Groups -- 3. Clifford-analytic Modular Forms -- Bibliography -- Index |
ISBN: | 9783764378042 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Integral transforms , Operational calculus , Potential theory (Mathematics) , Sequences (Mathematics) , Special functions , Number theory , Mathematics , Special Functions , Integral Transforms, Operational Calculus , Potential Theory , Sequences, Series, Summability , Number Theory |
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Call number: | SPRINGER-2004-9783662102251:ONLINE Show nearby items on shelf |
Title: | Tauberian Theory A Century of Developments |
Author(s): |
Jacob Korevaar |
Date: | 2004 |
Size: | 1 online resource (483 p.) |
Note: | 10.1007/978-3-662-10225-1 |
Contents: | I The Hardy—Littlewood Theorems -- II Wiener’s Theory -- III Complex Tauberian Theorems -- IV Karamata’s Heritage: Regular Variation -- V Extensions of the Classical Theory -- VI Borel Summability and General Circle Methods -- VII |
Tauberian Remainder Theory -- References | |
ISBN: | 9783662102251 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 329 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Approximation theory , Fourier analysis , Integral transforms , Operational calculus , Sequences (Mathematics) , Number theory , Mathematics , Analysis , Sequences, Series, Summability , Approximations and Expansions , Fourier Analysis , Integral Transforms, Operational Calculus , Number Theory |
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