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SPIRES-BOOKS: FIND KEYWORD FUNCTIONS OF A COMPLEX VARIABLE *END*INIT* use /tmp/qspiwww.webspi1/12636.77 QRY 131.225.70.96 . find keyword functions of a complex variable ( in books using www Cover
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Call number:SPRINGER-2016-9783319338774:ONLINE Show nearby items on shelf
Title:Spectral Theory of Infinite-Area Hyperbolic Surfaces
Author(s): David Borthwick
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (37 p.)
Note:10.1007/978-3-319-33877-4
Contents:Introduction -- Hyperbolic Surfaces -- Selberg Theory for Finite-Area Hyperbolic Surfaces -- Spectral Theory for the Hyperbolic Plane -- Model Resolvents for Cylinders -- The Resolvent -- Spectral and Scattering Theory -- Resonances and Scattering Poles -- Growth Estimates and Resonance Bounds -- Selberg Zeta Function -- Wave Trace and Poisson Formula -- Resonance Asymptotics -- Inverse Spectral Geometry -- Patterson-Sullivan Theory -- Dynamical Approach to the Zeta Function -- Numerical Computatio ns -- Appendix -- References -- Notation Guide -- Index
ISBN:9783319338774
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 318
Keywords: Mathematics , Functional analysis , Functions of complex variables , Partial differential equations , Hyperbolic geometry , Physics , Mathematics , Functional Analysis , Partial Differential Equations , Functions of a Complex Variable , Hyperbolic Geometry , Mathematical Methods in Physics
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Call number:SPRINGER-2016-9783319290003:ONLINE Show nearby items on shelf
Title:Divergent Series, Summability and Resurgence III Resurgent Methods and the First Painlevé Equation
Author(s): Eric Delabaere
Date:2016
Size:1 online resource (14 p.)
Note:10.1007/978-3-319-29000-3
Contents:Avant-Propos -- Preface to the three volumes -- Preface to this volume -- Some elements about ordinary differential equations -- The first Painlevé equation -- Tritruncated solutions for the first Painlevé equation -- A step beyond Borel-Laplace summability -- Transseries and formal integral for the first Painlevé equation -- Truncated solutions for the first Painlevé equation -- Supplements to resurgence theory -- Resurgent structure for the first Painlevé equation -- Index
ISBN:9783319290003
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2155
Keywords: Mathematics , Functions of complex variables , Differential equations , Sequences (Mathematics) , Special functions , Mathematics , Sequences, Series, Summability , Ordinary Differential Equations , Functions of a Complex Variable , Special Functions
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Call number:SPRINGER-2016-9783319263090:ONLINE Show nearby items on shelf
Title:Boundary Integral Equation Methods and Numerical Solutions Thin Plates on an Elastic Foundation
Author(s): Christian Constanda
Date:2016
Edition:1st ed. 2016
Size:1 online resource (196 p.)
Note:10.1007/978-3-319-26309-0
Contents:Preface -- 1. The Mathematical Model -- 2. The Layer Potentials -- 3. Existence of Solutions -- 4. Software Development -- 5. Computational Examples -- References -- Index
ISBN:9783319263090
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Developments in Mathematics: 35
Keywords: Mathematics , Functions of complex variables , Integral equations , Partial differential equations , Mathematics , Integral Equations , Partial Differential Equations , Functions of a Complex Variable
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Call number:SPRINGER-2016-9783319247113:ONLINE Show nearby items on shelf
Title:Dessins d'Enfants on Riemann Surfaces
Author(s): Gareth A Jones
Date:2016
Edition:1st ed. 2016
Size:1 online resource (259 p.)
Note:10.1007/978-3-319-24711-3
Contents:Historical and introductory background -- Graph embeddings -- Dessins and triangle groups -- Galois actions -- Quasiplatonic surfaces, and automorphisms -- Regular maps -- Regular embeddings of complete graphs -- Wilson operations -- Further exampl es -- Arithmetic aspects -- Beauville surfaces
ISBN:9783319247113
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebraic geometry , Group theory , Functions of complex variables , Hyperbolic geometry , Mathematics , Algebraic Geometry , Group Theory and Generalizations , Functions of a Complex Variable , Several Complex Variables and Analytic Spaces , Hyperbolic Geometry
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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-2014-9781461488279:ONLINE Show nearby items on shelf
Title:A Qualitative Approach to Inverse Scattering Theory [electronic resource]
Author(s): Fioralba Cakoni
David Colton
Date:2014
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
Note:Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms forsolving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to theinverse scattering problem which avoids the inc orrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques.These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties withoutmaking any weak scattering assumption and using essentially no a priori information on the nat ure of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on theuse of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posedproblems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an ear lier book by the authors published by Springer titled Qualitative Methods in InverseScattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized andeasy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to
Contents:1. Functional Analysis and Sobolev Spaces
2. Ill
Posed Problems
3. Scattering by Imperfect Conductors
4. Inverse Scattering Problems for Imperfect Conductors
5. Scattering by Orthotropic Media
6. Inverse Scattering Problems for Orthotropic Media
7. Factorization Methods
8. Mixed Boundary Value Problems
9. Inverse Spectral Problems for Transmission Eigenvalues
10. A Glimpse at Maxwell's Equations
ISBN:9781461488279
Series:eBooks
Series:SpringerLink
Series:Applied Mathematical Sciences, 0066-5452 : v188
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential equations, partial , Computer engineering
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Call number:SPRINGER-2014-9781461479468:ONLINE Show nearby items on shelf
Title:Calculus With Applications [electronic resource]
Author(s): Peter D Lax
Maria Shea Terrell
Date:2014
Edition:2nd ed. 2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physicalsciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings theinnovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is morenatural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers andcomplex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an intro duction to probability and information theory
Contents:1 Numbers and Limits
2 Functions and Continuity
3 The Derivative and Differentiation
4 The Theory of Differentiable Functions
5 Applications of the Derivative
6 Integration
7 Methods for Integration
8 Approximation of Integrals
9 Complex Numbers
10 Differential Equations
11 Probability
Answers to Selected Problems
Index
ISBN:9781461479468
Series:eBooks
Series:SpringerLink
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2014-9781447164340:ONLINE Show nearby items on shelf
Title:Mathematical Methods for Elastic Plates [electronic resource]
Author(s): Christian Constanda
Date:2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers andaircraft. This book emplo ys two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process ofbending than Kirchhoffs classical one. The fi rst method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on thebasis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hlder continuous and Hlder continuously differentiable) functions. The second technique rewrites the differential system in terms ofcomplex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system,which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. Thepresentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students wit h a basic knowledge of advanced calculus
Contents:Singular Kernels
Potentials and Boundary Integral Equations
Bending of Elastic Plates
The Layer Potentials
The Newtonian Potential
Existence of Regular Solutions
Complex Variable Treatment
Generalized Fourier Series
ISBN:9781447164340
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Integral equations , Materials
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Call number:SPRINGER-2013-9789491216862:ONLINE Show nearby items on shelf
Title:Single Variable Differential and Integral Calculus [electronic resource] : Mathematical Analysis
Author(s): Elimhan Mahmudov
Date:2013
Publisher:Paris : Atlantis Press : Imprint: Atlantis Press
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book Single variable Differential and Integral Calculus is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book isunique in the field of mathemat ical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important businessfields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequencesof functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems andexamples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Sti eltjes and Lebesque integrals are studied together and compared
Note:Springer eBooks
Contents:Introduction to Numbers and Set Theory
Sequences and Series
Limits and Continuity of Functions
Differential Calculus
Some Basic Properties of Differentiable Functions
Polynomials and Interpolations
Applications of Differential Calculus to Limit Calculations and Extremum Problems
The Indefinite Integral
The Definite Integral
Applications of the Definite Integral
ISBN:9789491216862
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations
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Call number:SPRINGER-2013-9783642338717:ONLINE Show nearby items on shelf
Title:Regular Functions of a Quaternionic Variable [electronic resource]
Author(s): Graziano Gentili
Caterina Stoppato
Daniele C Struppa
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the internationalresearch community. At the same time, the theory has already developed sturdy foundations. The richness of the theory of the holomorphic functions of one complex variable and its wide variety of applications are a strong motivation forthe study of its analogs in higher dimensi ons. In this respect, the four-dimensional case is particularly interesting due to its relevance in physics and its algebraic properties, as the quaternion forms the only associative realdivision algebra with a finite dimension n>2. Among other interestin g function theories introduced in the quaternionic setting, that of (slice) regular functions shows particularly appealing features. For instance, this class offunctions naturally includes polynomials and power series. The zero set of a slice regular func tion has an interesting structure, strictly linked to a multiplicative operation, and it allows the study of singularities. Integralrepresentation formulas enrich the theory and they are a fundamental tool for one of the applications, the construction of a noncommutative functional calculus. The volume presents a state-of-the-art survey of the theory and a briefoverview of its generalizations and applications. It is intended for graduate students and researchers in complex or hypercomplex analysis and geo metry, function theory, and functional analysis in general
Note:Springer eBooks
Contents:Introduction
1.Definitions and Basic Results
2.Regular Power Series
3.Zeros
4.Infinite Products
5.Singularities
6.Integral Representations
7.Maximum Modulus Theorem and Applications
8.Spherical Series and Differential
9.Fractional Transformations and the Unit Ball
10.Generalizations and Applications
Bibliography
Index
ISBN:9783642338717
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Functions of complex variables , Sequences (Mathematics)
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Call number:SPRINGER-2013-9783642275555:ONLINE Show nearby items on shelf
Title:Differential-Algebraic Equations: A Projector Based Analysis [electronic resource]
Author(s): Ren Lamour
Roswitha Mrz
Caren Tischendorf
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In thisrelatively short tim e, DAEs have become a widely acknowledged tool to model processes subjected to certain constraints in order to simulate and to control processes in various application fields such as network simulation, chemicalkinematics, mechanical engineering and syste ms biology. DAEs and their more abstract versions in infinite dimensional spaces comprise a great potential forthe future mathematical modeling of complex coupled processes. The purpose ofthe book is to expose the impressive complexity of general DAEs fro m an analytical point of view, to describe the state of the art as well as open problems andin sodoing to motivate further researchof this versatile,extraordinary topic from a broader mathematical perspective. The book elaborates on a new general, structu ral analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of specialprojector functions. Some issues on numerical integration and computational aspects are also treated in this context
Note:Springer eBooks
Contents:Notations
Introduction
Part I. Projector based approach
1 Linear constant coefficient DAEs
.2 Linear DAEs with variable coefficients
3 Nonlinear DAEs
Part II. Index
1 DAEs: Analysis and numerical treatment
4 Analysis
5 Numerical integration
6 Stability issues
Part III. Computational aspects
7 Computational linear algebra aspects
8 Aspects of the numerical treatment of higher index DAEs
Part IV. Advanced topics
9 Quasi
regular DAEs
10 Nonregular DAEs
11 Minimization with constraints described by DAEs
12 Abstract differential algebraic equations
ISBN:9783642275555
Series:e-books
Series:SpringerLink (Online service)
Series:Differential-Algebraic Equations Forum
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Computer science Mathematics
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Call number:SPRINGER-2013-9783034806367:ONLINE Show nearby items on shelf
Title:Introduction to Mathematical Analysis [electronic resource]
Author(s): Igor Kriz
Ale Pultr
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 begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus anddifferential equations. Af ter having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differentialgeometry and even functional analysis. Overall, this t ext provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today
Note:Springer eBooks
Contents:Preface
Introduction
Part 1. A Rigorous Approach to Advanced Calculus
1. Preliminaries
2. Metric and Topological Spaces I
3. Multivariable Differential Calculus
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration
6. Systems of Ordinary Differential Equations
7. System of Linear Differential Equations
8. Line Integrals and Green's Theorem
Part 2. Analysis and Geometry
9. An Introduction to Complex Analysis
10. Metric and Top
ISBN:9783034806367
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Functions of complex variables , Differential Equations , Sequences (Mathematics)
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Call number:SPRINGER-2013-9781441973238:ONLINE Show nearby items on shelf
Title:Complex Analysis [electronic resource] : In the Spirit of Lipman Bers
Author(s): Rub E Rodrguez
Irwin Kra
Jane P Gilman
Date:2013
Edition:2nd ed. 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:This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas ofmathematics, including the theor y of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects inmathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers. The book covers most, if not all, of the material contained in Lipman Berss courses on first yearcomplex analysis. In addition, topics of current interest, such as zeros of holom orphic functions and the connection between hyperbolic geometry and complex analysis, are explored. In addition to many new exercises, this second editionintroduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains necessary and sufficient conditions for the existence of abounded analytic function on the disc with prescribed zeros sections on subharmonic functions and Perron's principle and a se ction on the ring of holomorphic functions on a plane domain. There are three new appendices: the first isa contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the t hird appendix includes an alternate approach to the Cauchy theory
Note:Springer eBooks
Contents:Preface to Second Edition
Preface to First Edition
Standard Notation and Commonly Used Symbols
1 The Fundamental Theorem in Complex Function Theory
2 Foundations
3 Power Series
4 The Cauchy Theory
A Fundamental Theorem
5 The Cauchy Theory
Key Consequences
6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions
7 Sequences and Series of Holomorphic Functions
8 Conformal Equivalence and Hyperbolic Geometry
9 Harmonic Functions
10 Zeros of Holomorphic Functions
Bibliographical Notes
Bibliography
Index
ISBN:9781441973238
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v245
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables
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Call number:SPRINGER-2012-9783642293023:ONLINE Show nearby items on shelf
Title:Modular Forms with Integral and Half-Integral Weights [electronic resource]
Author(s): Xueli Wang
Dingyi Pei
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:Modular Forms with Integral and Half-Integral Weights focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series.It is a fundamental proble m to construct a basis of the orthogonal complement of the space of cusp forms as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that theconclusion holds true for weight 3/2 by explicit ly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. Thebook provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers andpractitioners in modular forms of mathematics. Dr. Xueli Wang is a Professor at South China No rmal University, China. Dingyi Pei is a Professor at Guangzhou University, China
Note:Springer eBooks
Contents:Theta Functions and Their Transformation Formulae
Eisenstein Series
The Modular Group and Its Subgroups
Modular Forms with Integral Weight or Half
integral Weight
Operators on the Space of Modular Forms
New Forms and Old Forms
Construction of Eisenstein Series
Weil Representation and Shimura Lifting
Trace Formula
Integers Represented by Positive Definite Quadratic Forms
ISBN:9783642293023
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Number theory
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Call number:SPRINGER-2012-9783034802215:ONLINE Show nearby items on shelf
Title:A Panorama of Modern Operator Theory and Related Topics [electronic resource] The Israel Gohberg Memorial Volume
Author(s): Harry Dym
Marinus A Kaashoek
Peter Lancaster
Heinz Langer
Leonid Lerer
Date:2012
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is dedicated to the memory of Israel Gohberg (19282009) one of the great mathematicians of our time who inspired innumerable fellow mathematicians and directed many students. The volume reflects the widespectrum of Gohbergs mathematical i nterests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single andmultivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structuredmatrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory
Note:Springer eBooks
ISBN:9783034802215
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v218
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Functional analysis , Operator theory , Differential equations, partial , Systems theory
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Call number:SPRINGER-2012-9783034801805:ONLINE Show nearby items on shelf
Title:Visual Complex Functions [electronic resource] : An Introduction with Phase Portraits
Author(s): Elias Wegert
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations so-called phase portraits which visualize functions as images ontheir domains. Reading Visua l Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course oncomplex analysis. With separate chapters on variou s construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline,running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endowindividual faces to analytic functions. Phase portraits enhance the intuitive understanding of conc epts in complex analysis and are expected to be useful tools for anybody working with special functions even experienced researchersmay be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion t o other texts or as a reference work for advanced readers who wish to know more about phase portraits
Note:Springer eBooks
Contents:Preface
1. Getting Acquainted
2. Complex Functions
3. Analytic Functions
4. Complex Calculus
5. Construction Principles
6. Conformal Mappings
7. Riemann Surfaces
ISBN:9783034801805
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Functions, special
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Call number:SPRINGER-2011-9783642205545:ONLINE Show nearby items on shelf
Title:Complex Analysis 2 [electronic resource] : Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions
Author(s): Eberhard Freitag
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Rochtheorem, Abel's theorem a nd Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the bookprovides an introduction into the theory of high er modular functions
Note:Springer eBooks
Contents:Chapter I. Riemann Surfaces
Chapter II. Harmonic Functions on Riemann Surfaces
Chapter III. Uniformization
Chapter IV. Compact Riemann Surfaces
Appendices to Chapter IV
Chapter V. Analytic Functions of Several Complex Variables
Chapter V. Analytic Functions of Several Complex Variable
Chapter VI. Abelian Functions
Chapter VII. Modular Forms of Several Variables
Chapter VIII. Appendix: Algebraic Tools
References
Index
ISBN:9783642205545
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Differential equations, partial
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Call number:SPRINGER-2011-9783642201929:ONLINE Show nearby items on shelf
Title:Statistics for High-Dimensional Data [electronic resource] : Methods, Theory and Applications
Author(s): Peter Bhlmann
Sara van de Geer
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso andversions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory onhigh-dimensional statistics combined with methodolo gy, algorithms and illustrations with real data examples. This in-depth approach highlights the methods great potential and practical applicability in a variety of settings. Assuch, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science
Note:Springer eBooks
Contents:Introduction
Lasso for linear models
Generalized linear models and the Lasso
The group Lasso
Additive models and many smooth univariate functions
Theory for the Lasso
Variable selection with the Lasso
Theory for l1/l2
penalty procedures
Non
convex loss functions and l1
regularization
Stable solutions
P
values for linear models and beyond
Boosting and greedy algorithms
Graphical modeling
Probability and moment inequalities
Author Index
Index
References
Problems at the end of each chapter
ISBN:9783642201929
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Series in Statistics, 0172-7397
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics , Computer science , Mathematical statistics
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Call number:SPRINGER-2011-9783034800785:ONLINE Show nearby items on shelf
Title:A Complex Analysis Problem Book [electronic resource]
Author(s): Daniel Alpay
Date:2011
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applicationsandaspects of the theory of analytic functions not always touchedupon in a first course. Usi ng appropriate exercisesshowthe students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, therealization of rational functions and its connections t o the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and theFock space) are given. The book also includes apart where relevant facts from topology, functional analysis and Lebesgue integration are reviewed
Note:Springer eBooks
Contents:Prologue
I Complex numbers
1 Complex numbers: algebra
2 Complex numbers: geometry
3 Complex numbers and analysis
4. Remarks and generalizations: quaternions, etc
II Functions of a complex variable
5 C
differentiable functions
6 Cauchy's theorem
7 First applications
8 Laurent expansions and applications
9 Computations of definite integrals
10 Harmonic functions
11 Conformal mappings
III Complements
12 Some useful theorems
13 Some topology
References
Index
ISBN:9783034800785
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables
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Call number:SPRINGER-2011-9780857296030:ONLINE Show nearby items on shelf
Title:Singularities of integrals [electronic resource] : Homology, hyperfunctions and microlocal analysis
Author(s): Frdric Pham
Date:2011
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Bringing together two fundamental texts from Frdric Phams research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Usingnotions developed by J. Leray i n the calculus of residues in several variables and R. Thoms isotopy theorems, Frdric Phams foundational study of the singularities of integrals lies at the interface between analysis andalgebraic geometry, culminating in the Picard-Lefschetz formulae. Th ese mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from thepoint of view of hyperfunction theory and microlocal analysis. Providing a must-have introduc tion to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. Thisbook will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frdr ic Pham, now retired, was Professor at the University of Nice. He has published several educational and researchtexts. His recent work concerns semi-classical analysis and resurgent functions
Note:Springer eBooks
Contents:Differentiable manifolds
Homology and cohomology of manifolds
Lerays theory of residues
Thoms isotopy theorem
Ramification around Landau varieties
Analyticity of an integral depending on a parameter
Ramification of an integral whose integrand is itself ramified
Functions of a complex variable in the Nilsson class
Functions in the Nilsson class on a complex analytic manifold
Analyticity of integrals depending on parameters
Sketch of a proof of Nilssons theorem
Examples: how to analyze integrals with singular integrands
Hyperfunctions in one variable,
ISBN:9780857296030
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Differential equations, partial
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Call number:SPRINGER-2011-9780857290304:ONLINE Show nearby items on shelf
Title:Holomorphic Function Theory in Several Variables [electronic resource] : An Introduction
Author(s): Christine Laurent-Thibaut
Date:2011
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques toseveral variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Threeappendices on differential manifolds, sheaf theory a nd functional analysis make the book self-contained. Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. Newconcepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter. Clear and succinct, this book will appeal to post-graduate students, young researchersseeking an introduction to holomorphic function theory in several variables and lecturers seeking a conci se book on the subject
Note:Springer eBooks
Contents:Elementary local properties of holomorphic functions of several complex variables
Currents and complex structures
The Bochner
Martinelli
Koppelman kernel and formula applications
Extensions of CR functions
Extensions of holomorphic and CR functions on manifolds
Domains of holomorphy and pseudoconvexity
The Levi problem and the resolution of in strictly pseudoconvex domains
Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary
Appendices
ISBN:9780857290304
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial
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Call number:SPRINGER-2010-9781441972880:ONLINE Show nearby items on shelf
Title:Complex Analysis [electronic resource]
Author(s): Joseph Bak
Donald J Newman
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:This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, thetext focuses on the au thentic complex-variable ideas and techniques. Notable additions to Complex Analysis, Third Edition, include: The solution of the cubic equation and Newtons method for approximating the zeroes of anypolynomial Expanded treatments of the Schwarz reflecti on principle and of the mapping properties of analytic functions on closed domains An introduction to Schwarz-Christoffel transformations and to Dirichlet series Astreamlined proof of the prime number theorem, and more. Accessible to students at their e arly stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical resultsand introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis,and a solid understanding of its wide applicability
Note:Springer eBooks
Contents:Preface
The Complex Numbers
Functions of the Complex Variable z
Analytic Functions
Line Integrals and Entire Functions
Properties of Entire Functions
Properties of Analytic Functions
Further Properties of Analytic Functions 8. Simply Connected Domains
Isolated Sigularities of an Analytic Function
The Residue Theorem
Applications of The Residue Theorem to the Evaluation of Integrals Sums
Further Contour Integral Techniques
Introduction to Conformal Mapping
The Riemann Mapping Theorem
Maximum
Modulus Theorems for Unbounded Domains
Harmonic Functions
ISBN:9781441972880
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056 : v0
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2010-9781441965813:ONLINE Show nearby items on shelf
Title:Principles of Discontinuous Dynamical Systems [electronic resource]
Author(s): Marat Akhmet
Date:2010
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:Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are anongoing topic of inte rest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whosesolutions have prescribed moments of impu lses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progressessystematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last twochapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems
Note:Springer eBooks
Contents:Description of the System with Fixed Moments of Impulses and Its Solutions
Stability and Periodic Solutions of Systems with Fixed Moments of Impulses
Basics of Linear Systems
Nonautonomous Systems with Variable Moments of Impulses
Differentiability Properties of Nonautonomous Systems
Periodic Solutions of Nonlinear Systems
Discontinuous Dynamical Systems
Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle
Chaos and Shadowing
ISBN:9781441965813
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2009-9783034601269:ONLINE Show nearby items on shelf
Title:Holomorphic Operator Functions of One Variable and Applications [electronic resource] : Methods from Complex Analysis in Several Variables
Author(s): Israel Gohberg
Jrgen Leiterer
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. It is based on methods and technics of complex analysis of severalvariables. The first part o f the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. In the second part, which is the main part of the theory,results are obtained by methods and tools adapted f rom complex analysis of functions of several variables. We have in mind the theory of holomorphic cocycles (fiber bundles) with values in infinite-dimensional non-commutative groups.As a rule, these results do not appear in traditional complex analysis of one variable, not even for matrix valued cocycles. The third part consists of applications to operator theory. Here applications are presented for holomorphicfamilies of subspaces and Plemelj-Muschelishvili factorization. The fourth part presents a gener alization of the theory of cocycles to cocycles with restrictions. This part contains also applications to interpolation problems, to theproblem of holomorphic equivalence and diagonalization
Note:Springer eBooks
Contents:Preface
Introduction
1. Elementary Properties of Holomorphic Functions
2. Solution of \bar\partial u=f and Applications
3. Splitting and Factorization w.r.t. a Contour
4. The Rouch Theorem for Operator Functions
5. Multiplicative Cocycles
6. Families of Subspaces
7. Plemelj
Muschelishvili Factorization
8. Wiener
Hopf Operators, Toeplitz Operators and Factorizations
9. Multiplicative Cocycles with Restrictions
10. Generalized Interpolation Problems
11. Holomorphic Equivalence, Linearization and Diagonalization
Bibliography
Index
ISBN:9783034601269
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v192
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Operator theory
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Call number:SPRINGER-2009-9783034600040:ONLINE Show nearby items on shelf
Title:Applied Pseudoanalytic Function Theory [electronic resource]
Author(s): Vladislav V Kravchenko
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients whichturns out to be closel y related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrdinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid ofcomplex-analytic methods. The book is dedicated to these r ecent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate studentsand researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations
Note:Springer eBooks
Contents:Pseudoanalytic Function Theory and Second
order Elliptic Equations
Definitions and Results from Bers Theory
Solutions of Second
order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions
Formal Powers
Cauchys Integral Formula
Complex Riccati Equation
Applications to Sturm
Liouville Theory
A Representation for Solutions of the Sturm
Liouville Equation
Spectral Problems and Darboux Transformation
Applications to Real First
order Systems
Beltrami Fields
Static Maxwell System in Axially Symmetric Inhomogeneous Media
Hyperbolic Pseudoan
ISBN:9783034600040
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Operator theory , Differential equations, partial , Mathematical physics
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Call number:SPRINGER-2009-9780387094342:ONLINE Show nearby items on shelf
Title:Modern Fourier Analysis [electronic resource]
Author(s): Loukas Grafakos
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:The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition ofnew material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation,Fourier Series, the Fourier Transform, Maximal Func tions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals ofNonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed t o graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. Theprerequisites for the first volume are satisfactory completion of courses in real and complex variables. The s econd volume assumes material from the first. This book is intended to present the selected topics in depth and stimulatefurther study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of a nalysis on the torus. This material is included for historical reasons, as the genesis of Fourieranalysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: Grafakos's book is very user-friendly w ith numerous examples illustrating the definitions and ideas... Thetreatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises. - Kenneth Ross, MAA Online
Note:Springer eBooks
Contents:Smoothness and Function Spaces
and Carleson Measures
Singular Integrals of Nonconvolution Type
Weighted Inequalities
Boundedness and Convergence of Fourier Integrals
Time Frequency Analysis and the CarlesonHunt Theorem
ISBN:9780387094342
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v250
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functional analysis
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Call number:SPRINGER-2009-9780387094328:ONLINE Show nearby items on shelf
Title:Classical Fourier Analysis [electronic resource]
Author(s): Loukas Grafakos
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:The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition ofnew material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation,Fourier Series, the Fourier Transform, Maximal Func tions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals ofNonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed t o graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. Theprerequisites for the first volume are satisfactory completion of courses in real and complex variables. The s econd volume assumes material from the first. This book is intended to present the selected topics in depth and stimulatefurther study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of a nalysis on the torus. This material is included for historical reasons, as the genesis of Fourieranalysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: Grafakos's book is very user-friendly w ith numerous examples illustrating the definitions and ideas... Thetreatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises. - Kenneth Ross, MAA Online
Note:Springer eBooks
Contents:Preface
Lp Spaces and Interpolation
Maximal Functions, Fourier Transform, and Distributions
Fourier Analysis on the Torus
Singular Integrals of Convolution Type
Littlewood
Paley Theory and Multipliers
Gamma and Beta Functions
Bessel Functions
Rademacher Functions
Spherical Coordinates
Some Trigonometric Identities and Inequalities
Summation by Parts
Basic Functional Analysis
The Minimax Lemma
The Schur Lemma
The Whitney Decomposition of Open Sets in Rn
Smoothness and Vanishing Moments
Glossary
References
Index
ISBN:9780387094328
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v249
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functional analysis
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Call number:SPRINGER-2008-9783764386146:ONLINE Show nearby items on shelf
Title:The Mathematics of Minkowski Space-Time [electronic resource] With an Introduction to Commutative Hypercomplex Numbers
Author(s): Francesco Catoni
Dino Boccaletti
Roberto Cannata
Vincenzo Catoni
Enrico Nichelatti
Paolo Zampetti
Date:2008
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers isextensively studied in t he book. In particular, an exhaustive solution of the twin paradox is given, followed by a detailed exposition of space-time geometry and trigonometry. Finally, an appendix on general properties ofcommutative hypercomplex systems with four unities is pres ented
Note:Springer eBooks
Contents:N
Dimensional Commutative Hypercomplex Numbers
The Geometries Generated by Hypercomplex Numbers
Trigonometry in the Minkowski Plane
Uniform and Accelerated Motions in the Minkowski Space
Time (Twin Paradox)
General Two
Dimensional Hypercomplex Numbers
Functions of a Hyperbolic Variable
Hyperbolic Variables on Lorentz Surfaces
Constant Curvature Lorentz Surfaces
Generalization of Two
Dimensional Special Relativity (Hyperbolic Transformations and the Equivalence Principle)
ISBN:9783764386146
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis (Mathematics) , Geometry , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2008-9783764374785:ONLINE Show nearby items on shelf
Title:Analysis II [electronic resource]
Author(s): Herbert Amann
Joachim Escher
Date:2008
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and cleardevelopment that started in Volume I (3-7643-7153-6) continues. In this way a sustainable basis will be created which allows to deal with interesting applications that sometimes go considerably beyond the material that is representedin traditional textbooks. This applies, for ins tance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations. Another exampleis the presentation of the local theory of submanifolds of Rn
Note:Springer eBooks
Contents:Preface
VI. Integral Calculus in One Variable
1. Step Continuous Functions
2. Continuous Extensions
3. The Cauchy
Riemann Integral
4. Properties of the Integral
5. The Technology of Integration
6. Sums and Integrals
7. Fourier Series
8. Improper Integrals
9. The Gamma Function
VII. Differential Calculus in Several Variables
1. Continuous Linear Mappings
2. Differentiability
3. Calculation Rules
4. Multilinear Mappings
5. Higher Derivatives
6. Nemytski Operators and Calculus of Variations
7. Inverse Mappings
8. Implicit Functions
9. Manifolds
10. Tang
ISBN:9783764374785
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Functions of complex variables , Functions, special
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Call number:SPRINGER-2008-9780817647032:ONLINE Show nearby items on shelf
Title:Shape-Preserving Approximation by Real and Complex Polynomials [electronic resource]
Author(s): Sorin G Gal
Date:2008
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems thatarise in science and engin eering and require an optimal mathematical representation of physical reality. The main topics are structured in four chapters, followed by an appendix: shape-preserving approximation and interpolation of realfunctions of one real variable by real polynom ials shape-preserving approximation of real functions of several real variables by multivariate real polynomials shape-preserving approximation of analytic functions of one complexvariable by complex polynomials in the unit disk and shape-preserving appro ximation of analytic functions of several complex variables on the unit ball or the unit polydisk by polynomials of several complex variables. The appendixtreats related results of non-polynomial and non-spline approximations preserving shape including th ose by complexified operators with applications to complex partial differential equations. Shape-Preserving Approximation by Real andComplex Polynomials contains many open problems at the end of each chapter to stimulate future research along with a rich and updated bibliography surveying the vast literature. The text will be useful to graduate students andresearchers interested in approximation theory, mathematical analysis, numerical analysis, computer aided geometric design, robotics, data fitting, che mistry, fluid mechanics, and engineering
Note:Springer eBooks
Contents:Preface
Shape Preserving Approximation by Real Univariate Polynomials
Shape Preserving Approximation by Real Multivariate Polynomials
Shape Preserving Approximation by Complex Univariate Polynomials
Shape Preserving Approximation by Complex Multivariate Polynomials
Appendix: Some Related Topics
References
Index
ISBN:9780817647032
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Functions of complex variables , Computer science Mathematics , Engineering mathematics
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Call number:SPRINGER-2007-9780387747156:ONLINE Show nearby items on shelf
Title:Complex Analysis [electronic resource] : In the Spirit of Lipman Bers
Author(s): Jane P Gilman
Irwin Kra
Rub E Rodrguez
Date:2007
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study ofmany current and rapi dly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory. Complex analysis hasconnections and applications to many other sub jects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education ofevery practicing mathematician, and it will also be of interest to comp uter scientists, physicists, and engineers. The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity. The manyways of formulating the concept of an analytic function are summarized in what is termed the Fundamental Theorem for functions of a complex variable. The organization of these conditions into a single unifying theorem with an emphasison clarity and elegance is a hallmark of Lipman Bers's mathematical style. Here it provides a conceptual framewor k for results that are highly technical and often computational. The framework comes from an insight that, oncearticulated, will drive the subsequent mathematics and lead to new results. In the second part, the text proceeds to a leisurely exploration of interesting ramifications of the main concepts. The book covers most, if not all, of thematerial contained in Berss courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection b etween hyperbolic geometry and complex analysis are explored
Note:Springer eBooks
Contents:Preface
Standard Notation and Commonly used Symbols
The Fundamental Theorem in Complex Function Theory
Foundations
Power Series
The Cauchy Theory
A Fundamental Theorem
The Cauchy Theory
Key Consequences
Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions
Sequences and Series of Holomorphic Functions
Conformal Equivalence
Harmonic Functions
Zeros of Holomorphic Functions
Bibliographical Notes
Bibliography
Index
ISBN:9780387747156
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v245
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Differential equations, partial
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Call number:SPRINGER-2006-9783764375454:ONLINE Show nearby items on shelf
Title:The Fourfold Way In Real Analysis [electronic resource] An Alternative to the Metaplectic Representation
Author(s): Andr Unterberger
Date:2006
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that whichdeals with Fourier a nalysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way toa pseudo-Hilbert space, on which a new t ranslation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangiansubspaces of R2n that plays the usual role of the complex Siegel dom ain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers. Even though the whole development touches uponnotions of representation theory, pseudodifferential operator theory, and algebraic geometry, i t remains completely elementary in all these aspects. The book should be of interest to researchers working in analysis in general, inharmonic analysis, or in mathematical physics
Note:Springer eBooks
Contents:The One
dimensional Anaplectic Representation
The n
dimensional Anaplectic Analysis
Towards the Anaplectic Symbolic Calculi
The One
dimensional Case Revisited
ISBN:9783764375454
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v250
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Harmonic analysis , Functions of complex variables , Mathematical physics
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Call number:SPRINGER-2006-9783540344599:ONLINE Show nearby items on shelf
Title:Partial Differential Equations 1 [electronic resource] : Foundations and Integral Representations
Author(s): Friedrich Sauvigny
Date:2006
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEsand complex variable m ethods. In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potentialtheory and spherical harmonics, Linear part ial differential equations. While we solve the partial differential equations via integral representations in this volume, we shall present functional analytic solution methods in the secondvolume. This textbook can be chosen for a course over several sem esters on a medium level. Advanced readers may study each chapter independently from the others
Note:Springer eBooks
Contents:Differentiation and Integration on Manifolds
Foudations of Functional Analysis
Brouwers Degree of Mapping with Geometric Applications
Generalized Analytic Functions
Potential Theory and Spherical Harmonics
Linear Partial Differential Equations in Rn
ISBN:9783540344599
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Mathematical physics
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Call number:SPRINGER-2006-9780817645151:ONLINE Show nearby items on shelf
Title:Topics in the Theory of Algebraic Function Fields [electronic resource]
Author(s): Gabriel Daniel Villa Salvador
Date:2006
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraicviewpoint to the study of fu nction fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore thegeometric-analytic aspects of function fields, but le aves an in-depth examination from this perspective to others. Key topics and features: * Contains an introductory chapter on algebraic and numerical antecedents, includingtranscendental extensions of fields, absolute values on Q, and Riemann surfaces * Fo cuses on the RiemannRoch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more * Includes chapters onextensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the RiemannH urwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, andDrinfeld modules * Explains both the similarities and fundamental differences between function fields and number fields * Includes many exe rcises and examples to enhance understanding and motivate further study The only prerequisitesare a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 1-4 can serve asthe base of an introductory undergraduate course for mathematics majors, while chapters 5-9 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions willalso find the work an excellent reference
Note:Springer eBooks
Contents:Algebraic and Numerical Antecedents
Algebraic Function Fields of One Variable
The Riemann
Roch Theorem
Examples
Extensions and Galois Theory
Congruence Function Fields
The Riemann Hypothesis
Constant and Separable Extensions
The Riemann
Hurwitz Formula
Cryptography and Function Fields
to Class Field Theory
Cyclotomic Function Fields
Drinfeld Modules
Automorphisms and Galois Theory
ISBN:9780817645151
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics: Theory & Applications
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Field theory (Physics) , Global analysis (Mathematics) , Functions of complex variables , Number theory
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Call number:SPRINGER-2005-9783764373238:ONLINE Show nearby items on shelf
Title:Analysis I [electronic resource]
Author(s): Herbert Amann
Joachim Escher
Date:2005
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is the first of a three volume introduction to analysis. It is distinguished by its modern and clear presentation, concentrating always on the essential concepts. In contrast to most other textbooks, there is noartificial separation between the theories of one variable and that of many variables. Emphasis is placed on the early development of a solid foundation in topology. As well, the basics of complex analysis are covered. This book isdirected primarily to the students and instructors of beginning courses in analysis. But, with the many examples, exercises and the supplementary material, it is also suitable for self-study, as preparation for advanced study, and as abasis for other research in mathematics and physics. This textbook provid es an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential.'' Zeitschrift fr Analysisund ihre Anwendung 18, No. 4 (G. Berger, review of the first German edition) One advantage of this p resentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications.'' W. Grlz, reviewof the first German edition
Note:Springer eBooks
Contents:Preface
I. Basics
II.Convergence
III. Continuous Functions
IV. Calculus in One Variable
V. Sequences of Functions
Bibliography
Index
ISBN:9783764373238
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2005-9783764373030:ONLINE Show nearby items on shelf
Title:Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations [electronic resource]
Author(s): Daniel Alpay
Victor Vinnikov
Date:2005
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Operator theory, system theory, scattering theory, and the theory of analytic functions of one complex variable are deeply related topics, and the relationships between these theories are well understood. When one leaves thesetting of one operator an d considers several operators, the situation is much more involved. There is no longer a single underlying theory, but rather different theories, some of them loosely connected and some not connected at all.These various theories, which one could call mul tidimensional operator theory, are topics of active and intensive research. The present volume contains a selection of papers in multidimensional operator theory. Topics consideredinclude the non-commutative case, function theory in the polydisk, hyponorm al operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. The volume will be of interest to a wide audience of pureand applied mathematicians, electrical engineers and theoretical physicists
Note:Springer eBooks
ISBN:9783764373030
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v157
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Operator theory , Differential Equations
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Call number:SPRINGER-2005-9780387275390:ONLINE Show nearby items on shelf
Title:Spaces of Holomorphic Functions in the Unit Ball [electronic resource]
Author(s): Kehe Zhu
Date:2005
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spacesdiscussed include the Bergma n spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. Thecentral idea in almost all these proofs is based o n integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group. The unit ball was chosen as thesetting since most results can be achieved there using straightforward form ulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis no prerequisite on several complex variablesis required. The author has included exercises at the end of each chapter that vary greatly in th e level of difficulty. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include OperatorTheory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springe r 2000), and An Introduction to Operator Algebras (CRC Press 1993)
Note:Springer eBooks
Contents:Preliminaries
Bergman Spaces
The Bloch Space
Hardy Spaces
Functions of Bounded Mean Oscillation
Besov Spaces
Lipschitz Spaces
References
Index
ISBN:9780387275390
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v226
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential equations, partial
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Call number:SPRINGER-2004-9783642593154:ONLINE Show nearby items on shelf
Title:Elements of Mathematics Functions of a Real Variable Elementary Theory
Author(s): Nicolas Bourbaki
Date:2004
Size:1 online resource (338 p.)
Note:10.1007/978-3-642-59315-4
Contents:I Derivatives -- § 1. First Derivative -- § 2. The Mean Value Theorem -- § 3. Derivatives of Higher Order -- § 4. Convex Functions of a Real Variable -- Exercises on §1 -- Exercises on §2 -- Exercises on §3 -- Exercises on §4 -- II
Primitives and Integrals -- § 1. Primitives and Integrals -- § 2. Integrals Over Non-Compact Intervals -- § 3. Derivatives and Integrals of Functions Depending on a Parameter -- Exercises on §1 -- Exercises on §2 -- Exercises on §3 --
III Elementary Functions -- § 1. Derivatives of the Exponential and Circular Functions -- § 2. Expansions of the Exponential and Circular Functions, and of the Functions Associated with Them -- Exercises on §1 -- Exercises on §2 --
Historical Note (Chapters I-II-III) -- IV Differential Equations -- § 1. Existence Theorems -- § 2. Linear Differential Equations -- Exercises on §1 -- Exercises on §2 -- Historical Note -- V Local Study of Functions -- § 1. Comparison
of Functions on a Filtered Set -- § 2. Asymptotic Expansions -- § 3. Asymptotic Expansions of Functions of a Real Variable -- § 4. Application to Series with Positive Terms -- Exercises on §1 -- Exercises on §3 -- Exercises on §4 --
Exercises on Appendix -- VI Generalized Taylor Expansions. Euler-Maclaurin Summation Formula -- § 1. Generalized Taylor Expansions -- § 2. Eulerian Expansions of the Trigonometric Functions and Bernoulli Numbers -- § 3. Bounds for the
Remainder in the Euler-Maclaurin Summation Formula -- Exercises on §1 -- Exercises on §2 -- Exercises on §3 -- Historical Note (Chapters V and VI) -- VII The Gamma Function -- § 1. The Gamma Function in the Real Domain -- § 2. The
Gamma Function in the Complex Domain -- Exercises on §1 -- Exercises on §2 -- Historical Note -- Index of Notation
ISBN:9783642593154
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functions of real variables , Mathematics , Real Functions
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Call number:SPRINGER-2004-9783642189210:ONLINE Show nearby items on shelf
Title:Theory of Stein Spaces
Author(s): Hans Grauert
Date:2004
Size:1 online resource (254 p.)
Note:10.1007/978-3-642-18921-0
Contents:A. Sheaf Theory -- B. Cohomology Theory -- I. Coherence Theory for Finite Holomorphic Maps -- II. Differential Forms and Dolbeault Theory -- III. Theorems A and B for Compact Blocks ?m -- IV. Stein Spaces -- V. Applications of
Theorems A and B -- VI. The Finiteness Theorem -- VII. Compact Riemann Surfaces -- Table of Symbols -- Addendum -- Errors and Misprints
ISBN:9783642189210
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebraic geometry , Functions of complex variables , Mathematics , Functions of a Complex Variable , Several Complex Variables and Analytic Spaces , Algebraic Geometry
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Call number:SPRINGER-2004-9783642187605:ONLINE Show nearby items on shelf
Title:MuPAD Pro Computing Essentials
Author(s): Miroslaw Majewski
Date:2004
Edition:Second Edition
Size:1 online resource (538 p.)
Note:10.1007/978-3-642-18760-5
Contents:1.1 For whom this book was written -- 1.2 The goal -- 1.3 Why we should care about MuPAD -- 1.4 What is inside -- 1.5 Style conventions -- 1.6 Writing “between” -- A Quick Introduction to MuPAD -- 2.1 The Very First Look -- 2.2
Getting Started -- 2.3 A Quick Look at MuPAD’s Interface -- 2.4 Formatting Documents in MuPAD -- 2.5 Getting Help -- 2.6 Chapter Summary -- 2.7 Review Exercises -- Programming in MuPAD — Declarations -- 3.1 Writing Formulae in MuPAD --
3.2 Declaring Variables and Constants -- 3.3 Declaring Functions and Operations -- 3.4 Writing More than One Line of Code -- 3.5 The Basics of the Domain Concept -- 3.6 Chapter Summary -- 3.7 Review Exercises -- Programming in MuPAD —
Control Structures -- 4.1 Decisions -- 4.1.1 MuPAD Syntax: the “if” Statement -- 4.1.2 Indentation in MuPAD -- 4.1.3 Quadratic Equation Example -- 4.1.4 Formatting Output and Input -- 4.1.5 “elif” a Useful Shortcut -- 4.2 Programming
Itcrations in MuPAD -- 4.2.1 The “for” Loop -- 4.2.2 MuPAD Syntax: the “for” Loop -- 4.2.3 The “while” and “repeat” Loops -- 4.2.4 MuPAD Syntax: the “while” and “repeat” Loops -- 4.3 What is Wrong with my Loops and Conditions -- 4.4
Selections -- 4.4.1 MuPAD Syntax: the “case” Structure -- 4.5 Chapter Summary -- 4.6 Programming Exercises -- Programming in MuPAD — Procedures -- 5.1 What is a Procedure -- 5.2 Examples of Procedures -- 5.3 Getting Output from
Procedures -- 5.4 Returning Unevaluated or Symbolic Expressions -- 5.5 Shall We use Global or Local Variables? -- 5.6 Introduction to Types and Domains -- 5.7 Using MuPAD Types and Domains -- 5.8 Using Procedures to Produce Data
Structures -- 5.8.1 Sequences -- 5.8.2 Lists -- 5.8.3 Sets -- 5.8.4 Strings -- 5.8.5 Vectors and Matrices -- 5.9 Procedures with a Variable Number of Input Parameters -- 5.10 Recursive Procedures -- 5.11 Using Libraries -- 5.12 User
Defined Libraries of Procedures -- 5.13 Final Comments on MuPAD Coding Guidelines -- 5.13.1 Magic Numbers -- 5.13.2 Comments -- 5.13.3 Braces -- 5.14 Chapter Summary -- 5.15 Programming Exercises -- to MuPAD Graphics -- 6.1 Obtaining
Quick Plots -- 6.1.1 Procedure plotfunc2d -- 6.1.2 Your First Animation with MuPAD -- 6.1.3 Procedure plotfunc3d -- 6.2 General Concept of MuPAD Plots -- 6.2.1 Object Attributes’ Options -- 6.3 Canvas, Scene and Coordinate System
Options -- 6.3.1 Options for Canvas -- 6.3.2 Options for Scene2d -- 6.3.3 Options for Sccnc3d -- 6.3.4 The Coordinate System in 2D and 3D -- 6.4 Options Related to Primitives -- 6.4.1 Basic Options for Primitives -- 6.4.2 Working with
Color -- 6.4.3 Mesh and Other Options -- 6.5 Operations on Graphical Objects -- 6.5.1 Operation modify -- 6.6 Chapter Summary -- 6.7 Programming Exercises -- Interactive Graphics’ Animation with VCam -- 7.1 Learning the Virtual Camera
Environment -- 7.2 Using VCam to Improve 2D Graphs -- 7.3 Using VCam to Improve 3D Graphs -- 7.4 Interactive Development of Animations -- 7.5 Saving MuPAD Graphs -- 7.6 Chapter Summary -- 7.7 Exercises -- Exploring Mathematical Curves
and Surfaces -- 8.1 Plots in 2D Space’ Plot Types -- 8.1.1 Class Function2d -- 8.1.2 Class Curve2d -- 8.1.3 Developing Polar Plots -- 8.1.4 Developing Implicit Plots -- 8.2 Plots in 3D Space -- 8.2.1 Class Function3d -- 8.2.2 Class
Surface -- 8.2.3 Class Spherical -- 8.2.4 Class Cylindrical -- 8.2.5 Class Implicit3d -- 8.2.6 Classes Curve3d and Tube -- 8.3 Chapter Summary -- 8.4 Programming Exercises -- A Few Applications of MuPAD Graphics -- 9.1 Calculus
Graphics -- 9.1.1 Plotting Contours -- 9.1.2 Developing Density Plots -- 9.1.3 Vector Fields -- 9.1.4 Plotting Areas -- 9.1.5 Surfaces of Revolution -- 9.2 Presentation Graphics -- 9.3 Working with Geometry Objects -- 9.4
Transformations of Graphical Objects -- 9.5 Turtle Graphics & L-systems -- 9.5.1 Turtle Graphics in MuPAD -- 9.5.2 Plotting L-systems -- 9.6 Chapter Summary -- 9.7 Programming Exercises -- Exploring Numbers with MuPAD -- 10.1 Integers
in MuPAD -- 10.2 Rational Numbers in MuPAD -- 10.3 Real Numbers in MuPAD -- 10.4 Complex Numbers in MuPAD -- 10.5 Chapter Summary -- 10.6 Programming Exercises -- Elementary Algebra and Trigonometry in MuPAD -- 11.1 Polynomials -- 11.2
Rational Expressions -- 11.3 Algebraic Expressions -- 11.4 Trigonometric and Other Functions -- 11.5 Solving Equations and Inequalities -- 11.6 Chapter Summary -- 11.7 Programming Exercises -- Working with Sets and Sentences MuPAD --
12.1 Logic in MuPAD -- 12.1.1 Polish Notation -- 12.2 Working with Sets -- 12.3 Chapter Summary -- 12.4 Programming Exercises -- Exploring Calculus with MuPAD -- 13.1 Limits -- 13.2 Derivatives -- 13.3 Working with Integrals -- 13.4
Infinite Series and Products -- 13.5 Calculus of Two Variables -- 13.5.1 Limits of Functions of Two Variables -- 13.5.2 Partial Derivatives -- 13.6 Chapter Summary -- 13.7 Programming Exercises -- A Short Introduction to Linear Algebra
-- 14.1 Checking Resources -- 14.2 Solving Linear Equations -- 14.3 Matrices and Operations on Matrices -- 14.3.1 Declaring Matrices in MuPAD -- 14.3.2 Global Operations on Matrices -- 14.3.3 Local Matrix Operations -- 14.4
Determinants -- 14.5 Chapter Summary -- 14.6 Programming Exercises -- Appendix 1: MuPAD Libraries and Procedures -- MuPAD Libraries (ver. 3.0, 21/02/2004) -- Operators Represented by Symbols -- MuPAD Standard Collection -- Procedures
in Standard Collection -- Functions in Standard Collection -- Library ‘adt’ — — Abstract Data Types -- Library ‘Ax’ — — Basic Axiom Constructors -- Library ‘Cat’ — — Category Constructors -- Library ‘combinat’ — — Com binatorial
Functions -- Library ‘detools’ — — Methods for Differential Equations -- Library ‘Dom’ — — Domain Constructors -- Library ‘fp’ — — Utilities for Functional Programming -- Library ‘generate’ — — Generate Foreign Format s -- Library
‘Graph’ — — Utilities for Directed and Undirected Graphs -- Library ‘groebner’ — — Utilities for Groebner Bases -- Library ‘import’ — — Utilities for Reading Data -- Library ‘intlib’ — — Definite and Indefinite Integr ation -- Library
‘linalg’ — — the Linear Algebra Package -- Library ‘linopt’ — — Tools for Linear Optimization -- Library ‘listlib’ — Operations on Lists -- Library ‘matchlib’ — Pattern Matching Tools -- Library ‘module’ — Module Ma nagement Tools --
Library ‘numeric’ — Tools for Numerical Methods -- Library ‘numlib’ — Elementary Number Theory -- Library ‘orthpoly’ — Orthogonal Polynomials -- Library ‘output’ — Tools for the Output of Data -- Library ‘plot’ — 2D and 3D Graphical
Objects -- Library ‘polylib’ — Tools for Polynomials -- Library ‘prog’ — Programming Utilities -- Library ‘property’ — Properties of Identifiers -- Library ‘RGB’ — Color Names and Color Functions -- Library’ series’ — T ools for Series
Expansions -- Library’ solvclib’ — Tools for Solving Equations -- Library’ stats’ — Statistical Functions -- Library’ stringlib’ — Tools for String Manipulation -- Library’ student’ — the Student Package -- Library ‘transfo rm’ —
Integral Transformations -- Library ‘Type’ — Predefined Types -- MuPAD Environmental Variables -- Appendix 2: MuPAD Resources
ISBN:9783642187605
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Computer mathematics , Computer software , Mathematics , Computational Science and Engineering , Mathematical Software
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Call number:SPRINGER-2004-9783540707462:ONLINE Show nearby items on shelf
Title:Spectral Properties of Noncommuting Operators
Author(s): Brian Jefferies
Date:2004
Size:1 online resource (184 p.)
Note:10.1007/b97327
Contents:Introduction -- Weyl Calculus -- Clifford Analysis -- Functional Calculus for Noncommuting Operators -- The Joint Spectrum of Matrices -- The Monogenic Calculus for Sectorial Operators -- Feynman's Operational Calculus -- References
-- Index
ISBN:9783540707462
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1843
Keywords: Mathematics , Mathematical analysis , Analysis (Mathematics) , Fourier analysis , Functions of complex variables , Operator theory , Mathematics , Analysis , Operator Theory , Functions of a Complex Variable , Fourier Analysis
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Call number:SPRINGER-2004-9783034879361:ONLINE Show nearby items on shelf
Title:Projective Geometry and Formal Geometry
Author(s): Lucian Bădescu
Date:2004
Size:1 online resource (214 p.)
Note:10.1007/978-3-0348-7936-1
Contents:I Special Chapters of Projective Geometry -- 1 Extensions of Projective Varieties -- 2 Proof of Theorem 1.3 -- 3 Counterexamples and Further Consequences -- 4 The Zak Map of a Curve. Gaussian Maps -- 5 Quasi-homogeneous Singularities
and Projective Geometry -- 6 A Characterization of Linear Subspaces -- 7 Cohomological Dimension and Connectedness Theorems -- 8 A Problem of Complete Intersection -- II Formal Functions in Algebraic Geometry -- 9 Basic Definitions and
Results -- 10 Lefschetz Theory and Meromorphic Functions -- 11 Connectedness and Formal Functions -- 12 Further Results on Formal Functions -- 13 Formal Functions on Homogeneous Spaces -- 14 Quasi-lines on Projective Manifolds --
Glossary of Notation
ISBN:9783034879361
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) : 65
Keywords: Mathematics , Algebraic geometry , Functions of complex variables , Global analysis (Mathematics) , Manifolds (Mathematics) , Geometry , Mathematics , Algebraic Geometry , Functions of a Complex Variable , Global Analysis and Analysis on Manifolds , Geometry
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Call number:SPRINGER-2004-9783034878715:ONLINE Show nearby items on shelf
Title:Complex Convexity and Analytic Functionals
Author(s): Mats Andersson
Date:2004
Size:1 online resource (164 p.)
Note:10.1007/978-3-0348-7871-5
Contents:1 Convexity in Real Projective Space -- 1.1 Convexity in real affine space -- 1.2 Real projective space -- 1.3 Convexity in real projective space -- 2 Complex Convexity -- 2.1 Linearly convex sets -- 2.2 ?-convexity: Definition and
examples -- 2.3 ?-convexity: Duality and invariance -- 2.4 Open ?-convex sets -- 2.5 Boundary properties of ?-convex sets -- 2.6 Spirally connected sets -- 3 Analytic Functionals and the Fantappiè Transformation -- 3.1 The basic
pairing in affine space -- 3.2 The basic pairing in projective space -- 3.3 Analytic functionals in affine space -- 3.4 Analytic functionals in projective space -- 3.5 The Fantappiè transformation -- 3.6 Decomposition into partial
fractions -- 3.7 Complex Kergin interpolation -- 4 Analytic Solutions to Partial Differential Equations -- 4.1 Solvability in ?-convex sets -- 4.2 Solvability and P-convexity for carriers -- References
ISBN:9783034878715
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 225
Keywords: Mathematics , Functional analysis , Functions of complex variables , Partial differential equations , Convex geometry , Discrete geometry , Mathematics , Functional Analysis , Functions of a Complex Variable , Partial Differential Equations , Convex and Discrete Geometry
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Call number:SPRINGER-2004-9781461302216:ONLINE Show nearby items on shelf
Title:Finite or Infinite Dimensional Complex Analysis and Applications
Author(s):
Date:2004
Size:1 online resource (381 p.)
Note:10.1007/978-1-4613-0221-6
Contents:I. Plenary Talks and Surveys -- 1 Nevanlinna theory and Diophantine approximations -- 2 In Ramanujan’s Shadow -- 3 Holomorphic functions on the Lie ball and related topics -- 4 Invariance of Plurigenera and Torsion-Freeness of Direct
Image Sheaves of Pluricanonial Bundles -- 5 Maxwell’s equations in Clifford calculus framework — an overview on the development -- 6 Generalized Analytic Functions and their contributions to the development of Mathematical Analysis --
II. Complex Methods in the Plane -- 7 On qp sequences -- 8 Reconstruction of an Analytic Function from a Sequence of Values: Existence and Regularization -- 9 p-adic Interpolation and Applications -- 10 Refined Order and the Paley
Problem in Vector Spaces -- 11 Integral representation of p-adic functions -- 12 Malmquist-Yosida type theorems for algebraic differential equations -- 13 Transformation techniques for partial differential equations -- 14 Besov-type
Characterizations for Quaternionic Bloch Functions -- 15 Bergman and Bauer Operators for Elliptic Equations in two Independent Variables -- 16 Some results on QK-type spaces -- III. Analysis in Higher Dimensions -- 17 Representations
in Polydomains -- 18 On Bq spaces of hyperholomorphic functions and the Bloch space in R3 -- 19 Regeneration in complex, quaternion and Clifford analysis -- 20 A note on sesquilinear forms and the generalized uncertainty relations in
*-algebras -- 21 The Hartogs Extension Theorem for the Multi-regular functions Taking Values in a Clifford algebra -- 22 The extension of entire functions of nuclear type on locally convex spaces -- 23 Some Properties of the
Inhomogeneous Generalized Cauchy-Riemann Systems in Quaternionic Algebra and its Applications -- 24 The Fundamental Solution of the Hyperbolic Dirac-Equation -- 25 Inhomogeneous ordinary differential equations and local cohomologies
and residues -- 26 Infinite dimensional CR category
ISBN:9781461302216
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Advances in Complex Analysis and Its Applications : 2
Keywords: Mathematics , Functions of complex variables , Partial differential equations , Special functions , Mathematics , Several Complex Variables and Analytic Spaces , Partial Differential Equations , Functions of a Complex Variable , Special Functions
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Call number:SPRINGER-2004-9781402079511:ONLINE Show nearby items on shelf
Title:Value Distribution Theory and Related Topics
Author(s):
Date:2004
Size:1 online resource (333 p.)
Note:10.1007/b131070
Contents:Geometric value distribution theory -- A New Program of Investigations in Analysis: Gamma-Lines Approaches -- On Level Sets of Quasiconformal Mappings -- Classical value distribution theory -- On the Unintegrated Nevanlinna
Fundamental Inequality for Meromorphic Functions of Slow Growth -- On Some New Concept of Exceptional Values -- Maximum Modulus Points, Deviations and Spreads of Meromorphic Functions -- Composition Theorems, Multiplier Sequences and
Complex Zero Decreasing Sequences -- Nevanlinna Theory in an Annulus -- On Strong Asymptotic Tracts of Functions Holomorphic in a Disk -- Complex differential and functional equations -- A New Trend in Complex Differential Equations:
Quasimeromorphic Solutions -- On the Functional Equation P(F)=Q(G) -- Value Distribution of the Higher Order Analogues of the First Painlevé Equation -- Some Further Results on the Functional Equation P(F)=Q(G) -- Several variables
theory -- Recent Topics in Uniqueness Problem for Meromorphic Mappings -- On Interpolation Problems in Cn -- Jet Bundles and its Applications in Value Distribution of Holomorphic Mappings -- Normal Families of Meromorphic Mappings of
Several Complex Variables into the Complex Projective Space
ISBN:9781402079511
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Advances in Complex Analysis and Its Applications : 3
Keywords: Mathematics , Functions of complex variables , Differential equations , Mathematics , Functions of a Complex Variable , Several Complex Variables and Analytic Spaces , Ordinary Differential Equations
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Call number:SPRINGER-2004-9781402021879:ONLINE Show nearby items on shelf
Title:Abel’s Theorem in Problems and Solutions Based on the lectures of Professor V.I. Arnold
Author(s): V.B Alekseev
Date:2004
Size:1 online resource (270 p.)
Note:10.1007/1-4020-2187-9
Contents:From the contents: Preface for the English edition V.I. Arnold -- Preface -- Introduction -- 1: Groups -- 2: The complex numbers -- 3: Hints, Solutions and Answers -- Appendix. Solvability of equations by explicit formulae A.
Khovanskii -- Bibliography -- Appendix V.I. Arnold -- Index
ISBN:9781402021879
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Field theory (Physics) , Group theory , Topological groups , Lie groups , Functions of complex variables , Mathematics , Group Theory and Generalizations , Functions of a Complex Variable , Field Theory and Polynomials , Topological Groups, Lie Groups
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Call number:SPRINGER-2004-9780817681982:ONLINE Show nearby items on shelf
Title:Methods of Applied Mathematics with a MATLAB Overview
Author(s): Jon H Davis
Date:2004
Size:1 online resource (721 p.)
Note:10.1007/978-0-8176-8198-2
Contents:1 Introduction -- 1.1 An Overview -- 1.2 Topics by Chapter -- 1.3 Applying Mathematics -- References -- 2 Fourier Series -- 2.1 Introduction -- 2.2 Inner Products and Fourier Expansions -- 2.3 Convergence of Fourier Series -- 2.4
Pointwise and Uniform Convergence of Fourier Series -- 2.5 Gibb’s Phenomenon and Summation Methods -- 2.6 Summation Methods -- 2.7 Fourier Series Properties -- 2.8 Periodic Solutions of Differential Equations -- 2.9 Impedance Methods
and Periodic Solutions -- 2.10 Power Spectrum and Parseval’s Theorem -- References -- 3 Elementary Boundary Value Problems -- 3.1 Introduction -- 3.2 The One-Dimensional Diffusion Equation -- 3.3 The Wave Equation -- 3.4 The Potential
Equation -- 3.5 Discrete Models of Boundary Value Problems -- 3.6 Separation of Variables -- 3.7 Half-Range Expansions and Symmetries -- 3.8 Some Matters of Detail -- References -- 4 Sturm-Liouville Theory and Boundary Value Problems
-- 4.1 Further Boundary Value Problems -- 4.2 Selfadjoint Eigenvalue Problems -- 4.3 Sturm-Liouville Problems -- 4.4 Power Series and Singular Sturm-Liouville Problems -- 4.5 Cylindrical Problems and Bessel’s Equation -- 4.6
Multidimensional Problems and Forced Systems -- 4.7 Finite Differences and Numerical Methods -- 4.8 Variational Models and Finite Element Methods -- 4.9 Computational Finite Element Methods -- References -- 5 Functions of a Complex
Variable -- 5.1 Complex Variables and Analytic Functions -- 5.2 Domains of Definition of Complex Functions -- 5.3 Integrals and Cauchy’s Theorem -- 5.4 Cauchy’s Integral Formula, Taylor Series, and Residues -- 5.5 Complex Variables and
Fluid Flows -- 5.6 Conformal Mappings and the Principle of the Argument -- References -- 6 Laplace Transforms -- 6.1 Introduction -- 6.2 Definitions of the Laplace Transform -- 6.3 Mechanical Properties of Laplace Transforms -- 6.4
Elementary Transforms and Fourier Series Calculations -- 6.5 Elementary Applications to Differential Equations -- 6.6 Convolutions, Impulse Responses, and Weighting Patterns -- 6.7 Vector Differential Equations -- 6.8 Impedance Methods
-- References -- 7. Fourier Transforms -- 7.1 Introduction -- 7.2 Basic Fourier Transforms -- 7.3 Formal Properties of Fourier Transforms -- 7.4 Convolutions and Parseval’s Theorem -- 7.5 Comments on the Inversion Theorem -- 7.6
Fourier Inversion by Contour Integration -- 7.7 The Laplace Transform Inversion Integral -- 7.8 An Introduction to Generalized Functions -- 7.9 Fourier Transforms, Differential Equations and Circuits -- 7.10 Transform Solutions of
Boundary Value Problems -- 7.11 Band-limited Functions and Communications -- References -- 8 Discrete Variable Transforms -- 8.1 Some Discrete Variable Models -- 8.2 Z-Transforms -- 8.3 Z-Transform Properties -- 8.4 z-Transform
Inversion Integral -- 8.5 Discrete Fourier Transforms -- 8.6 Discrete Fourier Transform Properties -- 8.7 Some Applications of Discrete Transform Methods -- 8.8 Finite and Fast Fourier Transforms -- 8.9 Finite Fourier Properties --
8.10 Fast Finite Transform Algorithm -- 8.11 Computing The 1-1.1 -- References -- 9 Additional Topics -- 9.1 Local Waveform Analysis -- 9.2 Uncertainty Principle -- 9.3 Short-Time Fourier Transforms -- 9.4 Function Shifts and Scalings
-- 9.5 Orthonormal Shifts -- 9.6 Multi-Resolution Analysis and Wavelets -- 9.7 On Wavelet Applications -- 9.8 Two-Sided Transforms -- 9.9 Walsh Functions -- 9.10 Geometrically Based Transforms -- References -- A Linear Algebra Overview
-- A.1 Vector spaces -- A.2 Linear Mappings -- A.3 Inner Products -- A.4 Linear Functionals and Dual Spaces -- A.5 Canonical Forms -- References -- B Software Resources -- B.1 Computational and Visualization Software -- B.2 MATLAB Data
Structures -- B.3 MATLAB Operators and Syntax -- B.4 MATLAB Programming Structures -- B.5 MATLAB Programs and Scripts -- B.6 Common Idioms -- B.7 Graphics -- B.8 Toolboxes and Enhancemants -- References -- C Transform Tables -- C.1
Laplace Transforms -- C.2 Fourier Transforms -- C.3 Z Transforms -- C.4 Discrete Fourier Transforms
ISBN:9780817681982
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functions of complex variables , Applied mathematics , Engineering mathematics , Computer mathematics , Physics , Mathematics , Fourier Analysis , Computational Mathematics and Numerical Analysis , Theoretical, Mathematical and Computational Physics , Applications of Mathematics , Abstract Harmonic Analysis , Functions of a Complex Variable
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Call number:SPRINGER-2004-9780817681708:ONLINE Show nearby items on shelf
Title:Arithmetic of Higher-Dimensional Algebraic Varieties
Author(s):
Date:2004
Edition:1
Size:1 online resource (287 p.)
Note:10.1007/978-0-8176-8170-8
Contents:Diophantine equations: progress and problems -- Rational points and analytic number theory -- Weak approximation on algebraic varieties -- Counting points on varieties using universal torsors -- The Cox ring of a Del Pezzo surface --
Counting rational points on threefolds -- Remarques sur l’approximation faible sur un corps de fonctions d’une variable -- K3 surfaces over number fields with geometric Picard number one -- Jumps in Mordell-Weil rank and Arithmetic
Surjectivity -- Universal torsors and Cox rings -- Random diophantine equations -- Descent on simply connected surfaces over algebraic number fields -- Rational points on compactifications of semi-simple groups of rank 1 -- Weak
Approximation on Del Pezzo surfaces of degree 4 -- Transcendental Brauer-Manin obstruction on a pencil of elliptic curves
ISBN:9780817681708
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 226
Keywords: Mathematics , Algebraic geometry , Algebra , Field theory (Physics) , Functions of complex variables , Number theory , Mathematics , Number Theory , Algebraic Geometry , Field Theory and Polynomials , Several Complex Variables and Analytic Spaces
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Call number:SPRINGER-2004-9780817681661:ONLINE Show nearby items on shelf
Title:Analysis of Dirac Systems and Computational Algebra
Author(s): Fabrizio Colombo
Date:2004
Size:1 online resource (332 p.)
Note:10.1007/978-0-8176-8166-1
Contents:1 Background Material -- 1.1 Algebraic tools -- 1.2 Analytical tools -- 1.3 Elements of hyperfunction theory -- 1.4 Appendix: category theory -- 2 Computational Algebraic Analysis -- 2.1 A primer of algebraic analysis -- 2.2 The
Ehrenpreis-Palamodov Fundamental Principle -- 2.3 The Fundamental Principle for hyperfunctions -- 2.4 Using computational algebra software -- 3 The Cauchy-Fueter System and its Variations -- 3.1 Regular functions of one quaternionic
variable -- 3.2 Quaternionic hyperfunctions in one variable -- 3.3 Several quaternionic variables: analytic approach -- 3.4 Several quaternionic variables: an algebraic approach -- 3.5 The Moisil-Theodorescu system -- 4 Special First
Order Systems in Clifford Analysis -- 4.1 Introduction to Clifford algebras -- 4.2 Introduction to Clifford analysis -- 4.3 The Dirac complex for two, three and four operators -- 4.4 Special systems in Clifford analysis -- 5 Some First
Order Linear Operators in Physics -- 5.1 Physics and algebra of Maxwell and Proca fields -- 5.2 Variations on Maxwell system in the space of biquaternions -- 5.3 Properties of DZ-regular functions -- 5.4 The Dirac equation and the
linearization problem -- 5.5 Octonionic Dirac equation -- 6 Open Problems and Avenues for Further Research -- 6.1 The Cauchy-Fueter system -- 6.2 The Dirac system -- 6.3 Miscellanea
ISBN:9780817681661
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematical Physics : 39
Keywords: Mathematics , Algebra , Matrix theory , Partial differential equations , Physics , Mathematics , Algebra , Partial Differential Equations , Linear and Multilinear Algebras, Matrix Theory , Mathematical Methods in Physics , Numerical and Computational Physics
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Call number:SPRINGER-2004-9780817644147:ONLINE Show nearby items on shelf
Title:Mathematical Analysis Approximation and Discrete Processes
Author(s): Mariano Giaquinta
Date:2004
Size:1 online resource (388 p.)
Note:10.1007/978-0-8176-4414-7
Contents:1. Real Numbers and Natural Numbers -- 1.1 Introduction -- 1.2 The Axiomatic Approach to Real Numbers -- 1.3 Natural Numbers -- 1.4 Summing Up -- 1.5 Exercises -- 2. Sequences of Real Numbers -- 2.1 Sequences -- 2.2 Equivalent
Formulations of the Continuity Axiom -- 2.3 Limits of Sequences and Continuity -- 2.4 Some Special Sequences -- 2.5 An Alternative Definition of Exponentials and Logarithms -- 2.6 Summing Up -- 2.7 Exercises -- 3. Integer Numbers:
Congruences, Counting and Infinity -- 3.1 Congruences -- 3.2 Combinatorics -- 3.3 Infinity -- 3.4 Summing Up -- 3.5 Exercises -- 4. Complex Numbers -- 4.1 Complex Numbers -- 4.2 Sequences of Complex Numbers -- 4.3 Some Elementary
Applications -- 4.4 Summing Up -- 4.5 Exercises -- 5. Polynomials, Rational Functions and Trigonometric Polynomials -- 5.1 Polynomials -- 5.2 Solutions of Polynomial Equations -- 5.3 Rational Functions -- 5.4 Sinusoidal Functions and
Their Sums -- 5.5 Summing Up -- 5.6 Exercises -- 6. Series -- 6.1 Basic Facts -- 6.2 Taylor Series, e and ? -- 6.3 Series of Nonnegative Terms -- 6.4 Series of Terms of Arbitrary Sign -- 6.5 Series of Products -- 6.6 Products of Series
-- 6.7 Rearrangements -- 6.8 Summing Up -- 6.9 Exercises -- 7. Power Series -- 7.1 Basic Theory -- 7.2 Further Results -- 7.3 Some Applications -- 7.4 Further Applications -- 7.5 Summing Up -- 7.6 Exercises -- 8. Discrete Processes --
8.1 Recurrences -- 8.2 One-Dimensional Dynamical Systems -- 8.3 Two-Dimensional Dynamical Systems -- 8.4 Exercises -- A. Mathematicians and Other Scientists -- B. Bibliographical Notes -- C. Index
ISBN:9780817644147
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Mathematical analysis , Analysis (Mathematics) , Functions of complex variables , Differential equations , Applied mathematics , Engineering mathematics , Statistics , Mathematics , Analysis , Functions of a Complex Variable , Ordinary Differential Equations , Applications of Mathematics , Statistical Theory and Methods
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