Introduction to Partial Differential Equations: From Fourier Series to Boundary-Value Problems (Dover Books on Mathematics)

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9780486661582: Introduction to Partial Differential Equations: From Fourier Series to Boundary-Value Problems (Dover Books on Mathematics)

This exceptionally well-written and well-organized text is the outgrowth of a course given every year for 45 years at the Chalmers University of Technology, Goteborg, Sweden. The object of the course was to give students a basic knowledge of Fourier analysis and certain of its applications. The text is self-contained with respect to such analysis; however, in areas where the author relies on results from branches of mathematics outside the scope of this book, references to widely used books are given.
Table of Contents:
Chapter 1. Fourier series
1.1 Basic concepts
1.2 Fourier series and Fourier coefficients
1.3 A minimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem
1.4 Convergence of Fourier series
1.5 The Parseval formula
1.6 Determination of the sum of certain trigonometric series
Chapter 2. Orthogonal systems
2.1 Integration of complex-valued functions of a real variable
2.2 Orthogonal systems
2.3 Complete orthogonal systems
2.4 Integration of Fourier series
2.5 The Gram-Schmidt orthogonalization process
2.6 Sturm-Liouville problems
Chapter 3. Orthogonal polynomials
3.1 The Legendre polynomials
3.2 Legendre series
3.3 The Legendre differential equation. The generating function of the Legendre polynomials
3.4 The Tchebycheff polynomials
3.5 Tchebycheff series
3.6 The Hermite polynomials. The Laguerre polynomials
Chapter 4. Fourier transforms
4.1 Infinite interval of integration
4.2 The Fourier integral formula: a heuristic introduction
4.3 Auxiliary theorems
4.4 Proof of the Fourier integral formula. Fourier transforms
4.5 The convention theorem. The Parseval formula
Chapter 5. Laplace transforms
5.1 Definition of the Laplace transform. Domain. Analyticity
5.2 Inversion formula
5.3 Further properties of Laplace transforms. The convolution theorem
5.4 Applications to ordinary differential equations
Chapter 6. Bessel functions
6.1 The gamma function
6.2 The Bessel differential equation. Bessel functions
6.3 Some particular Bessel functions
6.4 Recursion formulas for the Bessel functions
6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions
6.6 Bessel series
6.7 The generating function of the Bessel functions of integral order
6.8 Neumann functions
Chapter 7. Partial differential equations of first order
7.1 Introduction
7.2 The differential equation of a family of surfaces
7.3 Homogeneous differential equations
7.4 Linear and quasilinear differential equations
Chapter 8. Partial differential equations of second order
8.1 Problems in physics leading to partial differential equations
8.2 Definitions
8.3 The wave equation
8.4 The heat equation
8.5 The Laplace equation
Answers to exercises; Bibliography; Conventions; Symbols; Index
Written on an advanced level, the book is aimed at advanced undergraduates and graduate students with a background in calculus, linear algebra, ordinary differential equations, and complex analysis. Over 260 carefully chosen exercises, with answers, encompass both routing and more challenging problems to help students test their grasp of the material.

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Descripción Dover Publications Inc., United States, 2010. Paperback. Estado de conservación: New. New edition. Language: English . Brand New Book. This exceptionally well-written and well-organized text is the outgrowth of a course given every year for 45 years at the Chalmers University of Technology, Goteborg, Sweden. The object of the course was to give students a basic knowledge of Fourier analysis and certain of its applications. The text is self-contained with respect to such analysis; however, in areas where the author relies on results from branches of mathematics outside the scope of this book, references to widely used books are given. Table of Contents: Chapter 1. Fourier series 1.1 Basic concepts 1.2 Fourier series and Fourier coefficients 1.3 A minimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem 1.4 Convergence of Fourier series 1.5 The Parseval formula 1.6 Determination of the sum of certain trigonometric series Chapter 2. Orthogonal systems 2.1 Integration of complex-valued functions of a real variable 2.2 Orthogonal systems 2.3 Complete orthogonal systems 2.4 Integration of Fourier series 2.5 The Gram-Schmidt orthogonalization process 2.6 Sturm-Liouville problems Chapter 3. Orthogonal polynomials 3.1 The Legendre polynomials 3.2 Legendre series 3.3 The Legendre differential equation. The generating function of the Legendre polynomials 3.4 The Tchebycheff polynomials 3.5 Tchebycheff series 3.6 The Hermite polynomials. The Laguerre polynomials Chapter 4. Fourier transforms 4.1 Infinite interval of integration 4.2 The Fourier integral formula: a heuristic introduction 4.3 Auxiliary theorems 4.4 Proof of the Fourier integral formula. Fourier transforms 4.5 The convention theorem. The Parseval formula Chapter 5. Laplace transforms 5.1 Definition of the Laplace transform. Domain. Analyticity 5.2 Inversion formula 5.3 Further properties of Laplace transforms. The convolution theorem 5.4 Applications to ordinary differential equations Chapter 6. Bessel functions 6.1 The gamma function 6.2 The Bessel differential equation. Bessel functions 6.3 Some particular Bessel functions 6.4 Recursion formulas for the Bessel functions 6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions 6.6 Bessel series 6.7 The generating function of the Bessel functions of integral order 6.8 Neumann functions Chapter 7. Partial differential equations of first order 7.1 Introduction 7.2 The differential equation of a family of surfaces 7.3 Homogeneous differential equations 7.4 Linear and quasilinear differential equations Chapter 8. Partial differential equations of second order 8.1 Problems in physics leading to partial differential equations 8.2 Definitions 8.3 The wave equation 8.4 The heat equation 8.5 The Laplace equation Answers to exercises; Bibliography; Conventions; Symbols; Index Written on an advanced level, the book is aimed at advanced undergraduates and graduate students with a background in calculus, linear algebra, ordinary differential equations, and complex analysis. Over 260 carefully chosen exercises, with answers, encompass both routing and more challenging problems to help students test their grasp of the material. Nº de ref. de la librería AAC9780486661582

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Descripción 2010. PAP. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Nº de ref. de la librería IB-9780486661582

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Editorial: Dover Publications Inc., United States (2010)
ISBN 10: 048666158X ISBN 13: 9780486661582
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Descripción Dover Publications Inc., United States, 2010. Paperback. Estado de conservación: New. New edition. Language: English . Brand New Book. This exceptionally well-written and well-organized text is the outgrowth of a course given every year for 45 years at the Chalmers University of Technology, Goteborg, Sweden. The object of the course was to give students a basic knowledge of Fourier analysis and certain of its applications. The text is self-contained with respect to such analysis; however, in areas where the author relies on results from branches of mathematics outside the scope of this book, references to widely used books are given. Table of Contents: Chapter 1. Fourier series 1.1 Basic concepts 1.2 Fourier series and Fourier coefficients 1.3 A minimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem 1.4 Convergence of Fourier series 1.5 The Parseval formula 1.6 Determination of the sum of certain trigonometric series Chapter 2. Orthogonal systems 2.1 Integration of complex-valued functions of a real variable 2.2 Orthogonal systems 2.3 Complete orthogonal systems 2.4 Integration of Fourier series 2.5 The Gram-Schmidt orthogonalization process 2.6 Sturm-Liouville problems Chapter 3. Orthogonal polynomials 3.1 The Legendre polynomials 3.2 Legendre series 3.3 The Legendre differential equation. The generating function of the Legendre polynomials 3.4 The Tchebycheff polynomials 3.5 Tchebycheff series 3.6 The Hermite polynomials. The Laguerre polynomials Chapter 4. Fourier transforms 4.1 Infinite interval of integration 4.2 The Fourier integral formula: a heuristic introduction 4.3 Auxiliary theorems 4.4 Proof of the Fourier integral formula. Fourier transforms 4.5 The convention theorem. The Parseval formula Chapter 5. Laplace transforms 5.1 Definition of the Laplace transform. Domain. Analyticity 5.2 Inversion formula 5.3 Further properties of Laplace transforms. The convolution theorem 5.4 Applications to ordinary differential equations Chapter 6. Bessel functions 6.1 The gamma function 6.2 The Bessel differential equation. Bessel functions 6.3 Some particular Bessel functions 6.4 Recursion formulas for the Bessel functions 6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions 6.6 Bessel series 6.7 The generating function of the Bessel functions of integral order 6.8 Neumann functions Chapter 7. Partial differential equations of first order 7.1 Introduction 7.2 The differential equation of a family of surfaces 7.3 Homogeneous differential equations 7.4 Linear and quasilinear differential equations Chapter 8. Partial differential equations of second order 8.1 Problems in physics leading to partial differential equations 8.2 Definitions 8.3 The wave equation 8.4 The heat equation 8.5 The Laplace equation Answers to exercises; Bibliography; Conventions; Symbols; Index Written on an advanced level, the book is aimed at advanced undergraduates and graduate students with a background in calculus, linear algebra, ordinary differential equations, and complex analysis. Over 260 carefully chosen exercises, with answers, encompass both routing and more challenging problems to help students test their grasp of the material. Nº de ref. de la librería AAC9780486661582

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Descripción Dover Publications Inc., United States, 2010. Paperback. Estado de conservación: New. New edition. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. This exceptionally well-written and well-organized text is the outgrowth of a course given every year for 45 years at the Chalmers University of Technology, Goteborg, Sweden. The object of the course was to give students a basic knowledge of Fourier analysis and certain of its applications. The text is self-contained with respect to such analysis; however, in areas where the author relies on results from branches of mathematics outside the scope of this book, references to widely used books are given. Table of Contents: Chapter 1. Fourier series 1.1 Basic concepts 1.2 Fourier series and Fourier coefficients 1.3 A minimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem 1.4 Convergence of Fourier series 1.5 The Parseval formula 1.6 Determination of the sum of certain trigonometric series Chapter 2. Orthogonal systems 2.1 Integration of complex-valued functions of a real variable 2.2 Orthogonal systems 2.3 Complete orthogonal systems 2.4 Integration of Fourier series 2.5 The Gram-Schmidt orthogonalization process 2.6 Sturm-Liouville problems Chapter 3. Orthogonal polynomials 3.1 The Legendre polynomials 3.2 Legendre series 3.3 The Legendre differential equation. The generating function of the Legendre polynomials 3.4 The Tchebycheff polynomials 3.5 Tchebycheff series 3.6 The Hermite polynomials. The Laguerre polynomials Chapter 4. Fourier transforms 4.1 Infinite interval of integration 4.2 The Fourier integral formula: a heuristic introduction 4.3 Auxiliary theorems 4.4 Proof of the Fourier integral formula. Fourier transforms 4.5 The convention theorem. The Parseval formula Chapter 5. Laplace transforms 5.1 Definition of the Laplace transform. Domain. Analyticity 5.2 Inversion formula 5.3 Further properties of Laplace transforms. The convolution theorem 5.4 Applications to ordinary differential equations Chapter 6. Bessel functions 6.1 The gamma function 6.2 The Bessel differential equation. Bessel functions 6.3 Some particular Bessel functions 6.4 Recursion formulas for the Bessel functions 6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions 6.6 Bessel series 6.7 The generating function of the Bessel functions of integral order 6.8 Neumann functions Chapter 7. Partial differential equations of first order 7.1 Introduction 7.2 The differential equation of a family of surfaces 7.3 Homogeneous differential equations 7.4 Linear and quasilinear differential equations Chapter 8. Partial differential equations of second order 8.1 Problems in physics leading to partial differential equations 8.2 Definitions 8.3 The wave equation 8.4 The heat equation 8.5 The Laplace equation Answers to exercises; Bibliography; Conventions; Symbols; Index Written on an advanced level, the book is aimed at advanced undergraduates and graduate students with a background in calculus, linear algebra, ordinary differential equations, and complex analysis. Over 260 carefully chosen exercises, with answers, encompass both routing and more challenging problems to help students test their grasp of the material. Nº de ref. de la librería BTE9780486661582

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Descripción Paperback. Estado de conservación: New. Paperback. This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 192 pages. 0.215. Nº de ref. de la librería 9780486661582

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