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Introduction to Partial Differential Equations: From Fourier Series to BoundaryValue Problemsby Arne Broman
Synopses & ReviewsPublisher Comments:This wellwritten, advancedlevel text introduces students to Fourier analysis and some of its applications. The selfcontained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition. Synopsis:The selfcontained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. 266 exercises with solutions. 1970 edition. Description:Includes bibliographical references (p. 174175) and index.
Table of ContentsChapter 1. Fourier series
1.1 Basic concepts 1.2 Fourier series and Fourier coefficients 1.3 A mimimizing property of the Fourier coefficients. The RiemannLebesgue theorem 1.4 Convergence of Fourier series 1.5 The Parseval formula 1.6 Determination of the sum of certain trigonemetric series Chapter 2. Orthogonal systems 2.1 Integration of complexvalued functions of a real variable 2.2 Orthogonal systems 2.3 Complete orthogonal systems 2.4 Integration of Fourier series 2.5 The GramSchmidt orthogonalization process 2.6 SturmLiouville 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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