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Introduction to Partial Differential Equations: From Fourier Series to Boundary-Value Problems

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Introduction to Partial Differential Equations: From Fourier Series to Boundary-Value Problems Cover

 

Synopses & Reviews

Publisher Comments:

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 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 self-contained 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. 174-175) and index.

Table of Contents

Chapter 1. Fourier series

  1.1 Basic concepts

  1.2 Fourier series and Fourier coefficients

  1.3 A mimimizing 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 trigonemetric 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

Product Details

ISBN:
9780486661582
Author:
Broman, Arne
Publisher:
Dover Publications
Author:
Mathematics
Location:
New York :
Subject:
Mathematics
Subject:
Differential Equations
Subject:
Algebra - General
Subject:
Differential Equations - Partial Differential Equations
Subject:
Differential equations, partial
Subject:
General Mathematics
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
v. 8
Publication Date:
20101031
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
192
Dimensions:
8.25 x 5.63 in 0.5 lb

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Related Subjects

Science and Mathematics » Electricity » General Electronics
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » General
Science and Mathematics » Physics » Meteorology

Introduction to Partial Differential Equations: From Fourier Series to Boundary-Value Problems New Trade Paper
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Product details 192 pages Dover Publications - English 9780486661582 Reviews:
"Synopsis" by ,
The self-contained 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.
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