Fourier Series and Boundary Value Problems, 8/e (Paperback)

Ruel V Churchill Prof

Fourier Series and Boundary Value Problems, 8/e (Paperback)

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商品描述

Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus.

 There are two main objectives of this text. The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations.

 The book is a thorough revision of the seventh edition and much care is taken to give the student fewer distractions when determining solutions of eigenvalue problems, and other topics have been presented in their own sections like Gibbs' Phenomenon and the Poisson integral formula

商品描述(中文翻譯)

自1941年首版以來，這本經典教材由麥格羅希爾出版，介紹了傅立葉級數及其在工程和物理的偏微分方程邊界值問題中的應用。主要供具備普通微分方程和高等微積分背景的學生使用。

本書有兩個主要目標。第一個目標是介紹正交函數集的概念，以及使用這些函數集中的函數的級數表示。第二個目標是清晰地介紹在解邊界值問題時使用的經典分離變量方法，並借助這些表示來解決問題。

本書是第七版的全面修訂，非常注重讓學生在確定特徵值問題的解時減少干擾，並將其他主題以自己的章節呈現，如吉布斯現象和泊松積分公式。

目錄大綱

Chapter 1 Fourier Series
Chapter 2 Convergence of Fourier Series
Chapter 3 Partial Differential Equations of Physics
Chapter 4 The Fourier Method
Chapter 5 Boundary Value Problems
Chapter 6 Fourier Integrals and Applications
Chapter 7 Orthonormal Sets
Chapter 8 Sturm-Liouville Problems and Applications
Chapter 9 Bessel Functions and Applications
Chapter 10 Legendre Polynomials and Applications
Chapter 11 Verification of Solutions and Uniqueness

目錄大綱(中文翻譯)

第1章 傅立葉級數
第2章 傅立葉級數的收斂性
第3章 物理偏微分方程
第4章 傅立葉方法
第5章 邊界值問題
第6章 傅立葉積分與應用
第7章 正交集合
第8章 斯特姆-李維爾問題與應用
第9章 貝塞爾函數與應用
第10章 勒讓德多項式與應用
第11章 解的驗證與唯一性

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