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偏微分方程第4版

版次：1
页数：
字数：
印刷时间：2009年06月01日
开本：24开
纸张：胶版纸
包装：平装
是否套装：否
国际标准书号ISBN：9787510004865

作者:（德）约翰　著出版社:世界图书出版公司出版时间:2009年06月

内容简介

本书是一部非常优秀的介绍偏微分方程的入门书籍，可以作为研究生阶段学习的基石。本书详尽地介绍了偏微分方程理论的重要方面，并从数学分析的角度做了进一步的探讨。本书是第4版，增加了全新的一章讲述无解线性方程的Lewy例子。

目　　录

Chapter 1　The Single First-Order Equation
　1. Introduction
　2. Examples
　3. Analytic Solution and Approximation Methods in a Simple Example
　　Problems
　4. Quasi-linear Equations
　5. The Cauchy Problem for the Quasi-linear Equation
　6. Examples
　　Problems
　7. The General First-Order Equation for a Function of Two Variables
　8. The Cauchy Problem
　9. Solutions Generated as Envelopes
　　Problems
Chapter 2　Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables

Chapter 1　The Single First-Order Equation 　1. Introduction 　2. Examples 　3. Analytic Solution and Approximation Methods in a Simple Example 　　Problems 　4. Quasi-linear Equations 　5. The Cauchy Problem for the Quasi-linear Equation 　6. Examples 　　Problems 　7. The General First-Order Equation for a Function of Two Variables 　8. The Cauchy Problem 　9. Solutions Generated as Envelopes 　　Problems Chapter 2　Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 　1. Characteristics for Linear and Quasi-linear Second-order Equations 　2. Propagation of Singularities 　3. The Linear Second-Order Equation 　　Problems 　4. The One-Dimensional Wave Equation 　　Problems 　5. Systems of First-Order Equations 　6. A Quasi-linear System and Simple Waves 　　Problem Chapter 3　Characteristic Manifolds and the Cauchy Problem 　1. Notation of Laurent Schwartz 　　Problems 　2. The Cauchy Problem 　　Problems 　3. Real Analytic Functions and the Cauchy-Kowalevski Theorem 　　(a) Multiple infinite series 　　　Problems 　　(b) Real analytic functions 　　　Problems 　　(c) Analytic and real analytic functions 　　　Problems 　　(d) The proof of the Cauchy-Kowalevski theorem 　　　Problems 　4. The Lagrange-Green Identity 　5. The Uniqueness Theorem of Holmgren 　　Problems 　6. Distribution Solutions 　　Problems Chapter 4　The Laplace Equation 　1. Green's Identity. Fundamental Solutions, and Poisson's Equation 　　Problems 　2. The Maximum Principle 　 Problems 　3. The Dirichlet Problem, Green's Function, and Poisson's Formula 　　Problems 　4. Proof of Existence of Solutions for the Dirichlet Problem Using Subharmonic Functions ("Perron's Method") 　　Problems 　5. Solution of the Dirichlet Problem by Hilbert-Space Methods 　　Problems Chapter 5　Hyperbolic Equations in Higher Dimensions 　1. The Wave Equation in n-Dimensional Space 　　(a) The method of spherical means 　 Problems 　 (b) Hadamard's method of descent 　 　Problems 　　…… Chapter 6　Higher-Order Elliptic Equations with Constant Chapter 7 Parabolic Equations Chapter 8 H.Lewy's Example of a Linear Equation Bibliography Glossary Index

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