偏微分方程(第4版影印版)(英文版)
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作者(美)F.约翰
出版社世界图书出版公司
ISBN9787519255800
出版时间2019-07
装帧其他
开本其他
定价79元
货号30670500
上书时间2024-05-22
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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
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")
内容摘要
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。
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