偏微分方程.pdf

偏微分方程.pdf
 

书籍描述

编辑推荐
《偏微分方程(第4版)(英文版)》是由世界图书出版公司出版的。

作者简介
作者:(德国)约翰(John.F.)

目录
Chapter 1The 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 2Second-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 3Characteristic 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 4The 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 5Hyperbolic 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

序言
A considerable amount of new material has been added to this edition.There is an extensive discussion of real analytic functions of several variablesin Chapter 3. This permits estimation of the size of the domain of existencein the Cauchy-Kowalevski theorem. A first application of these estimatesconsists in a rigorous proof of a new version of Holmgren's uniquenesstheorem for linear analytic partial differential equations (only sketched inthe earlier editions). As another application (following Schauder) we give asecond proof for existence of solutions of the initial value problem forsymmetric hyperbolic systems in Chapter 5. Chapter 6 now includes a moredetailed study of the Hilbert spaces with applications to the boundarybehavior of solutions of the Dirichlet problem in higher dimensions. ToChapter 7 there has been added a proof of Widder's theorem on non-negativesolutions of the heat equation. Finally, a new chapter, Chapter 8, containsH. Lewy's construction of a linear differential equation without solutions.There are also more problems, designed, in part, to extend the materialdiscussed in the text. 1 am particularly indebted to my colleague Percy A. Deift of the CourantInstitute of New York University, to Prof. A. Garder of the Southern IllinoisUniversity at Edwardsville, Illinois, and to Dr. George Dassios of theNational Technical University of Athens, Greece, for taking the trouble tocompile lists of errors in the third edition. I hope that these have all beencorrected and not too many new ones added in the present edition.

文摘
插图:

偏微分方程

内容简介
《偏微分方程(第4版)(英文版)》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。《偏微分方程(第4版)(英文版)》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。《偏微分方程(第4版)(英文版)》是第4版,增加了全新的一章讲述无解线性方程的Lewy例子。

购买书籍

当当网购书 京东购书 卓越购书

PDF电子书下载地址

相关书籍

搜索更多