偏微分方程（第4版）（英文版）

图书标准信息

• 作者 [德]约翰 著
• 出版社 世界图书出版公司
• 出版时间 2009-06
• 版次 1
• ISBN 9787510004865
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 249页
• 正文语种 英语

【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。

【目录】

Chapter1　TheSingleFirst-OrderEquation
1.Introduction
2.Examples
3.AnalyticSolutionandApproximationMethodsinaSimpleExample
Problems
4.Quasi-linearEquations
5.TheCauchyProblemfortheQuasi-linearEquation
6.Examples
Problems
7.TheGeneralFirst-OrderEquationforaFunctionofTwoVariables
8.TheCauchyProblem
9.SolutionsGeneratedasEnvelopes
Problems
Chapter2　Second-OrderEquations:HyperbolicEquationsforFunctionsofTwoIndependentVariables
1.CharacteristicsforLinearandQuasi-linearSecond-orderEquations
2.PropagationofSingularities
3.TheLinearSecond-OrderEquation
Problems
4.TheOne-DimensionalWaveEquation
Problems
5.SystemsofFirst-OrderEquations
6.AQuasi-linearSystemandSimpleWaves
Problem
Chapter3　CharacteristicManifoldsandtheCauchyProblem
1.NotationofLaurentSchwartz
Problems
2.TheCauchyProblem
Problems
3.RealAnalyticFunctionsandtheCauchy-KowalevskiTheorem
(a)Multipleinfiniteseries
Problems
(b)Realanalyticfunctions
Problems
(c)Analyticandrealanalyticfunctions
Problems
(d)TheproofoftheCauchy-Kowalevskitheorem
Problems
4.TheLagrange-GreenIdentity
5.TheUniquenessTheoremofHolmgren
Problems
6.DistributionSolutions
Problems
Chapter4　TheLaplaceEquation
1.GreensIdentity.FundamentalSolutions,andPoissonsEquation
Problems
2.TheMaximumPrinciple
Problems
3.TheDirichletProblem,GreensFunction,andPoissonsFormula
Problems
4.ProofofExistenceofSolutionsfortheDirichletProblemUsingSubharmonicFunctions("PerronsMethod")
Problems
5.SolutionoftheDirichletProblembyHilbert-SpaceMethods
Problems
Chapter5　HyperbolicEquationsinHigherDimensions
1.TheWaveEquationinn-DimensionalSpace
(a)Themethodofsphericalmeans
Problems
(b)Hadamardsmethodofdescent
　Problems
……
Chapter6　Higher-OrderEllipticEquationswithConstant
Chapter7ParabolicEquations
Chapter8H.LewysExampleofaLinearEquation
Bibliography
Glossary
Index