调和函数理论

出版时间：2004-4  出版社：世界图书出版公司  作者：Paul Bourdon  页数：259  
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内容概要

Harmonic functions--the solutions of Laplace's equation--play a crucial role in many areas of mathematics, physics, and engineering. But learning about them is not always easy. At times the authors have agreed with Lord Kelvin and Peter Tait, who wrote ([18], Preface) There can be but one opinion as to the beauty and utility of this analysis of Laplace; but the manner in which it has been hitherto presented has seemed repulsive to the ablest mathematicians, and difficult to ordinary mathematical students.

书籍目录

Preface Acknowledgments CHAPTER 1   Basic Properties of Harmonic Functions   Definitions and Examples   Invariance Properties   The Mean-Value Property   The Maximum Principle   The Poisson Kernel for the Ball   The Dirichlet Problem for the Ball   Converse of the Mean-Value Property   Real Analyticity and Homogeneous Expansions   Origin of the Term "Harmonic"   Exercises CHAPTER 2 Bounded Harmonic Functions   Liouvfile‘s Theorem   Isolated Singularities   Cauchy‘s Estimates   Normal Families   Maximum Principles  Limits Along Rays  Bounded Harmonic Functions on the Ball  ExercisesCHPATER 3  Positive Harmonic FunctionsCHPATER 4  The Kelvin TransformCHPATER 5  Harmonic PolynomialsCHPATER 6  Harmonic Hardy SpacesCHPATER 7  Harmonic Funtions on Half-SpacesCHAPTER 8  Harmonic Bergaman SpacesCHAPTER 9  The Decomposition TheoremCHAPTER 10  Annular RegionsCHAPTER 11  The Dirichlet Problem and Boundary BehaviorAPPENDIX A Volume,Surface Area,and Interation on SpheresAPPENDIX B Harmonic Function Theory and MathematicaReferencesSymbol IndexIndex

用户评论 (总计5条)

•   很好的书哦。努力学习
•   需要的时候还是要常翻番的
•   比较容易看懂
•   都是为了考试而买！看着还行！
•   内容没有看，但觉得有点坑，原来就是本一般平装的书，纸质也有点差，竟然四十多，不过，也可能是书的内容很有价值吧，看过后再评论。