偏微分方程讲义

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作　者：	（俄罗斯）阿诺德著
出版社：	世界图书出版公司
丛编项：
标　签：	微积分

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ISBN：	9787510005046	出版时间：	2009-08-01	包装：	平装
开本：	24开	页数：	157	字数：

内容简介

　　In the mid-twentieth century the theory of partial differential equations wasconsidered the summit of mathematics， both because of the difficulty andsignificance of the problems it solved and because it came into existence laterthan most areas of mathematics.Nowadays many are inclined to look disparagingly at this remarkable areaof mathematics as an old-fashioned art of juggling inequalities or as a testingground for applications of functional analysis. Courses in this subject haveeven disappeared from the obligatory program of many universities （for ex-ample， in Paris）. Moreover， such remarkable textbooks as the classical three-volume work of Goursat have been removed as superfluous from the library ofthe University of Paris-7 （and only through my own intervention was it possi-ble to save them， along with the lectures of Klein， Picard， Hermite， Darboux，Jordan　）

作者简介

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图书目录

Preface to the Second Russian Edition
1. The General Theory for One First-Order Equation Literature
2. The General Theory for One First-Order Equation(Continued)Literature
3. Huygens' Principle in the Theory of Wave Propagation.
4. The Vibrating String (d'Alembert's Method)
　4.1. The General Solution
　4.2. Boundary-Value Problems and the Ca'uchy Problem
　4.3. The Cauehy Problem for an Infinite Strifig. d'Alembert's Formula
　4.4. The Semi-Infinite String
　4.5. The Finite String. Resonance
　4.6. The Fourier Method
5. The Fourier Method (for the Vibrating String)
　5.1. Solution of the Problem in the Space of Trigonometric Polynomials
　5.2. A Digression
　5.3. Formulas for Solving the Problem of Section 5.1
　5.4. The General Case
　5.5. Fourier Series
　5.6. Convergence of Fourier Series
　5.7. Gibbs' Phenomenon
6. The Theory of Oscillations. The Variational Principle Literature
7. The Theory of Oscillations. The Variational Principle(Continued)
8. Properties of Harmonic Functions
　8.1. Consequences of the Mean-Value Theorem
　8.2. The Mean-Value Theorem in the Multidimensional Case
9. The Fundamental Solution for the Laplacian. Potentials
　9.1. Examples and Properties
　9.2. A Digression. The Principle of Superposition
　9.3. Appendix. An Estimate of the Single-Layer Potential
10. The Double-Layer Potential
　10.1. Properties of the Double-Layer Potential
11 Spherical Functions. Maxwell's Theorem. The Removable
　Singularities Theorem
12. Boundary-Value Problems for Laplaee's Equation. Theory of Linear Equations and Systems
　12.1. Four Boundary-Value Problems for Laplace's Equation
　12.2. Existence and Uniqueness of Solutions
　12.3. Linear Partial Differential Equations and Their Symbols
A. The Topological Content of Maxwell's Theorem on the Multifield Representation of Spherical Functions
　A.1. The Basic Spaces and Groups
　A.2. Some Theorems of Real Algebraic Geometry
　A.3. From Algebraic Geometry to Spherical Functions
　A.4. Explicit Formulas
　A.5. Maxwell's Theorem and Cp2/con≈S4
　A.6. The History of Maxwell's Theorem
　Literature
B. Problems
　B.1. Material frorn the Seminars
　B.2. Written Examination Problems.