《偏微分方程講義》是2009年8月1日世界圖書出版公司出版的圖書。本書主要為讀者提供了偏微分方程的講解方法，是適合老師使用的一部講義。
基本介紹
- 書名：偏微分方程講義
- 又名：Lectuers on Partial Differential Equations
- ISBN：7510005043, 9787510005046
- 頁數： 157頁
- 出版社： 世界圖書出版公司;
- 出版時間：2009年8月1日)
- 開本：24
- 正文語種：英語
作者簡介,內容簡介,目錄,
作者簡介
作者：(俄羅斯)阿諾德
內容簡介
《偏微分方程講義(英文版)》講述了：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 ）
目錄
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.
