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Lectures on Cauchy's Problem in Linear Partial Differential Equations

样章
作者：
Hadamard（阿达马）
定价：
98.00元
ISBN：
978-7-04-044804-7
版面字数：
490.000千字
开本：
16开
全书页数：
283页
装帧形式：
精装
重点项目：
暂无
出版时间：
2016-03-07
物料号：
44804-00
读者对象：
高等教育
一级分类：
数学与统计学类
二级分类：
数学与应用数学专业课
三级分类：
偏微分方程

这些讲义是一个开创性的研究。 基于Riemann, Kirchhoff和Volterra的研究，运用其关于所有正常的双曲型方程组的球面和柱面波的相关理论，阿达马扩展和改进了Volterra的工作。主题包括柯西问题的一般性质，基本公式和基本解，具有奇数独立变量的方程和具有偶数独立变量的方程。

  • Front Matter
  • BOOK I. GENERAL PROPERTIES OF CAUCHY’S PROBLEM
    • I. CAUCHY’S FUNDAMENTAL THEOREM CHARACTERISTICS
    • II. DISCUSSION OF CAUCHY’S RESULT
  • BOOK II. THE FUNDAMENTAL FORMULA AND THE ELEMENTARY SOLUTION
    • I. CLASSIC CASES AND RESULTS
    • II. THE FUNDAMENTAL FORMULA
    • III. THE ELEMENTARY SOLUTION
      • 1. General Remarks
      • 2. Solutions with an Algebroid Singularity
      • 3. The Case of the Characteristic Conoid.The Elementary Solution
      • Additional Note on the Equations of Geodesics
  • BOOK III. THE EQUATIONS WITH AN ODD NUMBER OF INDEPENDENT VARIABLES
    • I. INTRODUCTION OF A NEW KIND OF IMPROPER INTEGRAL
      • 1. Discussion of Preceding Results
      • 2. The Finite Part of an Infinite Simple Integral
      • 3. The Case of Multiple Integrals
      • 4. Some Important Examples
    • II. THE INTEGRATION FOR AN ODD NUMBER OF INDEPENDENT VARIABLES
    • III. SYNTHESIS OF THE SOLUTION OBTAINED
    • IV. APPLICATIONS TO FAMILIAR EQUATIONS
  • BOOK IV. THE EQUATIONS WITH AN EVEN NUMBER OF INDEPENDENT VARIABLES AND THE METHOD OF DESCENT
    • I. INTEGRATION OF THE EQUATION IN 2m1 VARIABLES
      • 1. General Formulæ
      • 2. Familiar Examples
      • 3. Application to a Discussion of Cauchy’s Problem
    • II. OTHER APPLICATIONS OF THE PRINCIPLE OF DESCENT
      • 1. Descent from m Even to m Odd
      • 2. Properties of the Coefficients in the Elementary Solution
      • 3. Treatment of Non-Analytic Equations
  • INDEX