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偏微分方程：理论和应用（影印版）

样章
作者：
András Vasy
定价：
135.00元
ISBN：
978-7-04-055651-3
版面字数：
500.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2021-03-09
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
偏微分方程
暂无
  • 前辅文
  • Chapter 1. Introduction
    • §1. Preliminaries and notation
    • §2. Partial differential equations
    • Additional material: More on normed vector spaces and metric spaces
    • Problems
  • Chapter 2. Where do PDE come from?
    • §1. An example: Maxwell’s equations
    • §2. Euler-Lagrange equations
    • Problems
  • Chapter 3. First order scalar semilinear equations
    • Additional material: More on ODE and the inverse function theorem
    • Problems
  • Chapter 4. First order scalar quasilinear equations
    • Problems
  • Chapter 5. Distributions and weak derivatives
    • Additional material: The space L1
    • Problems
  • Chapter 6. Second order constant coefficient PDE: Types and d’Alembert’s solution of the wave equation
    • §1. Classification of second order PDE
    • §2. Solving second order hyperbolic PDE on R2
    • Problems
  • Chapter 7. Properties of solutions of second order PDE: Propagation, energy estimates and the maximum principle
    • §1. Properties of solutions of the wave equation: Propagation phenomena
    • §2. Energy conservation for the wave equation
    • §3. The maximum principle for Laplace’s equation and the heat equation
    • §4. Energy for Laplace’s equation and the heat equation
    • Problems
  • Chapter 8. The Fourier transform: Basic properties, the inversion formula and the heat equation
    • §1. The definition and the basics
    • §2. The inversion formula
    • §3. The heat equation and convolutions
    • §4. Systems of PDE
    • §5. Integral transforms
    • Additional material: A heat kernel proof of the Fourier inversion formula
    • Problems
  • Chapter 9. The Fourier transform: Tempered distributions, the wave equation and Laplace’s equation
    • §1. Tempered distributions
    • §2. The Fourier transform of tempered distributions
    • §3. The wave equation and the Fourier transform
    • §4. More on tempered distributions
    • Problems
  • Chapter 10. PDE and boundaries
    • §1. The wave equation on a half space
    • §2. The heat equation on a half space
    • §3. More complex geometries
    • §4. Boundaries and properties of solutions
    • §5. PDE on intervals and cubes
    • Problems
  • Chapter 11. Duhamel’s principle
    • §1. The inhomogeneous heat equation
    • §2. The inhomogeneous wave equation
    • Problems
  • Chapter 12. Separation of variables
    • §1. The general method
    • §2. Interval geometries
    • §3. Circular geometries
    • Problems
  • Chapter 13. Inner product spaces, symmetric operators, orthogonality
    • §1. The basics of inner product spaces
    • §2. Symmetric operators
    • §3. Completeness of orthogonal sets and of the inner product space
    • Problems
  • Chapter 14. Convergence of the Fourier series and the Poisson formula on disks
    • §1. Notions of convergence
    • §2. Uniform convergence of the Fourier transform
    • §3. What does the Fourier series converge to?
    • §4. The Dirichlet problem on the disk
    • Additional material: The Dirichlet kernel
    • Problems
  • Chapter 15. Bessel functions
    • §1. The definition of Bessel functions
    • §2. The zeros of Bessel functions
    • §3. Higher dimensions
    • Problems
  • Chapter 16. The method of stationary phase
    • Problems
  • Chapter 17. Solvability via duality
    • §1. The general method
    • §2. An example: Laplace’s equation
    • §3. Inner product spaces and solvability
    • Problems
  • Chapter 18. Variational Problems
    • §1. The finite dimensional problem
    • §2. The infinite dimensional minimization
    • Problems
  • Bibliography
  • Index

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