图书信息
图书目录
偏微分方程：理论和应用（影印版）
暂无简介
作者：
András Vasy
定价：
135.00元
出版时间：
2021-03-09
ISBN：
978-7-04-055651-3
物料号：
55651-00
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
重点项目：
暂无
版面字数：
500.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
