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偏微分方程-115-第1卷-第2版 本书特色
泰勒编著《偏微分方程(第1卷第2版)》在引入连续统力学、电磁学和复分析和实例的基础上,介绍了许多解决实际问题的方法,如傅里叶分析、分布理论和索伯列夫空间,这些方法可用于解决线性偏微分方程的基本问题。书中涉及的线性偏微分方程有拉普拉斯方程、热方程、波动方程、一般椭圆方程、双曲方程和抛物方程等。
偏微分方程-115-第1卷-第2版 目录
Contents of Volumes II and III
Preface
Basic Theory of ODE and Vector Fields
l The derivative
2 Fundamental local existence theorem for ODE
3 Inverse function and implicit function theorems
4 Constant-coefficient linear systems; exponentiation of matrices
5 Variable-coefficient linear systems of ODE: Duhamel's principle
6 Dependence of solutions on initial data and on other parameters
7 Flows and vector fields
8 Lie brackets
9 Commuting flows; Frobenius's theorem
10 Hamiltonian systems
11 Geodesics
12 Variational problems and the stationary action principle
Contents of Volumes II and III
Preface
Basic Theory of ODE and Vector Fields
l The derivative
2 Fundamental local existence theorem for ODE
3 Inverse function and implicit function theorems
4 Constant-coefficient linear systems; exponentiation of matrices
5 Variable-coefficient linear systems of ODE: Duhamel's principle
6 Dependence of solutions on initial data and on other parameters
7 Flows and vector fields
8 Lie brackets
9 Commuting flows; Frobenius's theorem
10 Hamiltonian systems
11 Geodesics
12 Variational problems and the stationary action principle
13 Differential forms
14 The symplectic form and canonical transformations
15 First-order, scalar, nonlinear PDE
16 Completely integrable hamiltonian systems
17 Examples of integrable systems; central force problems
18 Relativistic motion
19 Topological applications of differential forms
20 Critical points and index of a vector field
A Nonsmooth vector fields
References
The Laplace Equation and Wave Equation
1 Vibrating strings and membranes
2 The divergence of a vector field
3 The covariant derivative and divergence of tensor fields
4 The Laplace operator on a Riemannian manifold
5 The wave equation on a product manifold and energy conservation
6 Uniqueness and finite propagation speed
7 Lorentz manifolds and stress-energy tensors
8 More general hyperbolic equations; energy estimates
……
偏微分方程-115-第1卷-第2版 节选
泰勒编著《偏微分方程(第1卷第2版)》在引入连续统力学、电磁学和复分析和实例的基础上,介绍了许多解决实际问题的方法,如傅里叶分析、分布理论和索伯列夫空间,这些方法可用于解决线性偏微分方程的基本问题。书中涉及的线性偏微分方程有拉普拉斯方程、热方程、波动方程、一般椭圆方程、双曲方程和抛物方程等。
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