《偏微分方程：第1卷》是2014年世界圖書出版公司出版的圖書。
基本介紹
- 中文名：偏微分方程：第1卷
- 作者：[美]Michael E.Taylor
- 類別：理學圖書
- 出版社：世界圖書出版公司
- 出版時間：2014年
- 開本：16 開
- 裝幀：平裝
- ISBN：9787510068133
內容簡介
圖書目錄
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 ofmatrices
5 Variable-coefficient linear systems of ODE: Duhamel'sprinciple
6 Dependence of solutions on initial data and on otherparameters
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 actionprinciple
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 forceproblems
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 tensorfields
4 The Laplace operator on a Riemannian manifold
5 The wave equation on a product manifold and energyconservation
6 Uniqueness and finite propagation speed
7 Lorentz manifolds and stress-energy tensors
8 More general hyperbolic equations; energy estimates
……
