作者：(美)泰勒
页数：654
出版社：世界图书出版公司
出版日期：2014
ISBN：9787510068133
电子书格式：pdf/epub/txt
内容简介
这是一套3卷集经典名著，第一版曾影印出版，广受好评。第2版新增内容312页（3卷），这是第1卷。本卷在引入连续统力学、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。读者对象：偏微分方程、数学物理、微分几何、调和分析和复分析等专业的研究生科研人员。
作者简介
M.E.Taylor是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
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。
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
……
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
……
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。
