偏微分方程-115-第1卷-第2版_PDF下载[111MB-百度云]泰勒

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。

]

本书特色

[

]

Contents of Volumes II and IIIPrefaceBasic Theory of ODE and Vector Fieldsl The derivative2 Fundamental local existence theorem for ODE3 Inverse function and implicit function theorems4 Constant-coefficient linear systems; exponentiation of matrices5 Variable-coefficient linear systems of ODE: Duhamel’s principle6 Dependence of solutions on initial data and on other parameters7 Flows and vector fields8 Lie brackets9 Commuting flows; Frobenius’s theorem10 Hamiltonian systems11 Geodesics12 Variational problems and the stationary action principle Contents of Volumes II and IIIPrefaceBasic Theory of ODE and Vector Fieldsl The derivative2 Fundamental local existence theorem for ODE3 Inverse function and implicit function theorems4 Constant-coefficient linear systems; exponentiation of matrices5 Variable-coefficient linear systems of ODE: Duhamel’s principle6 Dependence of solutions on initial data and on other parameters7 Flows and vector fields8 Lie brackets9 Commuting flows; Frobenius’s theorem10 Hamiltonian systems11 Geodesics12 Variational problems and the stationary action principle13 Differential forms14 The symplectic form and canonical transformations15 First-order, scalar, nonlinear PDE16 Completely integrable hamiltonian systems17 Examples of integrable systems; central force problems18 Relativistic motion19 Topological applications of differential forms20 Critical points and index of a vector fieldA Nonsmooth vector fields ReferencesThe Laplace Equation and Wave Equation1 Vibrating strings and membranes2 The divergence of a vector field3 The covariant derivative and divergence of tensor fields4 The Laplace operator on a Riemannian manifold5 The wave equation on a product manifold and energy conservation6 Uniqueness and finite propagation speed7 Lorentz manifolds and stress-energy tensors8 More general hyperbolic equations; energy estimates……