偏微分方程（第1卷）（第2版） [Partial Differential Equations I Basic Theory] pdf epub mobi txt 电子书 下载 2025

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[美] 泰勒（Taylor M.E.） 著

出版社： 世界图书出版公司

ISBN：9787510068133

版次：3

商品编码：11352187

包装：平装

外文名称：Partial Differential Equations I Basic Theory

开本：24开

出版时间：2014-01-01

用纸：胶版纸

页数：654

正文语种：英文

内容简介

　　《偏微分方程（第1卷）（第2版）》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。目次：偏微分方程和向量场基本理论；拉普拉斯方程和波动方程；傅里叶分析、分布函数和常系数线性偏微分方程；索伯列夫空间；线性椭圆方程；线性发展方程；泛函分析概述；流形、向量丛和李群。

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目录

Contents of Volumes II and III
Preface
1Basic Theory of ODE and Vector Fields
1 The derivative
2 Fundamental local existence theorem for ODE
3 Inverse function and implicit function theorems
4 Constant-coefficientlinear systems; exponentiation of matrices
5 Variable-coefficientlinear systems of ODE: Duhamels principle
6 Dependence of solutions on initial data and on other parameters
7 Flows and vector fields
8 Lie brackets
9 Commuting flows; Frobeniuss theorem
10 Hamiltoniansystems
11 Geodesics
12 Variational problems and the stationary action principle
13 Differential forms N
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

2 The Laplace Equation and Wave Equation
1 Vibrating strings and membranes
2 The divergence of a vector field
3The 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
9 The symbol of a differential operator and a general Green-Stokes formula
10 The Hodge Laplacian on k-forms
11 Maxwells equations
References

3 FourierAnalysisDistributions and Constant-Coefficient Linear PDE
1 Fourier series
2 Harmonic functions and holomorphic functions in the plane
3 The Fourier transform
4 Distributions and tempered distributions
5 The classical evolution equations
6 Radial distributions polar coordinates and Bessel functions
7 The method ofimages and Poissons summation formula
8 Homogeneous distributions and principal value distributions
9 Elliptic operators
10 Local solvability ofconstant-coefficientPDE
11 The discrete Fourier transform
12 The fast Fourier transform
A The mighty Gaussian and the sublime gamma function
References

4 SobolevSpaces
1 Sobolev spaces on Rn
2 The complex interpolation method
3 Sobolev spaces on compact manifolds
4 Sobolev spaces on bounded domains
5 The Sobolev spaces H50（Ω）
6 The Schwartzkerneltheorem
7 Sobolev spaces on rough domains
References

5 Linear Elliptic Equations
1 Existence and regularity of solutions to the Dirichlet problem
2 The weak and strong maximum principles
3 The Dirichlet problem on the ba
4 The Riemann mapping theorem （smooth boundary）
5 The Dirichlet problem on a domain with a rough boundary
6 The Riemann mapping theorem （rough boundary）
7 The Neumann boundary problem
8 The Hodge decomposition and harmonic forms
9 Natural boundary problems for the Hodge Laplacian
10 Isothermal coordinates and conformal structures on surfaces
11 General elliptic boundary problems
12 Operator properties ofregular boundary problems
……
6 Linear Evolution Equations
A Outline of FunctionaIAnalysis
B Marufolds Vector Bundles and Lie Groups
……

前言/序言

评分☆☆☆☆☆

《偏微分方程（第1卷）（第2版）》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。目次：偏微分方程和向量场基本理论；拉普拉斯方程和波动方程；傅里叶分析、分布函数和常系数线性偏微分方程；索伯列夫空间；线性椭圆方程；线性发展方程；泛函分析概述；流形、向量丛和李群。 这本教材是作者在20年来于中国台湾与大陆给初学微积分的学生所作的两学期讲义的基础上写成的。它的写法是经典的，程度介于传统的美国初等微积分教程与高等微积分教程的水平之间。若要选择有信誉的微积分书籍，它可能是一个好的选择。这不是说进度是快的。恰恰相反，书中每一个概念的引入，都是通过对许多例子的讨论并给出完整的细节来阐明的。大部分习题都是计算题，但也有一些非常规的问题，它们需要证明及解释。书末的“习题解答”中含有部分题（绝大多数为奇数号题目）的详细解答与解释，从而使本

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Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds， it has developed into a body of material that interacts with many branches of math- ematics， such as differential geometry， complex analysis， and harmonic analysis， as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics.

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包装还行

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一个方向的书要多买几本不同人写的，才能从不同的角度去看！

评分☆☆☆☆☆

专业用的书，还好

评分☆☆☆☆☆

Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds， it has developed into a body of material that interacts with many branches of math- ematics， such as differential geometry， complex analysis， and harmonic analysis， as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics.

评分☆☆☆☆☆

这本书算是经典了，过段时间再看

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古代人们的生活更多地依赖于直接利用，或从中提取所需要的东西。由于这些物质的固有性能满足不了人们的需求，便产生了各种加工技术，把天然物质转变成具有多种性能的新物质，并且逐步在工业生产的规模上付诸实现。起初，生产这类产品的是手工作坊，后来演变为工厂，并逐渐形成了一个特定的生产部门，即化学工业。随着生产力的发展，有些生产部门，如冶金、炼油、造纸、制革等，已作为独立的生产部门从化学工业中划分出来。当大规模

评分☆☆☆☆☆

很好用，值得够买，下次还来