内容简介
这是当今偏微分方程(PDE)教材的第二版。它给出了PDE理论学习中现代技术的总览,特别注重非线性方程。《偏微分方程(第二版)(英文版)》内容广泛、阐述清晰,已经是PDE方面经典的研究生教材。在本版中,作者做了大量改动,包括
·新增非线性波动方程的一章
·超过80个新习题
·许多新的小节
·大大扩充了参考文献
内页插图
精彩书评
★此教科书的第二版讲述了PDE多的研究方向,更值得称赞的是,Evans教授花了大量时间和精力来使一本已经十分成功和精彩的书变得更好。无需赘言,我毫无保留热情地给每一个有兴趣研究PDE的人推荐此书。
——Mathematical Reviews
★对那些准备做PDE研究的研究生来说,此书是非常宝贵的。我希望能在研究生院使用它。
——MAA Reviews
目录
Preface to second edition
Preface to first edition
1. Introduction
1.1. Partial differential equations
1.2. Examples
1.2.1. Single partial differential equations
1.2.2. Systems of partial differential equations
1.3. Strategies for studying PDE
1.3.1. Well-posed problems, classical solutions
1.3.2. Weak solutions and regularity
1.3.3. Typical difficulties
1.4. Overview
1.5. Problems
1.6. References
PART I: REPRESENTATION FORMULAS FOR SOLUTIONS
2. Four Important Linear PDE
2.1. Transport equation
2.1.1. Initial-value problem
2.1.2. Nonhomogeneous problem
2.2. Laplace's equation
2.2.1. Fundamental solution
2.2.2. Mean-value formulas
2.2.3. Properties of harmonic functions
2.2.4. Green's function
2.2.5. Energy methods
2.3. Heat equation
2.3.1. Fundamental solution
2.3.2. Mean-value formula
2.3.3. Properties of solutions
2.3.4. Energy methods
2.4. Wave equation
2.4.1. Solution by spherical means
2.4.2. Nonhomogeneous problem
2.4.3. Energy methods
2.5. Problems .
2.6. References
3. Nonlinear First-Order PDE
3.1. Complete integrals, envelopes
3.1.1. Complete integrals
3.1.2. New solutions from envelopes
3.2. Characteristics
3.2.1. Derivation of characteristic ODE
3.2.2. Examples
3.2.3. Boundary conditions
3.2.4. Local solution
3.2.5. Applications
3.3. Introduction to Hamilton-Jacobi equations
3.3.1. Calculus of variations, Hamilton's ODE
3.3.2. Legendre transform, Hopf-Lax formula
3.3.3. Weak solutions, uniqueness
3.4. Introduction to conservation laws
3.4.1. Shocks, entropy condition
3.4.2. Lax-Oleinik formula
3.4.3. Weak solutions, uniqueness
……
PART Ⅱ: THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS
PART Ⅲ: THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
APPENDICES
Bibliography
Index
偏微分方程(第二版)(英文版) [Partial Differential Equations(Second Edition)] 下载 mobi epub pdf txt 电子书 格式
偏微分方程(第二版)(英文版) [Partial Differential Equations(Second Edition)] 下载 mobi pdf epub txt 电子书 格式 2024
偏微分方程(第二版)(英文版) [Partial Differential Equations(Second Edition)] mobi epub pdf txt 电子书 格式下载 2024