偏微分方程(第二版)(英文版) [Partial Differential Equations(Second Edition)] pdf epub mobi txt 電子書 下載 2024
內容簡介
這是當今偏微分方程(PDE)教材的第二版。它給齣瞭PDE理論學習中現代技術的總覽,特彆注重非綫性方程。《偏微分方程(第二版)(英文版)》內容廣泛、闡述清晰,已經是PDE方麵經典的研究生教材。在本版中,作者做瞭大量改動,包括
·新增非綫性波動方程的一章
·超過80個新習題
·許多新的小節
·大大擴充瞭參考文獻
內頁插圖
精彩書評
★此教科書的第二版講述瞭PDE多的研究方嚮,更值得稱贊的是,Evans教授花瞭大量時間和精力來使一本已經十分成功和精彩的書變得更好。無需贅言,我毫無保留熱情地給每一個有興趣研究PDE的人推薦此書。
——Mathematical Reviews
★對那些準備做PDE研究的研究生來說,此書是非常寶貴的。我希望能在研究生院使用它。
——MAA Reviews
目錄
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)] 下載 mobi epub pdf txt 電子書
偏微分方程(第二版)(英文版) [Partial Differential Equations(Second Edition)] pdf epub mobi txt 電子書 下載