图文详情
- ISBN:9787040469356
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:16开
- 页数:754
- 出版时间:2017-01-05
- 条形码:9787040469356 ; 978-7-04-046935-6
本书特色
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
内容简介
这是当今关于偏微分方程 (PDE) 的*权威教材的第二版。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。本书内容广泛,阐述清晰,已经是PDE方面经典的研究生教材。
目录
Preface to second editionPreface to first edition1. 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. ReferencesPART I: REPRESENTATION FORMULAS FOR SOLUTIONS2. 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. References3. 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 ……
4. Other Ways to Represent SolutionsPART II: THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS5. Sobolev Spaces6. Second-Order Elliptic Equations7. Linear Evolution EquationsPART III: THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS8. The Calculus of Variations9. Nonvariational Techniques10. Hamilton-Jacobi Equations11. Systems of Conservation Laws12. Nonlinear Wave EquationsAPPENDICESAppendix A: NotationAppendix B: InequalitiesAppendix C: CalculusAppendix D: Functional AnalysisAppendix E: Measure TheoryBibliographyIndex
展开全部
本类五星书
浏览历史
本类畅销
-
13次时空穿梭之旅
¥18.7¥59.0 -
勒维特之星-大发现系列丛书
¥5.0¥16.0 -
递归求解
¥9.4¥28.0 -
核科学基本原理
¥14.5¥39.8 -
130种美鸟彩图馆
¥15.3¥39.8 -
技术史入门
¥15.4¥48.0 -
天文学卷-异想天开-古今中外天文简史-《中国大百科全书》普及版
¥6.1¥19.0 -
科学哲学——科学家的视角
¥43.9¥78.0 -
发现之旅数的王国——世界共通的语言
¥41.1¥68.0 -
声音简史
¥23.9¥52.0 -
青少年及成.人普林斯顿数学分析读本
¥43.8¥69.0 -
趣味物理学问答
¥16.6¥46.0 -
疯狂实验史-II
¥23.7¥36.0 -
世纪幽灵-走近量子纠缠
¥9.4¥28.0 -
为了人人晓得相对论
¥4.9¥13.5 -
北宋科技思想研究纲要
¥9.8¥26.0 -
概率统计
¥5.7¥11.0 -
新科学时代的思考
¥46.2¥78.0 -
智慧宫029梦游者:西方宇宙观念的变迁
¥75.5¥128.0 -
现代生物特征识别技术
¥34.8¥49.0