傅立叶分析和偏微分方程
2003-9
世界图书出版公司
R.Iorio,V.de,M.Iorio编
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This book is the outcome of several courses and seminar talks held at the Instituto de Matematica Pura e Aplicada (IMPA) over the years.It is a greatly modified version of a previous work by the authors,Equacoes Diferenciais Parciais, Uma lntroducao, (Projeto Euclides, IMPA,1978). It has a twofold purpose, namely to introduce the student to the basic concepts of Fourier analysis and provide illustrations of recent applications where these concepts were used to study various properties of the solutions of some important nonlinear evolution equations.
Preface Part One: Fourier Series and Periodic Distributions 1 Preliminaries 1.1 Basic Definitions and Examples 1.2 Classification into Types 1.3 Boundary and/or Initial Value Problems 1.4 Separation of Variables: Heat Flow in a Bar 1.5 The Schrodinger and the Wave Equations 1.6 The Dirichlet Problem in the Unit Circle 1.7 Maximum Principles and Uniqueness 2 Fourier Series: Basic Theory 2.1 Spaces of Periodic Functions and Sequences 2.2 The Fourier Transform 2.3 Geometric Interpretation 2.4 Decay and Differentiability 2.5 The Inversion Formula: Pointwise Convergence 2.6 Periodic Heat Flow 2.7 Approximate Identities and Summability 2.8 Cesaro Summability 3 Periodic Distributions and Sobolev Spaces 3.1 C Peiodic Funcitons 3.2 Perodic Distributions 3.3 Topological Remakes 3.4 Fourier Series in 3.5 The Convolution in 3.6 Sobolev SpacesPart Two:Applications to Partial Dfferential Equations 4 Linear Equations 5 Nonlinear Evolution Equations 6 The Korteweg-de Vries Equation 7 Distributions,Fourier Transform and Linear Equations 8 KdV,BO and FriendsAppendix A Tools from the Theory of ODEsAppendix B Commutator EstimatesBibliographyIndex
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经典教材，不错
虽然很好，可是我是高计算的，看着费力呀
理论性
很好的书，非常有用
从405开始居然重复出现221-228的内容！纸张质量也很差——我容忍了，但前者无法忍受，一般的参考文献没有列进去！书页还留有手指印，居然。我想换货可是邮费谁出啊？（我记得以前是自己掏腰包退货的）网友们在购买本书和其他当当产品时请留意。