| 词条 | 傅里叶分析及其应用 |
| 释义 | 图书信息书 名: 傅里叶分析及其应用 作 者：弗雷特布拉德 出版社： 科学出版社 出版时间： 2011年6月1日 开本： 16开 定价: 69.00元 内容简介AcarefullypreparedaccountofthebasicideasinFourieranalysisanditsapplicationstothestudyofpartialdifferentialequations.Theauthorsucceedstomakehisexpositionaccessibletoreaderswithalimitedbackground,forexample,thosenotacquaintedwiththeLebesgueintegral.Readersshouldbefamiliarwithcalculus,linearalgebra,andcomplexnumbers.Atthesametime,theauthorhasmanagedtoincludediscussionsofmoreadvancedtopicssuchastheGibbsphenomenon,distributions,Sturm-Liouvilletheory,Cesarosummabilityandmulti-dimensionalFourieranalysis,topicswhichoneusuallydoesnotfindinbooksatthislevel.Avarietyofworkedexamplesandexerciseswillhelpthereaderstoapplytheirnewlyacquiredknowledge. 作者简介作者：（瑞典）弗雷特布拉德（Anders Vretblad） 图书目录Preface 1 Introduction 1.1 The classical partial differential equations 1.2 Well-posed problems 1.3 The one-dimensional wave equation 1.4 Fourier's method 2 Preparations 2.1 Complex exponentials 2.2 Complex-valued functions of a real variable 2.3 Ceshro summation of series 2.4 Positive summation kernels 2.5 The Riemann-Lebesgue lemma 2.6 *Some simple distributions 2.7 *Computing with ? 3 Laplace and Z transforms 3.1 The Laplace transfclrm 3.2 Operations 3.3 Applications to differential equations 3.4 Convolution 3.5 *Laplace transforms of distributions 3.6 The Z transform 3.7 Applications in control theory Summary of Chapter 3 4 FDurier series 4.1 Definitions 4.2 Dirichlet's and Fejdr's kernels；uniqueness 4.3 Diffrentiable functions 4.4 Pointwise convergence 4.5 Formulae for other periods 4.6 Some worked examples 4.7 The Gibbs phenomenon 4.8 *F0urier series for distributions Summary of Chapter 4 5 L2 Theory 5.1 Linear SlClaces over the complex numbers 5.2 Orthogonal projections 5.3 Some examples 5.4 Tlle F0urier system iS complete 5.5 Legendre polynomials 5.6 Other classical orthogonal polynomials Summary of Chapter 5 6 Separation of variables 6.1 The solution 0f F0urier's problem 6.2 Vaiations on Fourier's theme 6.3 The Dirichlet problem in the unit disk 6.4 Sturm-Liouville problems 6.5 Some singular Sturm-Liouville problems Summary of Chapter 6 7 Fourier transforms 7.1 Introduction 7.2 Definition of the Fourier transform 7.3 Properties 7.4 The inversion theorem 7.5 The convolution theorem 7.6 Plancherel's formula 7.7 Application 1 7.8 Application 2 7.9 Application 3：The sampling theorem 7.10 木Connection with the Laplace transfocrm 7.11 *Distributions and Fourier transforms Summary of Chapter 7 |
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