傅里叶分析及其应用 : 第2版

傅里叶分析及其应用 : 第2版

(瑞典) 弗雷特布拉德 (Vretblad,A.) , 主编

出版社:科学出版社

年代:2011

定价:69.0

书籍简介:

这本专著介绍了偏微分方程中用到的傅里叶分析及其应用的基本知识,作者以深入浅出的语言介绍此理论,即使基础知识较少的读者阅读此专著也不会觉得困难。其次,作者还介绍了更前沿的理论,例如,Gibbs现象,Sturm-Liouville定理,多维傅里叶分析等,而这些理论在其他此类专著中基本很难看到。而且此书中的一系列例题和习题可以帮助读者更好的理解书中的知识。

书籍目录:

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

内容摘要:

《傅里叶分析及其应用(影印版)》是国外数学名著系列之一。《傅里叶分析及其应用(影印版)》内容简介:A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.【作者简介】作者:(瑞典)弗雷特布拉德(Anders Vretblad)

书籍规格:

书籍详细信息
书名傅里叶分析及其应用 : 第2版站内查询相似图书
丛书名国外数学名著系列
9787030313775
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出版地北京出版单位科学出版社
版次影印本印次1
定价(元)69.0语种英文
尺寸24 × 17装帧精装
页数 270 印数

书籍信息归属:

傅里叶分析及其应用 : 第2版是科学出版社于2011.6出版的中图分类号为 O174.2 的主题关于 傅里叶分析-英文 的书籍。