基本信息
- 原书名：Fourier Analysis and Its Applications
- 原出版社： Springer
- 作者： Anders Vretblad
- 丛书名： 国外数学名著系列(影印版)
- 出版社：科学出版社
- ISBN：9787030313775
- 上架时间：2011-7-14
- 出版日期：2011 年6月
- 开本：16开
- 页码：269
- 版次：1-1
- 所属分类：数学 > 分析 > 傅里叶分析与小波分析
内容简介
书籍
数学书籍
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.
数学书籍
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.
目录
《傅里叶分析及其应用(影印版)》
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 Cesaro summation of series
2.4 Positive summation kernels
2.5 The Riemann-Lebesgue lemma
2.6 *Some simple distributions
2.7 *Computing with δ
3 Laplace and Z transforms
3.1 The Laplace transform
3.2 Operations
3.3 Applications to differential equations
3.4 Convolution
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 Cesaro summation of series
2.4 Positive summation kernels
2.5 The Riemann-Lebesgue lemma
2.6 *Some simple distributions
2.7 *Computing with δ
3 Laplace and Z transforms
3.1 The Laplace transform
3.2 Operations
3.3 Applications to differential equations
3.4 Convolution
