Applied Mathematical Sciences

Fourier Series, Fourier Transform and Their Applications to Mathematical Physics

Authors: Serov, Valery

  • Each chapter is self-contained and can be read independently
  • Content grew from a series of half-semester courses given at University of Oulu
  • Contains material only previously published in scientific journals
  • Useful to both students and researchers who have applications in mathematical physics and engineering sciences
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eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-319-65262-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-65261-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts.

The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations.

Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering. 

About the authors

Valery Serov is Professor of Mathematics at the University of Oulu. Professor Serov received his PhD in Applied Mathematics in 1979 from Lomonosov Moscow State University.  He has over 120 publications, including 3 textbooks published in Russian.

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Table of contents (45 chapters)

  • Introduction

    Serov, Valery

    Pages 3-10

  • Formulation of Fourier Series

    Serov, Valery

    Pages 11-15

  • Fourier Coefficients and Their Properties

    Serov, Valery

    Pages 17-22

  • Convolution and Parseval’s Equality

    Serov, Valery

    Pages 23-25

  • Fejér Means of Fourier Series. Uniqueness of the Fourier Series.

    Serov, Valery

    Pages 27-31

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-319-65262-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-65261-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fourier Series, Fourier Transform and Their Applications to Mathematical Physics
Authors
Series Title
Applied Mathematical Sciences
Series Volume
197
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-65262-7
DOI
10.1007/978-3-319-65262-7
Hardcover ISBN
978-3-319-65261-0
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XI, 534
Number of Illustrations and Tables
4 b/w illustrations
Topics