International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: http://www.sciepub.com/journal/ijpdea Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2014, 2(3), 44-57
DOI: 10.12691/ijpdea-2-3-2
Open AccessArticle

Fourier Transform Methods for Partial Differential Equations

Naol Tufa Negero1,

1Department of Mathematics, College of Natural and Computational Science, Wollega University, P. box. 395

Pub. Date: June 19, 2014

Cite this paper:
Naol Tufa Negero. Fourier Transform Methods for Partial Differential Equations. International Journal of Partial Differential Equations and Applications. 2014; 2(3):44-57. doi: 10.12691/ijpdea-2-3-2

Abstract

The purpose of this seminar paper is to introduce the Fourier transform methods for partial differential equations. The introduction contains all the possible efforts to facilitate the understanding of Fourier transform methods for which a qualitative theory is available and also some illustrative examples was given. The resulting Fourier transform maps a function defined on physical space to a function defined on the space of frequencies, whose values quantify the “amount” of each periodic frequency contained in the original function then inverse Fourier transform reconstructs the original function from its transform.

Keywords:
fourier transform partial differential equations

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References:

[1]  Agarwal R. and R. Donal, 2009. Ordinary and partial differential Equations With Special Functions, Fourier Series, and Boundary value Problems, Spring Street, New York.
 
[2]  Asmar N., 2000. Partial Differential Equations With Foureir Series And Boundary Value Problems, 2nd edition, Pealson Prentice Hall, United States of America.
 
[3]  Bandaru V., 2008. Higher Engineerering Mathematics, Tata Mc Graw-Hill Publishing Company Limited, Newdelhi.
 
[4]  Duffy D., 1998. Advanced Engineering Mathematics, CRC Press LLC, New York.
 
[5]  Haberman R., 1987. Elementary Applied partial Differential equations With Fourier series and Boundary Value Problems, Englewood Cliffs, New Jersey.
 
[6]  Pinkus A. and Zafrany S., 1997. Fourier Series and Integral Transforms, Cabridge University Press, United Kingdom.
 
[7]  Puri P., 1997. Partial Differential Equations and Mathematica, CRC Press, New York.
 
[8]  Tveito A., 1998. Introduction to Partial Differential Equations A Computational approach, Springer-Verlag, New York, Inc.