ENGLISH

Early Fourier Analysis

By Hugh L. Montgomery

Book information

Publisher
American Mathematical Society
Year
2014
ISBN
1470415607, 9781470415600
Language
english
Format
DJVU
Filesize
5 MB (4903603 bytes)
Series
Pure and Applied Undergraduate Texts 22
Pages
400\401
Orientation
portrait
Paginated
no
Scanned
yes
Time added
2016-04-21 16:16:50
Математика;Математический анализ

Description

Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line. The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a junior-senior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.

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