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**About this book :- **
**Early Fourier Analysis ** written by
** Hugh L. Montgomery **.

This book could be used for capstone course of an undergraduate program or for beginning graduate students as a way to motivate the study of the Lebegue integral.

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

(Hugh Montgomery)

**Book Detail :- **
** Title: ** Early Fourier Analysis
** Edition: **
** Author(s): ** Hugh L. Montgomery
** Publisher: ** American Mathematical Society
** Series: ** Pure and Applied Undergraduate Texts
** Year: ** 2014
** Pages: ** 401
** Type: ** PDF
** Language: ** English
** ISBN: ** 1470415607,978-1-4704-1560-0,9781470420383,1470420384
** Country: ** US
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**About Author :- **
The author ** Hugh Lowell Montgomery ** (born, 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis. As a Marshall scholar, Montgomery earned his Ph.D. from the University of Cambridge. For many years, Montgomery has been teaching at the University of Michigan.

He is best known for Montgomery's pair correlation conjecture, his development of the large sieve methods and for co-authoring (with Ivan M. Niven and Herbert Zuckerman) one of the standard introductory number theory texts, An Introduction to the Theory of Numbers, now in its fifth edition (ISBN 0471625469). In 2012 he became a fellow of the American Mathematical Society.

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**Book Contents :- **
**Early Fourier Analysis ** written by
** Hugh L. Montgomery **
cover the following topics.
'

0. Background

1. Complex Numbers

2. The Discrete Fourier Transorm

3. Fourier Coefficeints and First Fourier Series

4. Summability of Fourier Series

5. Fourier Series in Mean Square

6. Trigonometric Polyomials

7. Absolutely Convergent Fourier Series

8. Convergence of Fourier Series

9. Application of Fourier Series

10. The Fourier Tranform

11.Higher Dimensions

Appendix B the Binomial Theorem

Appendix C Chebyshev Polynomials

Appendix F Applications of the Fundamental Theorem of Algebra

Appendix I Inequalties

Appendix L Topics in Linear Algebra

Appendix O Orders of Magnitude

Appendix T Trigonometry

Refrences

Notation

Index

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