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This title in other editionsOther titles in the Undergraduate Texts in Mathematics series:
An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics)by Michael Frazier
Synopses & ReviewsPublisher Comments:This text was originally written for a "Capstone" course at Michigan State University. A Capstone course is intended for undergraduate mathematics majors, as one of the final courses taken in their undergraduate curriculum. Its purpose is to bring together different topics covered in the undergraduate curriculum and introduce students to current developments in mathematics and their applications. Basic wavelet theory seems to be a perfect topic for such a course. As a subject, it dates back only to 1985. Since then there has been an explosion of wavelet research, both pure and applied. Wavelet theory is on the boundary between mathematics and engineering. In particular it is a good topic for demonstrating to students that mathematics research is thriving in the modern day: Students can see nontrivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. This text is intended to be as elementary an introduction to wavelet theory as possible. It is not intended as a thorough or authoritative reference on wavelet theory.
Synopsis:This book offers a solid, yet basic view of wavelet theory as an active part of modern day mathematical research leading to important applications such as video compression and the numerical solution of differential equations.
Synopsis:Wavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Students can see nontrivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. Intended to be as elementary an introduction to wavelet theory as possible, the text does not claim to be a thorough or authoritative reference on wavelet theory.
Synopsis:The mathematical theory of wavelets is less than 15 years old, yet already wavelets have become a fundamental tool in many areas of applied mathematics and engineering. This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finitedimensional context, using only linear algebra. Then Fourier series are introduced in order to develop wavelets in the infinitedimensional, but discrete context. Finally, the text discusses Fourier transform and wavelet theory on the real line. The computation of the wavelet transform via filter banks is emphasized, and applications to signal compression and numerical differential equations are given. This text is ideal for a topics course for mathematics majors, because it exhibits and emerging mathematical theory with many applications. It also allows engineering students without graduate mathematics prerequisites to gain a practical knowledge of wavelets.
Description:Includes bibliographical references (p. 484490) and index.
Table of Contentsx Prologue: Compression of the FBI Fingerprint Files
x Background: Complex Numbers and Linear Algebra x The Discrete Fourier Transform x Wavelets on Zn x Wavelets on Z x Wavelets on R x Wavelets and Differential Equations What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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