An Introduction to Wavelets Through Linear Algebra / Edition 1

by Michael W. Frazier, K. A. Ribet, F. W. Gehring, Sheldon J. Axler

Overview

Mathematics majors at Michigan State University take a “Capstone” course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basicwavelettheoryisanaturaltopicforsuchacourse. Byname, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity. These are introduced in the first two sections of chapter 1. In the remainder of chapter 1 we review linear algebra. Students should be familiar with the basic definitions in sections 1. 3 and 1. 4. From our viewpoint, linear transformations are the primary object of study; v Preface vi a matrix arises as a realization of a linear transformation. Many students may have been exposed to the material on change of basis in section 1. 4, but may benefit from seeing it again. In section 1.

Product Details

ISBN-13:	9780387986395
Publisher:	Springer New York
Publication date:	06/11/1999
Series:	Undergraduate Texts in Mathematics
Edition description:	1999
Pages:	503
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Prologue: Compression of the FBI Fingerprint Files.- Background: Complex Numbers and Linear Algebra.- The Discrete Fourier Transform.- Wavelets on ZN.- Wavelets on Z.- Wavelets on R.- Wavelets and Differential Equations.