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An Introduction to Wavelets Through Linear Algebra

  • Textbook
  • © 1999

Overview

Authors:
  1. Michael W. Frazier

    1. Department of Mathematics, Michigan State University, East Lansing, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Prologue: Compression of the FBI Fingerprint Files

    • Michael W. Frazier
    Pages 1-6

  3. Background: Complex Numbers and Linear Algebra

    • Michael W. Frazier
    Pages 7-100

  4. The Discrete Fourier Transform

    • Michael W. Frazier
    Pages 101-164

  5. Wavelets on ℤ N

    • Michael W. Frazier
    Pages 165-263

  6. Wavelets on ℤ

    • Michael W. Frazier
    Pages 265-348

  7. Wavelets on ℝ

    • Michael W. Frazier
    Pages 349-450

  8. Wavelets and Differential Equations

    • Michael W. Frazier
    Pages 451-483

  9. Back Matter

    Pages 484-503
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Keywords

About this book

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. Basic wavelet theory is a natural topic for such a course. By name, 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.

Authors and Affiliations

  • Department of Mathematics, Michigan State University, East Lansing, USA

    Michael W. Frazier

Bibliographic Information

  • Book Title: An Introduction to Wavelets Through Linear Algebra

  • Authors: Michael W. Frazier

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-85570-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Softcover ISBN: 978-3-642-85572-6Published: 15 April 2014

  • eBook ISBN: 978-3-642-85570-2Published: 11 December 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XVI, 503

  • Number of Illustrations: 27 b/w illustrations

  • Topics: Analysis, Numerical Analysis

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