An Introduction to Wavelets Through Linear Algebra

✍ Scribed by Michael W. Frazier (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2000
• Tongue: English
• Leaves: 517
• Series: Undergraduate Texts in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Prologue: Compression of the FBI Fingerprint Files....Pages 1-6
Background: Complex Numbers and Linear Algebra....Pages 7-100
The Discrete Fourier Transform....Pages 101-164
Wavelets on ℤ N ....Pages 165-263
Wavelets on ℤ....Pages 265-348
Wavelets on ℝ....Pages 349-450
Wavelets and Differential Equations....Pages 451-483
Back Matter....Pages 484-503

✦ Subjects

Analysis; Numerical Analysis