An Introduction to Wavelets Through Linear Algebra

Michael W. Frazier

ISBN 10: 1475772998 / ISBN 13: 9781475772999

Published by Springer New York, Springer US Mär 2013, 2013

About this Item

Neuware -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 suf ciently 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 rst two sections of chapter 1. In the remainder of chapter 1 we review linear algebra. Students should be familiar with the basic de nitions 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 bene t from seeing it again. In section 1.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 524 pp. Englisch.

Seller Inventory # 9781475772999

Bibliographic Details

• Title: An Introduction to Wavelets Through Linear Algebra
• Publisher: Springer New York, Springer US Mär 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 1475772998
• ISBN 13: 9781475772999
• Binding: Taschenbuch
• Condition: Neu

About this title

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. 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 suf?ciently 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 ?rst two sections of chapter 1. In the remainder of chapter 1 we review linear algebra. Students should be familiar with the basic de?nitions 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 bene?t from seeing it again. In section 1.