An in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications.

Key Features

*The text is relatively elementary at the start, but the level of difficulty steadily increases *The book contains many clear, detailed examples, case studies and exercises *Many real world applications relating to measure theory and pure analysis *Introduction to wavelet analysis


The book is intended for a one year senior undergraduate or beginning graduate course in Real Analysis, Applied Analysis or Applied Mathematics found in mathematics, statistics, engineering and physics departments.

Table of Contents

Fundamentals; Measure Theory; The Lebesgue Integral; Special Topics of Lebesgue Integral & Applications; Vector Spaces, Hilbert Spaces, and the L2 Space; Fourier Analysis; Orthonormal Wavelet Bases; Compactly Supported Wavelets; Wavelets in Signal Processing


No. of pages:
© 2003
Academic Press
eBook ISBN:
Print ISBN:
Print ISBN:

About the authors

Don Hong

Affiliations and Expertise

East Tennessee State University, Johnson City, TN

Jianzhong Wang

Affiliations and Expertise

Sam Houston State University, Huntsville, TX

Robert Gardner

Affiliations and Expertise

East Tennessee State University, Johnson City, TN


"...the wavelet treatment makes it attractive and gives it an edge over many texts." - David Ruch, Metropolitan State College "The exercises I looked at were at a much more appropriate level than my current text. This book provides more exposition and more applications than traditional real analysis texts." - Doug Hardin, Vanderbilt University