Real Analysis and Foundations, Second Edition

Front Cover
CRC Press, Nov 15, 2004 - Mathematics - 470 pages
0 Reviews
Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-depth understanding of the subject. Further complicating this, the field has not changed much over the past 150 years, prompting few authors to address the lackluster or overly complex dichotomy existing among the available texts.

The enormously popular first edition of Real Analysis and Foundations gave students the appropriate combination of authority, rigor, and readability that made the topic accessible while retaining the strict discourse necessary to advance their understanding. The second edition maintains this feature while further integrating new concepts built on Fourier analysis and ideas about wavelets to indicate their application to the theory of signal processing. The author also introduces relevance to the material and surpasses a purely theoretical treatment by emphasizing the applications of real analysis to concrete engineering problems in higher dimensions.

Expanded and updated, this text continues to build upon the foundations of real analysis to present novel applications to ordinary and partial differential equations, elliptic boundary value problems on the disc, and multivariable analysis. These qualities, along with more figures, streamlined proofs, and revamped exercises make this an even more lively and vital text than the popular first edition.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Logic and Set Theory
1
EXERCISES
34
EXERCISES
67
Sequences
75
Series of Numbers
95
EXERCISES
122
Basic Topology
129
EXERCISES
149
EXERCISES
252
EXERCISES
278
Applications of Analysis to Differential Equations
285
EXERCISES
301
Introduction to Harmonic Analysis
307
EXERCISES
336
Functions of Several Variables
345
EXERCISES
375

EXERCISES
175
Differentiation of Functions
181
EXERCISES
201
EXERCISES
231
Sequences and Series of Functions
237
EXERCISES
414
A Glimpse of Wavelet Theory
421
Bibliography
445
Copyright

Common terms and phrases

References to this book

All Book Search results »

About the author (2004)

Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including "Calculus Demystified," another popular title in this series. He lives in St. Louis, Missouri.

Bibliographic information