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Other titles in the Studies in Advanced Mathematics series:
Real Analysis & Foundations 2ND Editionby Steven G Krantz
Synopses & 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.
Book News Annotation:
Because the universe has not changed much in about 150 years, neither has real analysis, sometimes known as "higher calculus." However, Krantz proves this time-tested discipline has applications to the real world by adding new descriptions of Fourier analysis and wavelets in signal processing to the engineering applications covered in his first edition. General topics of the 15 chapters include logic and set theory, number systems, sequences, series of numbers, basic topology, limits and continuity of functions, differentiation of equations, the integral, sequences and series of functions, elementary transcendental functions, applications of analysis to differential equations, harmonics analysis, functions of several variables, advanced topics and wavelet theory. Students should have backgrounds in calculus and differential equations.
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
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