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The book is recommended as a source for middle-level mathematical courses. It can be used not only at mathematical department, but also by physicists, engineers, economists and other experts in applied sciences who want to understand the main ideas of Analysis in order to use them at the study of mathematical models of different type processes.
-Zentralblatt MATH
The book contains many well-chosen examples and each of the fifteen chapters is followed by almost 500 exercises. ¡¦Illustrative pictures are instructive and the design of the book makes reading it a real pleasure. The book can be recommended for university libraries, teachers, and students.
-EMS Newsletter, Dec. 2005
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Preface to the Second Edition | |
Preface to the First Edition | |
Logic and Set Theory | |
Number Systems | |
Sequences | |
Series of Numbers | |
Basic Topology | |
Limits and Continuity of Functions | |
Differentiation of Functions | |
The Integral | |
Sequences and Series of Functions | |
Elementary Transcendental Functions | |
Applications of Analysis to Differential Equations | |
Introduction to Harmonic Analysis | |
Functions of Several Variables | |
Advanced Topics | |
A Glimpse of Wavelet Theory | |
Bibliography | |
Index | |
Table of Contents provided by Publisher. All Rights Reserved. |
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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.
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