Principles Of Mathematical Analysis
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Principles of Mathematical Analysis
Author: Walter Rudin
language: en
Publisher: McGraw-Hill Publishing Company
Release Date: 1976
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Real Analysis and Applications
Author: Kenneth R. Davidson
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-10-13
This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.
The Real Analysis Lifesaver
Author: Raffi Grinberg
language: en
Publisher: Princeton Lifesaver Study Guides
Release Date: 2017
Cover -- Title -- Copyright -- CONTENTS -- Preliminaries -- 1 Introduction -- 2 Basic Math and Logic* -- 3 Set Theory* -- Real Numbers -- 4 Least Upper Bounds* -- 5 The Real Field* -- 6 Complex Numbers and Euclidean Spaces -- Topology -- 7 Bijections -- 8 Countability -- 9 Topological Definitions* -- 10 Closed and Open Sets* -- 11 Compact Sets* -- 12 The Heine-Borel Theorem* -- 13 Perfect and Connected Sets -- Sequences -- 14 Convergence* -- 15 Limits and Subsequences* -- 16 Cauchy and Monotonic Sequences* -- 17 Subsequential Limits -- 18 Special Sequences -- 19 Series* -- 20 Conclusion -- Acknowledgments -- Bibliography -- Index