# Real Analysis and Foundations, 3rd Edition

## Book Description

*A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking*

Back by popular demand, **Real Analysis and Foundations, Third Edition** bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations.

*New to the Third Edition
*Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises.

*Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding
*This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.

### Table of Contents

Chapter 1 - Number Systems

Chapter 2 - Sequences

Chapter 3 - Series of Numbers

Chapter 4 - Basic Topology

Chapter 5 - Limits and Continuity of Functions

Chapter 6 - Differentiation of Functions

Chapter 7 - The Integral

Chapter 8 - Sequences and Series of Functions

Chapter 9 - Elementary Transcendental Functions

Chapter 10 - Applications of Analysis to Differential Equations

Chapter 11 - Introduction to Harmonic Analysis

Chapter 12 - Functions of Several Variables

Chapter 13 - Advanced Topics

Chapter 14 - Normed Linear Spaces

Appendix I - Elementary Number Systems

Appendix II - Logic and Set Theory

Appendix III - Review of Linear Algebra

## Book Details

- Title: Real Analysis and Foundations, 3rd Edition
- Author: Steven G. Krantz
- Length: 430 pages
- Edition: 3
- Language: English
- Publisher: Chapman and Hall/CRC
- Publication Date: 2013-06-24
- ISBN-10: 1466587318
- ISBN-13: 9781466587311

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