Real Analysis and Foundations, 3rd Edition

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