Real Analysis and Foundations, 4th Edition

The new edition of this popular text is revised to meet the suggestions of users of the previous edition. A readable yet rigorous approach to an essential part of mathematical thinking, this text 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.

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
Appendix I: Elementary Number Systems
Appendix II: Logic and Set Theory
Appendix III: Review of Linear Algebra