Features of the Third Edition:

Begins with a discussion of the axioms of the real number system.

The limit is introduced via sequences.

Examples motivate what is to come, highlight the need for hypothesis in a theorem, and make abstract ideas more concrete.

A new section on the Cantor set and the Cantor function.

Additional material on connectedness.

Exercises range in difficulty from the routine "getting your feet wet" types of problems to the moderately challenging problems.

Topology of the real number system is developed to obtain the familiar properties of continuous functions.

Some exercises are devoted to the construction of counterexamples.

Table of Contents

Preface

Introduction

1. The Real Number System
2. Sequences of Real Numbers
3. Topology of the Real Numbers
4. Continuous Functions
5. Differentiation
6. Integration
7. Series of Real Numbers
8. Sequences and Series of Functions
9. Fourier Series

Bibliography

Hints and Answers to Selected Exercises

Index

Biography

James R. Kirkwood holds a Ph.D. from University of Virginia. He has authored fifteen, published mathematics textbooks on various topics including calculus, real analysis, mathematical biology and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. His texts, Elementary Linear Algebra, Linear Algebra, and Markov Processes, are also published by CRC Press.