Milne Open Textbooks

**Publication Date:**April 16, 2021**ISBN:**978-1-942341-74-1**Affiliation:**SUNY Geneseo

**Author(s):**
Gary Towsley

This text is a conventional coverage of Real Analysis for undergraduate students. In it, the real numbers are developed via the Completeness Axiom. The topology of the real numbers is also explored. The coverage culminates in proving the two parts of the Fundamental Theorem of Calculus.

Preface

Introduction: A Quick History of the Development of Real Analysis

1 The Natural Numbers, the Rational Numbers and their Arithmetic

1.1 Exercises

2 Preliminaries Concerning Sets and Functions

2.1 Exercises

3 Moving from Q to R

3.1 Exercises

4 Cardinality

4.1 Exercises

5 Sequences and Series

5.1 Sequences

5.2 Series

Convergence Tests

5.3 Exercises

6 The Topology of the Real Numbers

6.1 Exercises

7 Limits and Continuity

7.1 Exercises

8 The Derivative

8.1 Exercises

9 The Riemann Integral

9.1 Exercises

10 What comes next in Real Analysis?

11 Supplemental Exercises

Bibliography

List of Definitions and Axioms

Alphabetical Index