Book:James R. Kirkwood/An Introduction to Analysis/Second Edition

James R. Kirkwood: An Introduction to Analysis (2nd Edition)

Published $\text {1995}$, Waveland Press

ISBN 978-1-57766-232-7

Subject Matter

• Analysis

Contents

Introduction

1. The Real Number System

1-1 Sets and Functions

1-2 Properties of the Real Numbers as an Ordered Field

1-3 The Completeness Axiom

2. Sequences of Real Numbers

2-1 Sequences of Real Numbers

2-2 Subsequences

2-3 The Bolzano-Weierstrass Theorem

3. Topology of the Real Numbers

3-1 Topology of the Real Numbers

4. Continuous Functions

4-1 Limits and Continuity

4-2 Monotone and Inverse Functions

5. Differentiation

5-1 The Derivative of a Function

5-2 Some Mean Value Theorems

6. Integration

6-1 The Riemann Integral

6-2 Some Properties and Applications of the Riemann Integral

6-3 The Riemann-Stieltjes Integral (optional)

7. Series of Real Numbers

7-1 Tests for Convergence of Series

7-2 Operations Involving Series

8. Sequences and Series of Functions

8-1 Sequences of Functions

8-2 Series of Functions

8-3 Taylor Series

9. Fourier Series

9-1 Fourier Coefficients

9-2 Representation by Fourier Series

Bibliography

Appendix: Hints and Answers for Selected Exercises

Index