Book:James R. Kirkwood/An Introduction to Analysis/Second Edition
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James R. Kirkwood: An Introduction to Analysis (2nd Edition)
Published $\text {1995}$, Waveland Press
- ISBN 978-1-57766-232-7
Subject Matter
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