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


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
Appendix: Hints and Answers for Selected Exercises