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These are some notes on introductory real analysis. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, differentiability, sequences and series of functions, and Riemann integration.
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Contents
- Chapter 1. Sets and Functions
- Chapter 2. Numbers
- Chapter 3. Sequences
- Chapter 4. Series
- Chapter 5. Topology of the Real Numbers
- Chapter 6. Limits of Functions
- Chapter 7. Continuous Functions
- Chapter 8. Differentiable Functions
- Chapter 9. Sequences and Series of Functions
- Chapter 10. Power Series
- Chapter 11. The Riemann Integral
- Chapter 12. Properties and Applications of the Integral
- Chapter 13. Metric, Normed, and Topological Spaces
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