# Real Analysis

## Edition: 2005

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 Real numbers and limits: Numbers and logic Infinity Sequences Functions and limits Topology: Open and closed sets Continuous functions Composition of functions Subsequences Compactness Existence of maximum Uniform continuity Connected sets and the intermediate value theorem The Cantor set and fractals Calculus: The derivative and the mean value theorem The Riemann integral The fundamental theorem of calculus Sequences of functions The Lebesgue theory Infinite series $\sum a_n$ Absolute convergence Power series Fourier series Strings and springs Convergence of Fourier series The exponential function Volumes of $n$-balls and the gamma function Metric spaces: Metric spaces Analysis on metric spaces Compactness in metric spaces Ascoli's theorem Partial solutions to exercises Greek letters Index