This definitive look at modern analysis includes applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. The self-contained treatment contains clear explanations and all the appropriate theorems and proofs. A selection of more than 750 exercises includes some hints and solutions. 1981 edition.

Preface        Preface to the Dover Edition        I Sets and Functions        II The Real Number System        III Set Equivalence        IV Sequences of Real Numbers        V Infinite Series        VI Limits of Real-Valued Functions and Continuous Functions on the Real Line        VII Metric Spaces        VIII Differential Calculus of the Real Line        IX The Riemann-Stieltjes Integral        X Sequences and Series of Functions        XI Transcendental Functions        XII Inner Product Spaces and Fourier Spaces        XIII Normed Linear Spaces and the Riesz Representation Theorem        XIV The Lebesgue Integral        Appendix: Vector Spaces        References        Hints to Selected Exercises        Index        Errata

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