Foundations of Mathematical Analysis

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, presented in a well-ordered and understandable fashion, along with necessary background on the limit concept. The first seven chapters could constitute a one-semester introductory course. More than 750 exercises; some hints and solutions. 1981 edition.

Richard Johnsonbaugh was a professor at DePaul University.

PrefacePreface to the Dover EditionI Sets and FunctionsII The Real Number SystemIII Set EquivalenceIV Sequences of Real NumbersV Infinite SeriesVI Limits of Real-Valued Functions and Continuous Functions on the Real LineVII Metric SpacesVIII Differential Calculus of the Real LineIX The Riemann-Stieltjes IntegralX Sequences and Series of FunctionsXI Transcendental FunctionsXII Inner Product Spaces and Fourier SpacesXIII Normed Linear Spaces and the Riesz Representation TheoremXIV The Lebesgue IntegralAppendix: Vector SpacesReferencesHints to Selected ExercisesIndexErrata