Foundations of Mathematical Analysis

by Johnsonbaugh, Richard; Pfaffenberger, W.E.

• ISBN13: 9780486477664
• ISBN10: 0486477665
• eBook ISBN(s): 9780486134772
• Format: Paperback
• Copyright: 2010-05-20
• Publisher: Dover Publications
• More Book Details

Summary

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.

Author Biography

Richard Johnsonbaugh was a professor at DePaul University.

Table of Contents

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