Counterexamples in Analysis

By: BERNARD R. GELBAUM

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Paperback | 4 June 2003

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218 Pages

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These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Applied Mathematics

Functions of a Real Variable
The Real Number System
Functions and Limits
Differentiation
Riemann Integration
Sequences
Infinite Series
Uniform Convergence
Sets and Measure on the Real Axis
Higher Dimensions
Functions of Two Variables
Plane Sets
Area
Metric and Topological Spaces
Function Spaces
Bibliography	p. 180
Special Symbols	p. 183
Index	p. 187
Errata	p. 195
Table of Contents provided by Ingram. All Rights Reserved.

Counterexamples in Analysis

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