Real Variables with Basic Metric Space Topology

Name: Real Variables with Basic Metric Space Topology
Brand: DOVER
Price: 27.99 AUD
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By: ROBERT B. ASH

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Paperback | 1 May 2009

At a Glance

Paperback
224 Pages

Age
21+

Dimensions(cm)
23.5 x 15.5 x 1.27

Paperback

$27.99

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Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis.
The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Topology

Preface	p. ix
Introduction	p. 1
Basic Terminology	p. 1
Finite and Infinite Sets; Countably Infinite and Uncountably Infinite Sets	p. 7
Distance and Convergence	p. 10
Minicourse in Basic Logic	p. 15
Limit Points and Closure	p. 21
Review Problems for Chapter 1	p. 23
Some Basic Topological Properties of R^p	p. 25
Unions and Intersections of Open and Closed Sets	p. 25
Compactness	p. 28
Some Applications of Compactness	p. 33
Least Upper Bounds and Completeness	p. 37
Review Problems for Chapter 2	p. 42
Upper and Lower Limits of Sequences of Real Numbers	p. 45
Generalization of the Limit Concept	p. 45
Some Properties of Upper and Lower Limits	p. 49
Convergence of Power Series	p. 52
Review Problems for Chapter 3	p. 56
Continuous Functions	p. 57
Continuity: Ideas, Basic Terminology, Properties	p. 57
Continuity and Compactness	p. 64
Types of Discontinuities	p. 70
The Cantor Set	p. 76
Review Problems for Chapter 4	p. 80
Differentiation	p. 81
The Derivative and Its Basic Properties	p. 81
Additional Properties of the Derivative; Some Applications of the Mean Value Theorem	p. 86
Review Problems for Chapter 5	p. 92
Riemann-Stieltjes Integration	p. 93
Definition of the Integral	p. 93
Properties of the Integral	p. 98
Functions of Bounded Variation	p. 106
Some Useful Integration Theorems	p. 111
Review Problems for Chapter 6	p. 115
Uniform Convergence and Applications	p. 117
Pointwise and Uniform Convergence	p. 117
Uniform Convergence and Limit Operations	p. 122
The Weierstrass M-test and Applications	p. 125
Equicontinuity and the Arzela-Ascoli Theorem	p. 130
The Weierstrass Approximation Theorem	p. 134
Review Problems for Chapter 7	p. 139
Further Topological Results	p. 141
The Extension Problem	p. 141
Baire Category Theorem	p. 144
Connectedness	p. 150
Semicontinuous Functions	p. 152
Review Problems for Chapter 8	p. 158
Epilogue	p. 161
Some Compactness Results	p. 161
Replacing Cantor's Nested Set Property	p. 164
The Real Numbers Revisited	p. 165
Solutions to Problems	p. 167
Index	p. 207
Table of Contents provided by Ingram. All Rights Reserved.

Real Variables with Basic Metric Space Topology

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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