Overview

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.

Full Product Details

Author:   Robert B ASH
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Dimensions:   Width: 14.90cm , Height: 2.20cm , Length: 22.40cm
Weight:   0.417kg
ISBN:  

9780486472201

ISBN 10:   0486472205
Pages:   224
Publication Date:   28 August 2009
Audience:   General/trade ,  General
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

INTRODUCTION Basic Terminology Finite and Infinite Sets; Countably Infinite and Uncountably Infinite Sets Distance and Convergence Minicourse in Basic Logic Limit Points and Closure Review Problems for Chapter 1 SOME BASIC TOPOLOGICAL PROPERTIES OF Rp Unions and Intersections of Open and Closed Sets Compactness Some Applications of Compactness Least Upper Bounds and Completeness Review Problems for Chapter 2 UPPER AND LOWER LIMITS OF SEQUENCES OF REAL NUMBERS Generalization of the Limit Concept Some Properties of Upper and Lower Limits Convergence of Power Series Review Problems for Chapter 3 CONTINUOUS FUNCTIONS Continuity: Ideas, Basic Terminology, Properties Continuity and Compactness Types of Discontinuities The Cantor Set Review Problems for Chapter 4 DIFFERENTIATION The Derivative and Its Basic Properties Additional Properties of the Derivative; Some Applications of the Mean Value Theorem Review Problems for Chapter 5 RIEMANN-STIELTJES INTEGRATION Definition of the Integral Properties of the Integral Functions of Bounded Variation Some Useful Integration Theorems Review Problems for Chapter 6 UNIFORM CONVERGENCE AND APPLICATIONS Pointwise and Uniform Convergence Uniform Convergence and Limit Operations The Weierstrass M-test and Applications Equicontinuity and the Arzela-Ascoli Theorem The Weierstrass Approximation Theorem Review Problems for Chapter 7 FURTHER TOPOLOGICAL RESULTS The Extension Problem Baire Category Theorem Connectedness Semicontinuous Functions Review Problems for Chapter 8 EPILOGUE Some Compactness Results Replacing Cantor's Nested Set Property The Real Numbers Revisited SOLUTIONS TO PROBLEMS INDEX

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Author Information

A Professor Emeritus of Mathematics at the University of Illinois, Robert Ash is the author of three other Dover books: Basic Abstract Algebra, Basic Probability Theory, and Complex Variables and Information Theory.

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