Real Variables with Basic Metric Space Topology 1st Edition by Robert B Ash ISBN 0486472205 9780486472201

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Product details:

ISBN 10: 0486472205

ISBN 13: 9780486472201 

Author: Robert B. Ash

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.

Table of contents:

Cover
Title Page
Contents
1. Introduction
2. Some Basic Topological Properties of Rp
3. Upper and Lower Limits of Sequences of Real Numbers
4. Continuous Functions
5. Differentiation
6. Riemann-Stieltjes Integration
7. Uniform Convergence and Applications
8. Further Topological Results
9. Epilogue
Solutions to Problems

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Tags: Robert B Ash, Real Variables, Metric Space, Topology