Elementary Real Analysis

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Paperback | 18 December 2008

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296 Pages

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21.59 x 13.97 x 1.7

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This textbook covers all the theoretical aspects of real variable analysis which undergraduates reading mathematics are likely to require during the first two or three years of their course. It is based on lecture courses which the author has given in the universities of Wales, Cambridge and London. The subject is presented rigorously and without padding. Definitions are stated explicitly and the whole development of the subject is logical and self-contained. Complex numbers are used but the complex variable calculus is not. 'Applied analysis', such as differential equations and Fourier series, is not dealt with. A large number of examples is included, with hints for the solution of many of them. These will be of particular value to students working on their own.

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You Can Find This Book In

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

Preface
Notation and Conventions
Preliminaries
Enumerability and sequences
Bounds for sets of numbers
Bounds for functions and sequences
Limits of the sequences
Monotonic sequences; two important examples ; irrational powers of positive real numbers
Upper and lower limits of real sequences: the general principle of convergence
Convergence of series; absolute convergence
Conditional convergence
Rearrangement and multiplication of absolutely convergent series
Double series
Power series
Point set theory
The Bolzano-Weierstrass, Cantor and Heine-Borel theorems
Functions defined over real or complex numbers
Functions of a single real variable; limits and continuity
Monotonic functions; functions of bounded variation
Differentiation; mean-value theorems
The nth mean-value theorem: Taylor's theorem
Convex and concave functions
The elementary transcendental functions
Inequalities
The Riemann integral
Integration and differentiation
The Riemann-Stiltjes integral
Improper integrals; convergence of integrals
Further tests for the convergence of series
Uniform convergence
Functions of two real variables. Continuity and differentiability
Hints on the solution of exercises and answers to exercises
Appendix
Index
Table of Contents provided by Publisher. All Rights Reserved.

Elementary Real Analysis

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Paperback

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