Mathematical Analysis

Satish Shiraldi, Harkrishan L. Vasudeva

440 pages, parution le 03/03/2006

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Résumé

This volume provides an exhaustive introduction to basic Mathematical Analysis suitable for senior undergraduate and beginning graduate students. Its leisurely approach to the subject matter ensures that the ideas take root gradually but firmly.

Thorough development of the real number system starting from axioms of a complete ordered field: definition of natural numbers as elements of the smallest inductive subset with a proof why k and k + 1 are consecutive, justification of the odd-even dichotomy and decimal representation.
Necessity of completeness if functions with everywhere zero derivative are to be constant.
Early proofs of basic properties of continuous functions.
Foundations of exponential and trigonometric functions without general properties of power series.
Possibility of "Precalculus" in a number system smaller than the reals.
Wealth of examples to illustrate concepts.
Over 400 exercises-to test understanding-with hints/solutions to most of them.
Alternative routes through the subject to suit a variety of courses. For instance, metric spaces can be omitted; the real number system may be defined either via Dedekind cuts or as a complete ordered field.

The book is ideal as a classroom text or for self study.

Sommaire

The Real Number System
More About the Real Number System
Continuous Functions on an Interval
Real and Complex Sequences
Real and Complex Series
Metric Spaces
Sequences and Series of Functions
Uniform Approximation
Differentiation
More About Differentiation
The Riemann Integral
More About the Riemann Integral
Stieltjes Integral
Additional Problems

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Alpha
Auteur(s)	Satish Shiraldi, Harkrishan L. Vasudeva
Parution	03/03/2006
Nb. de pages	440
Format	19 x 25
Couverture	Relié
Poids	1030g
Intérieur	Noir et Blanc
EAN13	9781842653210
ISBN13	978-1-84265-321-0