A Course in Calculus and Real Analysis

Sudhir R. Ghorpade, Balmohan Limaye - Collection Undergraduate Texts in Mathematics

442 pages, parution le 31/01/2006

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Résumé

This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis.

The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.

Written for: Undergraduate math students

Sommaire

Numbers and Functions
Sequences
Continuity and Limits
Differentiation
Applications of Differentiation
Integration
Elementary Transcendental Functions
Applications and Approximations of Riemann Integrals
Infinite Series and Improper Integrals
References
List of Symbols and Abbreviations

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Sudhir R. Ghorpade, Balmohan Limaye
Collection	Undergraduate Texts in Mathematics
Parution	31/01/2006
Nb. de pages	442
Format	16 x 24
Couverture	Relié
Poids	760g
Intérieur	Noir et Blanc
EAN13	9780387305301
ISBN13	978-0-387-30530-1