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Ghorpade, Sudhir R.; Limaye, Balmohan V.

A Course in Calculus and Real Analysis (Kartoniert / Broschiert / Paperback)


Reihe: Undergraduate Texts in Mathema

SPRINGER NATURE, Springer US, November 2010


Softcover of Or - 432 S. - Sprache: Englisch - 236x156x27 mm

ISBN: 1441921451 EAN: 9781441921451

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

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Produktdetails

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Giving due importance is given to computational techniques and applications, the authors distinguish between the intrinsic definition of a geometric notion and its analytic characterization. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses. Each chapter contains 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.

Inhaltsverzeichnis

Preface.- 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.- Index.

Kritikerstimmen

From the reviews: "The book is a self-contained and rigorous introduction to calculus of one variable. It covers the programme of the first-year in mathematical analysis. The main goal of the book is a clear and successful presentation of the basic ideas of analysis. The reader can see an attention of the authors to help students in understanding and further developing of the basic notions of the subject. ... are illustrated by a number of interesting examples and remarks. In some sense it is a book for self-education." (Sergi V. Rogosin, Zentralblatt MATH, Vol. 1100 (2), 2007)

ISBN 1-441921-45-1, ISBN 1-44-192145-1, ISBN 1-44192-145-1, ISBN 1-441-92145-1, ISBN 1-4419-2145-1

ISBN 978-1-441921-45-1, ISBN 978-1-44-192145-1, ISBN 978-1-44192-145-1, ISBN 978-1-441-92145-1, ISBN 978-1-4419-2145-1

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