A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics) - Tapa blanda

Libro 149 de 163: Undergraduate Texts in Mathematics

Ghorpade, Sudhir R.; Limaye, Balmohan V.

 
9783030827410: A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics)
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ISBN 10: 3030827410 ISBN 13: 9783030827410
Editorial: Springer Nature Switzerland AG, 2021

Sinopsis

Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single‐variable calculus.

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Acerca del autor

Sudhir R. Ghorpade is Institute Chair Professor in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He has received several awards, including the All India Council for Technical Education (AICTE) Career Award for Young Teachers and the Prof. S.C. Bhattacharya Award for Excellence in Pure Sciences. His research interests lie in algebraic geometry, combinatorics, coding theory, and commutative algebra.

Balmohan V. Limaye is Professor Emeritus in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He is the author of several research monographs and textbooks, including Linear Functional Analysis for Scientists and Engineers (Springer, 2016). He worked at IIT Bombay for more than 40 years and has twice received the Award for Excellence in Teaching from IIT Bombay. His research interests include Banach algebras, approximation theory, numerical functional analysis, and linear algebra.

The authors’ companion volume A Course in Multivariable Calculus and Analysis (2010) is also in the UTM series.

De la contraportada

Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single-variable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof. Each chapter contains numerous examples and a large selection of exercises, as well as a “Notes and Comments” section, which highlights distinctive features of the exposition and provides additional references to relevant literature.

This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises. A new chapter discusses sequences and series of real-valued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter. Two new appendices cover a construction of the real numbers using Cauchy sequences, and a self-contained proof of the Fundamental Theorem of Algebra.

In addition to the usual prerequisites for a first course in single-variable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs. This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis. The authors’ A Course in Multivariable Calculus is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting.

From reviews:
[The first edition is] a rigorous, well-presented and original introduction to the core of undergraduate mathematics — first-year calculus. It develops this subject carefully from a foundation of high-school algebra, with interesting improvements and insights rarely found in other books. […] This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously.  N.J. Wildberger, Aust. Math. Soc. Gaz.

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Editorial
Springer Nature Switzerland AG
Año de publicación
2021
Idioma
Inglés
ISBN 10 
3030827410
ISBN 13 
9783030827410
Encuadernación
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Número de edición
2
Número de páginas
547
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Otras ediciones populares con el mismo título

9783030013998: A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics)

Edición Destacada

ISBN 10:  3030013995 ISBN 13:  9783030013998
Editorial: Springer Nature Switzerland AG, 2018
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