A Course in Calculus and Real Analysis (Paperback)

Sudhir R. Ghorpade

ISBN 10: 3030827410 / ISBN 13: 9783030827410

Editore: Springer Nature Switzerland AG, Cham, 2021

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Paperback. Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to singlevariable 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 realvalued 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 selfcontained proof of the Fundamental Theorem of Algebra.In addition to the usual prerequisites for a first course in singlevariable 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. Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to singlevariable calculus. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9783030827410

Dati bibliografici

• Titolo: A Course in Calculus and Real Analysis (Paperback)
• Editore: Springer Nature Switzerland AG, Cham
• Data di pubblicazione: 2021
• Lingua: Inglese
• ISBN 10: 3030827410
• ISBN 13: 9783030827410
• Rilegatura: Paperback
• Edizione: seconda edizione
• Condizione: new

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.