A Course Calculus and Real Analysis

Ghorpade, Sudhir R.; Limaye, Balmohan V.

ISBN 10: 3030013995 / ISBN 13: 9783030013998

Published by Springer, 2018

About this Item

pp. 538. Seller Inventory # 18376388732

Bibliographic Details

Title: A Course Calculus and Real Analysis

Publisher: Springer

Publication Date: 2018

Binding: Hardcover

Condition: New

Edition: 2nd Edition

About this title

Synopsis:

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.

From the Back Cover:

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.