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A course in calculus and real analysis

Author: Sudhir Ghorpade; Balmohan Vishnu Limaye
Publisher: Cham : Springer, 2018.
Series: Undergraduate texts in mathematics
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sudhir Ghorpade; Balmohan Vishnu Limaye
ISBN: 9783030014001 3030014002 3030013995 9783030013998
OCLC Number: 1076485334
Description: 1 online resource (ix, 538 pages)
Contents: 1. Numbers and Functions --
2. Sequences --
3. Continuity and Limits --
4. Differentiation --
5. Applications of Differentiation --
6. Integration --
7. Elementary Transcendental Functions --
8. Applications and Approximations of Riemann Integrals --
9. Infinite Series and Improper Integrals --
10. Sequences and Series of Functions, Integrals Depending on a Parameter --
A. Construction of the Real Numbers --
B. Fundamental Theorem of Algebra --
References --
List of Symbols and Abbreviations --
Index.
Series Title: Undergraduate texts in mathematics
Responsibility: Sudhir R. Ghorpade, Balmohan V. Limaye.

Abstract:

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. Contains examples  Read more...

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"This book would be a valuable asset to a university library and that many instructors would do well to have a copy of this book in their personal libraries. In addition, I believe that some students Read more...

 
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    schema:description "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.--"@en ;
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