Overview
- Treats advanced aspects of the calculus of a single variable
- Enriches the reader's understanding of the breadth and power of calculus
- Develops the reader's mastery of calculus through many challenging and fascinating exercises
- Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization.
More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations.
Reviews
“This book is a friendly, accessible treatment of advanced calculus of functions of one variable, intended for readers who have completed a full-year course in introductory single-variable calculus. … Each chapter is accompanied by a healthy number of exercises whose range provides both practice and additional conceptual and topical development. Summing Up: Highly recommended. Lower- and upper-division undergraduates.” (S. J. Colley, Choice, Vol. 52 (10), June, 2015)
"... when we teach a course in calculus ... we are forced to omit many beautiful ideas ... The book under review is a remarkable resource to fill this gap ... The book is very well motivated and well written, and is very suitable for readers to follow as self-study. I recommend it highly for undergraduate students who have completed a course in calculus, and also for students who have a course in mathematical analysis. It will also serve well for anyone who is interested in developing undergraduate research at the calculus level."
—MAA Reviews
Authors and Affiliations
About the author
Bibliographic Information
Book Title: More Calculus of a Single Variable
Authors: Peter R. Mercer
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4939-1926-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2014
Hardcover ISBN: 978-1-4939-1925-3Published: 18 October 2014
Softcover ISBN: 978-1-4939-4681-5Published: 23 August 2016
eBook ISBN: 978-1-4939-1926-0Published: 17 October 2014
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: XVI, 411
Number of Illustrations: 60 b/w illustrations
Topics: Analysis