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© 2014

More Calculus of a Single Variable

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Peter R. Mercer
    Pages 1-24
  3. Peter R. Mercer
    Pages 25-52
  4. Peter R. Mercer
    Pages 53-71
  5. Peter R. Mercer
    Pages 73-95
  6. Peter R. Mercer
    Pages 97-117
  7. Peter R. Mercer
    Pages 119-158
  8. Peter R. Mercer
    Pages 159-169
  9. Peter R. Mercer
    Pages 171-208
  10. Peter R. Mercer
    Pages 209-248
  11. Peter R. Mercer
    Pages 249-281
  12. Peter R. Mercer
    Pages 283-310
  13. Peter R. Mercer
    Pages 311-329
  14. Peter R. Mercer
    Pages 331-355
  15. Peter R. Mercer
    Pages 357-391
  16. Back Matter
    Pages 393-411

About this book

Introduction

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.

Keywords

AGM inequality Taylor's theorem continuous functions mean value theorem

Authors and affiliations

  1. 1.Mathematics DepartmentSUNY Buffalo StateBuffaloUSA

About the authors

Peter R. Mercer is Professor of Mathematics at the State University of New York College at Buffalo.

Bibliographic information

  • Book Title More Calculus of a Single Variable
  • Authors Peter R. Mercer
  • Series Title Undergraduate Texts in Mathematics
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • DOI https://doi.org/10.1007/978-1-4939-1926-0
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4939-1925-3
  • Softcover ISBN 978-1-4939-4681-5
  • eBook ISBN 978-1-4939-1926-0
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 1
  • Number of Pages XVI, 411
  • Number of Illustrations 60 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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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