© 2014
More Calculus of a Single Variable
- 6 Citations
- 4 Mentions
- 80k Downloads
Part of the Undergraduate Texts in Mathematics book series (UTM)
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© 2014
Part of the Undergraduate Texts in Mathematics book series (UTM)
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.
“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)