More Calculus of a Single Variable, Softcover reprint of the original 1st ed. 2014
Undergraduate Texts in Mathematics Series

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 ?. 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.

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