More Calculus of a Single Variable

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

• Preface.- 1 The Real Numbers.- 2 Famous Inequalities.- 3 Continuous Functions.- 4 Differentiable Functions.- 5 The Mean Value Theorem.- 6 The Exponential Function.- 7 Other Mean Value Theorems.- 8 Convex Functions and Taylor's Theorem.- 9 Integration of Continuous Functions.- 10 The Fundamental Theorem of Calculus.- 11 Techniques of Integration.- 12 Classic Examples.- 13 Simple Quadrature Rules.- 14 Error Terms.- A The Proof of Theorem 9.1.- Index.

"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