Mercer P.R. More Calculus of a Single Variable

Springer Science+Business Media, New York, 2014. — 419 p. — (Undergraduate Texts in Mathematics) — ISBN: 9781493919253Many college students take a couple of courses in calculus. Afterwards, they either (i) take no more calculus, (ii) take calculus of several variables, or (iii) take real analysis. This book offers another option, not exclusive from options (ii) or (iii).
In the first two college calculus courses, much attention is given (naturally) to preparing students for things to come. But typically there is little time devoted to appreciating the bigger picture or for generally admiring the scenery. Many of the most appealing aspects of the subject are often left for students to pick up on their own. Unfortunately, however, students seldom do so.
The book could be used as a text for a third course in calculus of a single real variable, as a supplementary text for a first course in real analysis, or as a reference for anyone who teaches calculus. The book is almost entirely selfcontained, but readers would be best to have already taken the equivalent of two one-semester courses in single variable calculus. Some familiarity with sequences and some experience with proofs would be beneficial, though not entirely necessary.The Real Numbers
Famous Inequalities
Continuous Functions
Differentiable Functions
The Mean Value Theorem
The Exponential Function
Other Mean Value Theorems
Convex Functions and Taylor’s Theorem
Integration of Continuous Functions
The Fundamental Theorem of Calculus
Techniques of Integration
Classic Examples
Simple Quadrature Rules
Error Terms
The Proof of Theorem 9.1