Calculus for the Ambitious

A short introduction perfect for any 16- to 18-year-old, about to begin studies in mathematics.

T. W. Körner (Author)

9781107686748, Cambridge University Press

Paperback / softback, published 29 May 2014

174 pages, 15 b/w illus. 195 exercises
22.7 x 15.2 x 1 cm, 0.29 kg

From the author of The Pleasures of Counting and Naïve Decision Making comes a calculus book perfect for self-study. It will open up the ideas of the calculus for any 16- to 18-year-old, about to begin studies in mathematics, and will be useful for anyone who would like to see a different account of the calculus from that given in the standard texts. In a lively and easy-to-read style, Professor Körner uses approximation and estimates in a way that will easily merge into the standard development of analysis. By using Taylor's theorem with error bounds he is able to discuss topics that are rarely covered at this introductory level. This book describes important and interesting ideas in a way that will enthuse a new generation of mathematicians.

Introduction
1. Preliminary ideas
2. The integral
3. Functions, old and new
4. Falling bodies
5. Compound interest and horse kicks
6. Taylor's theorem
7. Approximations, good and bad
8. Hills and dales
9. Differential equations via computers
10. Paradise lost
11. Paradise regained
Bibliography
Index.

Subject Areas: Functional analysis & transforms [PBKF], Complex analysis, complex variables [PBKD], Calculus [PBKA], Calculus & mathematical analysis [PBK]