Book contents
- Frontmatter
- Epigraph
- Contents
- 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
- Further reading
- Index
Introduction
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Epigraph
- Contents
- 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
- Further reading
- Index
Summary
Over a century ago, Silvarnis P. Thompson wrote a marvellous little book [7] entitled
CALCULUS MADE EASY
Being a Very-Simplest Introduction to
Those Beautiful Methods of Reckoning
which Are Generally Called by the
Terrifying Names of the
Differential Calculus and the Integral Calculus
with the following prologue.
Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics – and they are mostly clever fools – seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.
For a variety of reasons, the first university course in rigorous calculus is often the first course in which students meet sequences of long and subtle proofs. Sometimes the lecturer compromises and provides rigorous proofs only of the easier theorems. In my opinion, there is much to be said in favour of proving every result and much to be said in favour of proving only the hardest results, but nothing whatsoever for proving the easy results and hand-waving for the harder.
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- Calculus for the Ambitious , pp. ix - xiiPublisher: Cambridge University PressPrint publication year: 2014