Ancient accountants laid pebbles in columns on a sand tray to help them do their sums. It is thought that the impression left in the sand when a pebble is moved to another location is the origin of our symbol for zero.
The word calculus has the same source, since it means a pebble in Latin. Nowadays it means any systematic way of working out something mathematical. We still speak of a calculator when referring to the modern electronic equivalent of an ancient sandtray and pebbles. However, since Isaac Newton invented the differential and integral calculus, the word is seldom applied to anything else. Although there are pebbles on its cover, this book is therefore about differentiating and integrating.
Students who don't already know what derivatives and integrals are would be wise to start with another book. Our aim is to go beyond the first steps to discuss how calculus works when it is necessary to cope with several variables all at once.
We appreciate that some readers will be rusty on the basics, and others will be doubtful that they ever really understood what they can remember. We therefore go over the material on the calculus of one variable in a manner that we hope will offer some new insights even to those rare souls who feel confident of their mathematical prowess. However, we strongly recommend against using this material as a substitute for a first course in calculus.
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