Elementary Calculus: An Infinitessimal Approach

Elementary Calculus: An infinitesimal Approach
This book by by H. Jerome Keisler tries to persuade you to adopt the view that the notion of small quantities, as peerceived by Liebniz, is a valid one after all. Abandoning the epsilon-delta approach in favour of an approach based on the small of infinitessimals, it introduces calculus from the point of view of the so-called nonstandard analysis of Abraham Robinson put forth in 1960.
Mathematicians by and large are lukewarm towards this interpretation of calculus. But then, for many of us of the engineering fraternity, it is like light at the end of a tunnel. Down with epsilon-delta! Let us give the infinitessimals a chance; at the very least, let us give it a try. So, over to Keisler.
The book is available on the net.

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