A Very Short Calculus Course

Abstract

Following up on the general idea of science as a combination of formulating and solving equations, we describe the bare elements of this picture from a mathematical point of view. We want to give a brief glimpse of the main themes of Calculus that will be discovered as we work through the volumes of this book. In particular, we will encounter the magical words of function, derivative, and integral. If you have some idea of these concepts already, you will understand some of the outline. If you have no prior acquaintance with these concepts, you can use this section to just get a first taste of what Calculus is all about without expecting to understand the details at this point. Keep in mind that this is just a glimpse of the actors behind the curtain before the play begins!

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on in its conclusions, except that in the height the identity fades out of sight. (Goethe)