Professor Daniel Kleitman, Emeritus Professor of Applied Mathematics at MIT

Calculus for Beginners and Artists

From Chapter 1 What is Calculus and Why do we Study it? “Calculus is the study of how things change. It provides a framework for modeling systems in which there is change, and a way to deduce the predictions of such models…It provides a way for us to construct relatively simple quantitative models of change, and to deduce their consequences.”

“With this you get the ability to find the effects of changing conditions on the system being investigated. By studying these, you can learn how to control the system to do make it do what you want it to do. Calculus, by giving engineers and you the ability to model and control systems gives them (and potentially you) extraordinary power over the material world.”

“The development of calculus and its applications to physics and engineering is probably the most significant factor in the development of modern science beyond where it was in the days of Archimedes. And this was responsible for the industrial revolution and everything that has followed from it including almost all the major advances of the last few centuries.”

This is the textbook for the MIT course Calculus for Applications. The course “is intended as a one and a half term course in calculus for students who have studied calculus in high school. It is intended to be self contained, so that it is possible to follow it without any background in calculus, for the adventurous.” In practice, if you don’t have basic calculus, you may find you need to divert to another online resources to aid your understanding.

The course uses Java applets to demonstrate calculus. The applets do not work at all in Edge or current versions of Chrome. In Internet Explorer they are blocked by Java security settings. You can modify the settings at your own risk to allow the applets to run. The applets contribute significantly to understanding the material.