Having the basics from Calculus 1, in this module we focus on more advanced topics about integration, but also will introduce simple differential equations and their solutions. The first half of the module is about learning many techniques for evaluating integrals. More specifically we investigate rational functions, consider integrals involving trigonometric functions and radicals using the two main techniques: integration by substitution and by parts. We continue by exploring some applications of definite integration. Depending on the pace of the classes, we will toch topics like calculating lengths, surface areas, volumes, but also may have more theoretical applications like proving that pi is irrational. Depending on the time left, we conclude the module by familiarising some standard first (and maybe second) order differential equations.
The classes mainly focus on exploring/learning the standard techniques instead of focusing on the rigorous theoretical arguments. We will cover the planned topics by considering and discussion the general situation via series of problems of increasing difficulty. The problems are designed in such a way that students can gradually figure out the general technique themselves. At many parts, we aim to arrive to the general conclusion by active class discussion.
A solid knowledge of Calculus 1 is an essential requirement. Students are asked to test their knowledge by doing the self assessment test. The module is ideal for Junior/Senior students willing to study a subject at university that is strongly built on mathematics, i.e. maths, physics and engineering.