Calculus is a very important part of mathematics that has rich applications in all fields of Numerical Sciences and beyond. It is amongst the most important parts of mathematics for higher education for many countries. Consequently, a series of Milestone modules is designed to cover the necessary material some of which is beyond the Hungarian curriculum. While the module builds from first principles and aims to prove the statements (with the rigour allowed by length of the classes), we concentrate on the results, techniques and their applications so the module is accessible to a wider audience. In any case, students are warned that the material is conceptually more difficult compared to the mathematics classes preceding these topics.
The aim of the current module is to familiarise students with the notion of integration starting from first principles, its connection to differentiation, the techniques of integration by parts and by substitution, and standard applications including geometry (area, volume) and potentially some from physics and probability. The module is suitable for students with no or limited knowledge in the topic, but knowledge of differentiation is essential. The module is highly recommended for students interested in mathematics, physics, engineering, computer sciences, but students interested in related fields are also welcome.