This course teaches the essentials from real analysis, which are relevant to informatics. It consists of five chapters. After revisiting basic facts about natural numbers, integers, and rational numbers, the first milestone is to understand the concept of real numbers and their properties. We then study sequences and series of real numbers and learn about the idea of convergence. The third chapter introduces real functions in one variable and focuses on the property of continuity and its consequences. Differentiation and integration are covered in the last two chapters. After finishing this course, students possess the mathematical skills required for solving basic problems in a formal and structured way and they will have developed a good understanding of differential and integral calculus. Whenever possible, applications of theoretical concepts are highlighted and part of the homework assignments deal with the implementation of numerical algorithms to practically experience the mathematical concepts.
- Kenneth A. Ross. Elementary Analysis: The Theory of Calculus. Undergraduate Texts in Mathematics. Springer, 1980
- Additional material will be provided through the course homepage.