Analysis I
Goals
The course Analysis I is the first lecture in the area of analysis and indispensable for understanding the contents of more advanced lectures during mathematical studies.
The lecture aims not only to convey the above contents to the students, but also to teach them more general skills, in particular the formulation and handling of mathematical statements. On the one hand, students are supposed to obtain an understanding of the basic notions of analysis, especially of the concepts of limits and continuity, to master the elementary methods and to aquire the skills necessary for actively using the contents of the lecture. On the other hand, they should learn the process of dealing with mathematical problems, develop mathematical intuition, practice to turn this intuition into precise reasoning and thus acquire skills for their entire studies.
Contents
According to the module handbook, the following topics are covered:
Natural numbers and mathematical induction; ordered fields, completeness of the real numbers; complex numbers; basic terms of topology in \(\mathbb{R}\); sequences and series: convergence, criteria for convergence, Bolzano-Weierstrass; functions in one variable: elementary functions, power series; limits of functions and continuity, applications.
Literature
- O. Forster: Analysis I, Vieweg
- H. Führ, A. Krieg, S. Walcher: Analysis I, Skript, RWTH Aachen H. Heuser: Lehrbuch der Analysis 1, Teubner
- C. Tretter: Analysis I, Birkhäuser