# Analysis I

Undergraduate Course, *Ruhr University Bochum*, 2018

- Lecturer: Prof. Dr. Abbondandolo
- Language: German
- Credits: 9 CP
- Programs: B.A./B.Sc. Mathematics
- Examination: 100 % Written Exam (240 Minutes) + 10 % Homework

# Course Description

After an introduction to the fundamentals of real and complex numbers, we will deal with functions of a real variable in Analysis I. Concrete topics will be:

- real and complex numbers
- sequences and series
- continuity
- differential and integral calculus

# Contents

- Mathematical induction
- Elementary set theory and elementary combinatorics
- Real numbers
- Complex numbers
- Polynomials
- Rational functions
- Convergence of functions
- Monotonous sequences
- Partial sequence and Theorem of Bolzano-Weierstraß
- Landau symbols
- Series
- Continous functions
- Limits of functions
- Potential series
- Exponential function
- Trigonometric functions
- Fundamental Theorem of Algebra