# Analysis II

Undergraduate Course, *Ruhr University Bochum*, 2019

- 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

The main subject of the lecture will be the analysis of functions of several variables.

# Contents

- Differential and integral calculus for functions in one variable
- Derivation of a function
- Mean value theorem and implications
- Higher order derivations and approximation with Tayler polynomials
- Convex functions
- Convergence of function sequences and function series
- Integrals
- Primitive integral and fundamental theorem of calculus
- Applications of differential and integral calculus

- Continuity and differential calculus for functions in multiple variables
- Norms and metrics
- Continous mappings
- Further properties of metric spaces
- Differentiability
- Further properties of differentiable functions and mappings
- Higher differentials and Taylor formula
- Maxima and minima
- Implicit functions

- Improper integrals and applications
- Improper integrals
- More about Convergence of function series: integration and differentiation
- Generalized factorial function and gamma function