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.


  • Differential and integral calculus for functions in one variable
    1. Derivation of a function
    2. Mean value theorem and implications
    3. Higher order derivations and approximation with Tayler polynomials
    4. Convex functions
    5. Convergence of function sequences and function series
    6. Integrals
    7. Primitive integral and fundamental theorem of calculus
    8. Applications of differential and integral calculus
  • Continuity and differential calculus for functions in multiple variables
    1. Norms and metrics
    2. Continous mappings
    3. Further properties of metric spaces
    4. Differentiability
    5. Further properties of differentiable functions and mappings
    6. Higher differentials and Taylor formula
    7. Maxima and minima
    8. Implicit functions
  • Improper integrals and applications
    1. Improper integrals
    2. More about Convergence of function series: integration and differentiation
    3. Generalized factorial function and gamma function