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

  1. Mathematical induction
  2. Elementary set theory and elementary combinatorics
  3. Real numbers
  4. Complex numbers
  5. Polynomials
  6. Rational functions
  7. Convergence of functions
  8. Monotonous sequences
  9. Partial sequence and Theorem of Bolzano-WeierstraƟ
  10. Landau symbols
  11. Series
  12. Continous functions
  13. Limits of functions
  14. Potential series
  15. Exponential function
  16. Trigonometric functions
  17. Fundamental Theorem of Algebra