• Lecturer: Prof. Dr. Abbondandolo
• Language: German
• Credits: 9 CP
• Progams: B.A./B.Sc./M.Ed./M.Sc. Mathematics
• Examination: 100 % Oral Exam (45 Minutes)

Contents

1. Uniformly Continuity
2. Compactness in metric spaces
3. Theorem of Arzelà-Ascoli
4. Bernstein polynomials and approximation theorem of Weierstraß
5. Differentiation Theorem of Lebesgue
6. Real measures and their representations
7. Applications of the theorem of Lebesgue-Radon-Nicodym
8. Differential forms on vector spaces
9. Differential and integral calculus on manifolds
10. Theorem of Stokes and implications
11. Harmonic functions
12. De-Rham Cohomology