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

Course Description

Contents:

• differential and integral calculus of several variables
• Lebesgue integration
• Introduction to the theory of ordinary differential equations
• differential forms and their integration on submanifolds of Euclidean space

Contents

1. Theorem of implicit functions I
2. Complete metric spaces
3. Banach fixed-point theorem
4. Diffeomorphism
5. Theorem of implicit functions II
6. Submanifolds
7. Ordinary Differential Equations
8. Linear Differential Equations
9. Abstract measure theory
10. Lebesgue measure
11. Theorems of Tonelli and Fubini
12. Transformation theorem
13. parameter-dependent integrals
14. Convolution
15. Approximation of functions
16. Length of a curve
17. Sector area of flat curves and applications
18. Integration on submanifolds of R^n
19. First-order differential forms
20. Higher-order differential forms
21. Differential calculus on submanifolds
22. Theorem of Stokes