NMAK18001U Analysis on Manifolds
MSc Programme in Mathematics
MSc Programme in Mathematics w. a minor subject
Basic properties of differential operators on manifolds,
Relations between ellipticity and Fredholm properties.
Riemannian geometry, Levi - Civita connection and Laplace operator.
Hodge theorem.
Dirac operators and properties of heat kernels
Knowledge:
The student will obtain detailed understanding of the properties of
elliptic differential operators on manifolds and their applications
to topology and geometry.
Skills:
At the end of the course the student will be able to prove basic
properties of elliptic differential operators and demonstrate the
ability to use them in applications.
Competences:
The student will be able to use analysis of differenial operators
on manifolds to study their topological and geometric
properties.
Steve Rosenberg, "The Laplacian on a Riemannian Manifold" or equivalent textbook
Academic qualifications equivalent to a BSc degree is recommended.
- Category
- Hours
- Class Exercises
- 27
- Course Preparation
- 134
- Lectures
- 45
- Total
- 206
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessment7 written assignments during the course of which the 5 best counts equally towards the final grade
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner.
- Re-exam
Resubmission of all 7 assignments from the continuous assessment of which the 5 best counts equally towards the final grade. Deadline 12 Noon Friday in the reexamination week.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK18001U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- C
- Course capacity
- No restrictions/no limitation
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Ryszard Nest (rnest@math.ku.dk)