Cancelled Analysis on Manifolds
Course content
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
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor
subject
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.
4 lectures and 3 exercise classes per week for 9 weeks
Steve Rosenberg, "The Laplacian on a Riemannian Manifold" or equivalent textbook
Previous contact with the theory of differentiable manifolds and
functional analysis.
Academic qualifications equivalent to a BSc degree is
recommended.
- ECTS
- 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.
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Category
- Hours
- Lectures
- 45
- Preparation
- 134
- Exercises
- 27
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK18001U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Schedulegroup
-
C
- Capacity
- No restrictions/no limitation
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Ryszard Nest (5-7470677576426f63766a306d7730666d)
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Courseinformation of students