| |
| Previous course: C0144 |
| Offered by:
Department of Mathematics
(MAT) |
| No credit points with: C0144 |
| Prerequisite: 01030/01031/01032/36260/01034 |
| Recommended semester:
4th -7th semester |
| Scope and form: 2 lecture modules and 1 hour of problem solving per week. |
| Examination:
Approval of coursework and oral examination
(
pass/fail
) |
Remarks: This course is a supplementary basic course.
Textbook: Vagn Lundsgaard Hansen: Grundbegreber i den Moderne Analyse. |
| Contact person: |
Vagn Lundsgaard Hansen, MAT, Building 303, Tel. +45 4525 3039 |
|
| Aim: Many advanced mathematical disciplines, such as Global Analysis, Global Variational Calculus, Dynamical Systems; Differential Geometry; Topology and The Theory of Lie Groups, have a common foundation. It is the purpose of this course to teach the students these fundamental concepts so as to give students a firm basis for attending advanced courses and for further studies of modern mathematical literature. |
| Contents: Fundamental concepts in general topology: Metric spaces, topological spaces, compactness, connectedness, function spaces. Fundamental concepts in analysis: Normed vector spaces, differentiability in normed vector spaces, the inverse function theorem in Banach spaces. Differentiable manifolds. Selected applications from one or more of the subjects: Dynamical systems, singularity theory, geometric control theory, geometric variational problems. |
