| 01250 Functional Analysis and Global Analysis |
| Danish title: Funktionalanalyse og global analyse |
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Language: English ECTS-creditpoints: 10
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| Type: , course at phd level, open university |
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Exam schedule:
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F4-A (jun 04 2002), E4-A (dec 18 2001) |
| Recommended semester: 4th -7th semester |
Scope and form: -lectures, where fundamental concepts, methods, and results are presented and perspectivized,
- tutorials, where the theory is discussed in more detail and exemplified by solution of exercises,
- larger sets of related exercises (smal projects). |
| Evaluation: Oral exam and approvel of coursework
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| Examination: 13-scale |
| Previous course: 01244, 01245 |
| Prerequisites: 01030 / 01031 / 01032 / 36260 / 01034 |
Aim: Many advanced mathematical disciplines, e.g. global analysis,the calculus of variations,dynamical systems, differential geometry, the theory of differential and integral operators, have a common foundation. It is the purpose of this course to outline the basic structures in this common foundation
and thereby make it easier for students to study more advanced courses and to grasp the newest technical and mathematical literature. |
| Contents: Topological concepts: Metric spaces, topological spaces, connectedness,compactness, mapping spaces. Fundamental concepts from Global analysis: Differentiability in Normed Vector Spaces, the Inverse Function Theorem, introduction to differentiable manifolds. Fundamental concepts from Functional Analysis: Banach spaces and Hilbert spaces, bounded and unbounded operators on Hilbert spaces, differential operators, the Spectral Theorem. Selected examples of applications within: Dynamical Systems, Singularity Theory, Control Theory, Calculus of Variations, Partial Differential Equations. |
| Contact: Vagn Lundsgaard Hansen, building 303, (+45) 4525 3039, v.l.hansen@mat.dtu.dk |
| Department: 001 Department of Mathematics |
| Course URL: http://www.mat.dtu.dk/courses/01250 |
| Keywords: Topological spaces, Differentiability in Normed Vector Spaces, Banach spaces, Operators on Hilbert spaces |
| Updated: 04-05-2001 |
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