| Type: | Open University
Language: English |
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Previous course: C0144
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No credit points with: C0144
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Prerequisite: 01030/01031/01032/36260/01034
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Recommended semester: 4th -7th semester
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Scope and form: 2 lecture modules and 1 hour of problem solving per week.
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Examination: Approval of compulsory coursework. with oral presentation (Pass/fail), or written exam (13-scale) (xx)
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Remarks: This course is a supplementary basic course.
Textbook: Vagn Lundsgaard Hansen: Grundbegreber i den Moderne Analyse.
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Department: Department of Mathematics
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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.
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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.
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