| NMAC21 | Differential geometry, 7,5 ECTS credits. /Differentialgeometri/ |
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Area of Education: Natural Sciences Subject area: Mathematics |
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| Advancement level
(A-D): C
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| Aim: The aim of the course is to provide knowledge of the geometry of curves and surfaces using calculus techniques. This in an integrating course that provides intuitive examples for many concepts in linear algebra, calculus and differential equations. These examples are fundamental to physics and mechanics: they play a role in our understanding of the movements of particles and relativity. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Linear algebra, Several variable calculus, Vector calculus. Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding. |
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| Organisation: Lectures and tutorials. |
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| Course contents: Curves: tangents, curvature and torsion. Contact. Different types of curves. Regular surfaces: tangent plane. The first fundamental form: normal and geodesic curvature. Geodesics and parallel transport. Gauss' formulae. The second fundamental form: Weingarten's equation, principal, Gauss and mean curvature. Minimal and developable surfaces. Riemann's and Ricci's tensors, Codazzi-Mainardi's equations. Gauss' ''Theorema Egregium''. Isometrical and conformal mappings. Gauss-Bonnet theorem. |
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| Course literature: A. Pressley: Elementary Differential Geometry (Springer-Verlag, 2001) |
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| Examination: | |||
| Assignments |
5 p |
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Course language is . Department offering the course: MAI. Director of Studies: Arne Enqvist Examiner: Milagros Izquierdo Barrios Link to the course homepage at the department Course Syllabus in Swedish |
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