Undergraduate Course: Geometry & Calculus of Variations (MATH09003)
Course Outline
School |
School of Mathematics |
College |
College of Science and Engineering |
Course type |
Standard |
Availability |
Available to all students |
Credit level (Normal year taken) |
SCQF Level 09 (Year 3 Undergraduate) |
Credits |
10 |
Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Honours) |
Course website |
http://student.maths.ed.ac.uk |
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Course description |
Optional course for Honours Degrees involving Mathematics and/or Statistics. Plane curves, regularity, curvature(moving frame analysis). Space curves, biregularity, curvature and torsion. Families of plane curves, functionals and their variation, Euler-Lagrange equations. Motion in a potential, energy. Surfaces, regularity, shape operator, mean and Gauss curvature. Geodesics as a variational problem. |
Course Delivery Information
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Delivery period: 2010/11 Semester 2, Available to all students (SV1)
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WebCT enabled: Yes |
Quota: None |
Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
King's Buildings | Lecture | | 1-11 | | 10:00 - 10:50 | | | | King's Buildings | Lecture | | 1-11 | | | | 10:00 - 10:50 | |
First Class |
First class information not currently available |
Additional information |
Tutorials: one of Tu, 1400-1450, We 1000-1050, 1110-1200.
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Summary of Intended Learning Outcomes
1. Isometry
2. How to define planar curves, check their regularity, and determine arc-length.
3. How to determine tangent, normal and curvature of a planar curve.
4. Definition of families of planar curves and construction of their envelopes.
5. The Equivalence Problem for planar curves.
6. Definition of a functional and its first variation.
7. Derivation of the Euler-Lagrange equation of a functional.
8. Integration of the Euler-Lagrange equation in the case of ignorable coordinates and other examples.
9. Definition of Space Curves and Biregularity.
10. Determination of Tangent, Normal, Binormal, Curvature and Torsion
11. The Equivalence Problem for space curves.
12. Definition of a surface and regularity. Calculation of Tangent Space and Normal.
13. Definition of a curve within a surface, its arc-length and calculation of the first fundamental form.
14. Conditions for stationary arc-length and definition of Geodesics.
15. Examples of Geodesics.
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Assessment Information
Coursework: 15%; Degree Examination: 85%.
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Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
Not entered |
Contacts
Course organiser |
Dr Adri Olde-Daalhuis
Tel: (0131 6)50 5992
Email: A.OldeDaalhuis@ed.ac.uk |
Course secretary |
Mrs Katherine Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
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copyright 2010 The University of Edinburgh -
1 September 2010 6:17 am
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