Differential Geometry (Ord) (U01639)

? Credit Points : 10 ? SCQF Level : 9 ? Acronym : MAT-3-DGeO

Syllabus summary: Differential forms, moving frames, first and second fundamental forms of a surface, curvature, adapted frames, results on surfaces, isometric surfaces, Theorem Egregium, geodesics on surfaces, integration of forms, statement of general Stokes' theorem, Euler characteristic, Gauss-Bonnet theorem (sketch proof only).

Entry Requirements

? Pre-requisites : MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM or MAT-2-am3, MAT-2-mm3, MAT-2-am4, MAT-2-mm4 or MAT-2-mi3, MAT-2-mi4

? Prohibited combinations : MAT-3-DGe

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Ordinary), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	11:10	12:00	KB
Lecture	Friday	11:10	12:00	KB

Summary of Intended Learning Outcomes

The following are the learning objectives for the Honours version, MAT-3-DGe; for this (Ordinary) version there is more emphasis on the technical, rather than conceptual elements, which will be reflected by a different examination.

1. An ability to perform simple manipulations with forms; being able to relate these to the standard differential formulae of 3 dimensions (grad, div, curl) if these have been covered in other courses.
2. An understanding of the fundamental forms of a surface (I, II) and its principal curvatures. An ability to compute simple examples.
3. Ability to translate the "general Stokes' theorem" into the examples of vector calculus.