Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Occurrence | Teaching cycle |
---|---|
A | Autumn Term 2019-20 |
The aim of the module is to describe how techniques from advanced calculus and linear algebra may be used to give meaning to the concept of "shape" for curves and surfaces in space.
At the end of the module you should be able to:
[Pre-requisite modules: students must either have Vector Calculus and Linear Algebra, or Maths for Sciences III.]
Syllabus
The geometry of smooth curves. Curvature; torsion; the Frenet formulas; congruence, and the fundamental theorem of space curves.
Smooth surfaces. Charts and atlases; tangent planes; the inverse function theorem; the regular value theorem; smooth mappings and their differentials; diffeomorphisms and local diffeomorphisms.
The geometry of smooth surfaces. First fundamental form (Riemannian metric); shape operator; normal curvature and principal curvatures; Gauss and mean curvatures; second fundamental form; local isometries; the "Theorema Egregium" of Gauss.
Task | Length | % of module mark |
---|---|---|
University - closed examination Differential Geometry |
2 hours | 100 |
None
Task | Length | % of module mark |
---|---|---|
University - closed examination Differential Geometry |
2 hours | 100 |
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
J McCleary, Geometry from a Differentiable Viewpoint, Cambridge University Press.
C Baer, Elementary Differential Geometry, Cambridge University Press
A N Pressley, Elementary Differential Geometry, available as both a book and an e-book