Differential Geometry (MATH3405)
Information valid for Semester 2, 2020
Course level
Undergraduate
Faculty
School
Mathematics & Physics School
Units
2
Duration
One Semester
Delivery mode
Flexible Delivery
Class hours
3 Lecture hours
1 Tutorial hour
Prerequisite
MATH2000 or MATH2001
Recommended prerequisite
(MATH2400 or MATH2401), MATH2301
Assessment methods
Assignments and examinations
Course enquiries
Study Abroad
This course is pre-approved for Study Abroad and Exchange students.
Current course offerings
| Course offerings | Location | Mode | Course Profile |
| Semester 2, 2025 (28/07/2025 - 22/11/2025) | St Lucia | In Person | Profile unavailable |
Please Note: Course profiles marked as not available may still be in development.
Course description
Curves: Parameterised curves, regular curves, arc length. Local theory, Frenet frame. Global properties of plane curves.
Regular surfaces: Change of parameterisation, differential functions on surfaces. The tangent plane, the differential of a map. First fundamental form, area functional.
Geometry of the Gauss map: fundamental properties, local coordinates. Vector fields. Minimal surfaces and other applications.
Intrinsic and extrinsic geometry of surfaces: isometries, conformal maps.
Selected topics from: Theorema egregium. Parallel transport, geodesics. Gauss-Bonnet Theorem and applications. Exponential map. Geodesic polar coordinates.
