Differential Geometry (MATH3405)
Information valid for Semester 2, 2024
Course level
Undergraduate
Faculty
School
Mathematics & Physics School
Units
2
Duration
One Semester
Attendance mode
In Person
Class hours
3 Lecture hours
1 Tutorial hour
Prerequisite
MATH2000
Recommended prerequisite
MATH2400, MATH2301
Assessment methods
Assignments and examinations
Course enquiries
Associate Professor Artem Pulemotov (Semester 2, Regular, St Lucia, In person)
Associcate Professor Artem Pulemotov
Study Abroad
This course is pre-approved for Study Abroad and Exchange students.
Current course offerings
| Course offerings | Location | Mode | Course Profile |
| Semester 2, 2024 (22/07/2024 - 18/11/2024) | St Lucia | In Person | Course Profile |
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.
