MMG720 V21 Differentialgeometri
This page contains the program of the course: lectures, exercise sessions and computer labs. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Program
The schedule of the course is in TimeEdit.
Lectures
| Week | Section | Contents |
|---|---|---|
| 12 | 1.1-1.5, 2.1-2.3 | Introduction, regular curves, arc length, Frenet-Serret trihedron, curvature and torsion |
| 15 | 3.1-3.3 | Isoperimetric inequality, four vertex theorem |
| 16 | 4.1-4.5, 5.1-5.3, 5.6 | Regular surfaces, examples, tangent plane |
| 17 | 6.1-6.4, 7.1-7.3 | First fundamental form, isometries, conformal maps, area, Gauss map, second fundamental form, normal curvature |
| 18 | 8.1-8.4 | Gaussian and mean curvature, constant curvature |
| 20 | 9.1-9.5 | Geodesics, geodesics as shortest path |
| 21 | 10.1-10.4, 13.1-13.4 | Theorema egregium, Mainardi-Codazzi equations, Gauss-Bonnet theorem |
Recommended exercises
| Week | Exercises |
|---|---|
| 12 | 1.1.1-5, 1.1.7, 1.2.1, 1.2.3-4, 1.3.1i,ii, 2.1.1i.ii,iv |
| 15 | 1.4.1, 2.1.2, 2.2.2, 2.3.1, 3.1.1, 3.3.3, 3.3.2 |
| 16 | 4.1.1-4, 4.2.3, 4.2.5, 4.4.1, 4.4.3, 5.1.2 |
| 18 | 6.1.1ii,iv, 6.2.2-3, 6.3.3-4, 7.1.1, 7.3.1-3 |
| 19 | 7.3.6-7, 8.1.1, 8.1.8-9, 8.2.2-3 |
| 20 | 8.2.7-8, 8.3.1i, 9.1.1, 9.2.1-, 9.3.1-2 |
| 21 | 9.1.5, 9.2.2, 9.5.1-2, 10.2.5, 10.1.1-2, 13.1.1 |
Homework
Solutions to homework 1
Computer labs
The use of GeoGebra is recommended.
Links
- Virtual Math Museum , a gallery of curves and surfaces
- Famous Curves. Click on the name of a curve to see its history and some of its associated curves.
- GeoGebra. A free interactive geometry, algebra and calculus application.
- Wolfram Math World . A site with many definitions and examples.
- Touching soap films, an online book on minimal surfaces.
- Surfer, free software to visualise zero sets of polynomials.
Course summary:
| Date | Details | Due |
|---|---|---|