MMG720, Differential Geometri, Spring 19

Latest news

Solutions to the reexams on 190823 and 200108 are posted under documents at the activity of the course in GUL.

Solutions for the exam.

Welcome to the course! The schedule for the course can be found in TimeEdit.

Teachers

Course coordinator:
Jan Stevens
room H5028, Tel. 772 5345, e-mail: stevens(at)chalmers(dot)se

Course literature


Andrew Pressley, Elementary Differential Geometry , Springer, London etc., 2nd ed, 2010.

Comments and additions:

Formulas for curves

The isoperimetric inequality

Gauss' Theorema Egregium

Reference literature:
M. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, 1976
Chr. Bär, Elementary Differential Geometry , Cambridge University Press, 2010.
L. M. Woodward and J. Bolton, A First Course in Differential Geometry: Surfaces in Euclidean Space. Cambridge University Press, 2018

English-Swedish mathematical dictionary

Program

Lectures

Days
 Section
 Contents
25 & 28/3
 1.1-1.5, 2.1-2.3
 Introduction, regular curves, arc length, Frenet-Serret trihedron, curvature and torsion
1 & 4/4
 3.1-3.3
 Isoperimetric inequality, four vertex theorem
8 & 11/4
 4.1-4.5, 5.1-5.3, 5.6
 Regular surfaces, examples, tangent plane
29/4, 2/5
 6.1-6.4, 7.1-7.3
 First fundamental form, isometries, conformal maps, area, Gauss map, second fundamental form, normal curvature
6 & 9/5
 8.1-8.4
 Gaussian and mean curvature, constant curvature
13 & 16/5
 9.1-9.5
 Geodesics, geodesics as shortest path
20 & 23/5
 10.1-10.4, 13.1-13.4
 Theorema egregium, Mainardi-Codazzi equations, Gauss-Bonnet theorem

Recommended exercises

Day
 Exercises
29/3
 1.1.1-3, 1.1.5, 1.1.7, 1.2.1, 1.2.3, 1.3.1, 1.4.1
5/4
 2.1.1-2, 2.2.2, 2.3.1, 3.1.1, 3.3.2
12/4
 4.1.1-4, 4.2.5, 4.4.1, 4.4.3, 5.1.2
3/5
 6.1.1ii,iv, 6.2.2-3, 6.3.3-4
10/5
 7.1.1, 7.3.2., 7.3.6-7, 8.1.1, 8.1.8-9
17/5
 8.2.3, 8.2.7-8, 8.3.1i, 9.1.1, 9.1.5
24/5
 9.2.1-2, 9.3.1-2, 10.1.1-2, 10.2.5

Course requirements

The learning goals of the course can be found in the course plan.

Read here about the theory on the exam.

Homework


Examination

The final exam is a written exam (no aids allowed) with 6 questions, which give together 25 points. For a pass (G) you need 12 points and for a pass with distinction (VG) you need 18 points.
The exam takes place on Wednesday June 5, in the afternoon (14-18).
There will be four possibilities to hand in homework. The homework can give up to two bonus points, which can be used at the exam (but not at re-exams) to reach a pass; for a pass with distinction the bonus points count only half.

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Old exams