## Latest news

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

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

Comments and additions:

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

- Homework 1. To be handed in at the latest Thursday April 4 at the end of the lecture
- Homework 2. To be handed in at the latest Monday April 29
- Homework 3. To be handed in at the latest Thursday May 9
- Homework 4. To be handed in at the latest Thursday May 23

## 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

- exam 170531, solutions
- exam 150603, solutions
- exam 130314, solutions
- exam 110312, solutions
- exam 090307, solutions

## 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.
- Desmos. A free site to explore mathematics, inclding plotting.
- 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.