Curves and Surfaces (2012, RU)

Course Description

Curves and surfaces in a three dimensional Euclidean space are discussed from the local differential geometric perspective. The following subjects will be discussed in the class:

• Frenet equations for curvature and torsion of curves
• First and second fundamental form
• Gaussian curvature and Theorema Egregium
• Gauss-Bonnet Theorem
• Geodesics

Prerequisites

This is a course on elementary differential geometry for students in the second year of the bachelor. We only assume familiarity with calculus and linear algebra.

Examination

Written exam: July 4, 2012, 8:30-11:30 h in HG00.068. Second chance: August 20, 2012, 14-17 h in HG00.068. The exam is not open book. However you are allowed to make a summary of at most two pages A4, which you can use to remember the various formulas. I will check these at the beginning of the exam. More than two pages is not allowed!

Literature

We use the text book Elementary Differential Geometry by Andrew Pressley (Springer Undergraduate Mathematics Series). In addition lecture notes (giving a resume) can be found here.

Locations, material covered and exercises

• Week 16: Lecture: Sections 1.1, 1.2, 1.3, 2.1, Exercise class: 1.1.2, 1.1.3, 1.1.8, 1.2.1, 1.3.2, 2.1.1
• Week 17: Lecture: Sections 2.3, Exercise class: 2.3.1, 2.3.2, 2.3.3, 2.3.6
• Week 19: Lecture: Sections 4.1, 4.2, 4.4, 4.5, 5.3, No exercise class on Friday May 11
• Week 20: Exercise class on May 16 during lecture time in HG00.068: 4.2.6, 4.2.7, 5.3.1, 5.3.3, 5.3.4, 5.4.1
• Week 21:
• Week 22: