Geometry of curves and surfaces, spring 2016

Last modified by mkankaan@helsinki_fi on 2024/03/27 10:27

Geometry of curves and surfaces, spring 2016

Teacher: Marja Kankaanrinta

Scope: 10 cr

Type: Advanced studies

Teaching:

Topics: We begin by studying the curvature and torsion of curves. After that we will study the geometry of surfaces. We will define the normal curvature of a surface and prove a theorem linking the geometry of a surface to linear algebra. We will study the Gauss and mean curvature of a surface and prove Gauss's Theorema Egregium. We will also prove the Gauss-Bonnet theorem for compact surfaces. Time permitting, we will study other topics, for example minimal surfaces.

Prerequisites: Students should know some multivariable calculus. For example, the course Vektorianalyysi (or Vektorianalyysi I and II) give a suitable background. We will also use some basic linear algebra like eigenvalues and eigenvectors.

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News

On Tuesday April 19 there will be no class, since that Tuesday is the department's recreation day.

Teaching schedule

Weeks 3-9 and 11-18, Tuesday 10-12 in room B120 and Thursday 10-12 in room C122. In addition, two hours of exercise classes per week.

Easter Holiday 24.-30.3.

Exams

One can pass the class by attending lectures and doing homework exercises. Alternatively, one can pass the class by taking an exam.

Course material

https://math.aalto.fi/~rkangasl/notes/kayrat_ja_pinnat.pdf

negat.curv.notes.pdf

geodesic.notes.pdf

hypgeomnotes.pdf

Suitable books are, for example,

A.N. Pressley: Elementary Differential Geometry.
John Oprea: Differential Geometry and Its Applications.

Registration

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Exercises

Assignments

Exercise classes

Group	Day	Time	Room	Instructor
1.	Wednesday	10-12	B321 (period III) / C321 (period IV)	Marja Kankaanrinta

Course feedback

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