MM512: Curves and Surfaces (5 ECTS)

STADS: 13001201

Level
Bachelor course

Teaching period
The course is offered in the spring semester.
4th quarter.

Teacher responsible
Email: swann@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal.

Prerequisites:
None

Academic preconditions:
The content of Calculus I+II must be known, Linear Algebra and Differential Equations must be known.

Course introduction
The course will introduce analytic techniques to deal with parameterized curves and surfaces in three dimensions and give the students methods to visualize the geometric results obtained.

Qualifications
Having successfully completed the course, the students can be expected to work analytically with the following concepts, understand the geometric content of and connections between these ideas, and to illustrate these concepts using a computer:

- arc-length, curvature and torsion for curves in the plane and three-dimensional space

- regularity of a parameterization

- principal, Gaussian and mean curvatures for a surface in three-dimensional space

- geodesic curves on parameterized surfaces in three-dimensions

Expected learning outcome
By the end of the course the student will be able to:

• reproduce definitions and results, together with their proofs, in the geometry of plane- and space-curves and of surfaces in space, within the scope of the course's syllabus
• apply these results to examples
• formulate and present definitions, proofs and computations in a mathematically rigorous way
• use a computer program to draw curves and surfaces and describe their properties within the scope of the course's syllabus

Subject overview
- Curves and arc-length

- Plane curves: signed curvature, the fundamental theorem, the isoperimetric inequality

- Space curves: curvature and torsion, the fundamental theorem

- Parameterized surfaces: regular patches, the tangent space, graphs, surfaces of revolution, normal curvature, geodesic curvature, the first and second fundamental forms, principal curvatures, Gaussian curvature, mean curvature.

- Geodesic curves and the equations describing them.

Literature

• Meddeles ved kursets start..

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Written exam. External examiner. Marks according to the Danish 7-scale.

Also a compulsory project, which is worked-on and handed-in during the course, pass/fail, examined internally by the teacher. The project has to be passed in order to be allowed to take part in the written exam.

Reexamination after 2. quarter.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger (28 timer), eksaminatorier/opgaveregning/computerlaboratorier (22 timer).
Educational activities

Language
This course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.