English

MM842: Curves and Surfaces (5 ECTS)

STADS: 13016701

Level
Master's level course

Teaching period
The course is offered in the spring semester.

Teacher responsible

Email: dellamor@cp3.dias.sdu.dk

Timetable

Group	Type	Day	Time	Classroom	Weeks
Common	I	Tuesday	08-10	U7	44-50
Common	I	Wednesday	14-16	U28A	44
Common	I	Wednesday	14-16	U7	45-50
H1	TE	Friday	08-10	U27A	44
H1	TE	Friday	08-10	U7	45-50

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Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM512

Prerequisites:
Bachelor’s degree in applied mathematics.

Academic preconditions:
Students taking the course are expected to be familiar with: systems of linear equations, matrices, determinants, polynomials, the concept of a function, real numbers, differentiation and integration of functions of one and several variables, vector calculus.

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.

The course builds on the knowledge acquired in the courses MM536 (Calculus for Mathematics), MM533 (Mathematical and Numerical Analysis) and MM505 (Linear Algebra). The course gives the prerequisites for more advanced courses in geometry.

The course is of high multidisciplinary value and gives an academic basis for a Master Project in several core areas of Natural Sciences.

In relation to the competence profile of the degree it is the explicit focus of the course to:

Give the competence to
a. handle complex and development-oriented situations in study and work contexts.
Give skills to
a. apply the thinking and terminology from the subject's basic disciplines.
b. analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model.
Give knowledge and understanding of
a. basic knowledge generation, theory and methods in mathematics.
b. how to conduct analyses using mathematical methods and critically evaluate scientific theories and models.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

explain 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 theorems and proofs in a mathematically rigorous way
design, implement and perform computations

Subject overview

The following main topics are contained in the course:

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.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
The re-exam may differ from the ordinary exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours, hereof:
- Tutorials: 14 hours

Educational activities

preparation of exercises in study groups
preparation of projects
contributing to online learning activities related to the course

Educational form

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Remarks

The course is co-read with: MM512

The course cannot be chosen by students who: passed MM512 or MM545.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.