MM842: Curves and Surfaces
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310008112, N310008102
Assessment: Second examiner: None, Second examiner: Internal
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master
STADS ID (UVA): N310008101
ECTS value: 5
Date of Approval: 30-04-2018
Duration: 1 semester
Version: Archive
Comment
Entry requirements
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.
The course can not be followed by students who: have passed MM512 or MM545.
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.
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.
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.
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
Content
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
Examination regulations
Exam element a)
Timing
Autumn
Tests
Mandatory assignments
EKA
N310008112
Assessment
Second examiner: None
Grading
Pass/Fail
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
0
Additional information
The examination form for re-examination may be different from the exam form at the regular exam.
Exam element b)
Timing
January
Tests
Bring-home exam at the end of the course
EKA
N310008102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
5
Additional information
The examination form for re-examination may be different from the exam form at the regular exam.
Indicative number of lessons
Teaching Method
At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.
Activities during the studyphase:
- preparation of exercises in study groups
- preparation of projects
- contributing to online learning activities related to the course