MM842: Curves and Surfaces
Study Board of Science
Teaching language: English
EKA: N310052112, N310052102
Assessment: Second examiner: None, Second examiner: Internal
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn, Spring
Level: Master
STADS ID (UVA): N310052101
ECTS value: 5
Date of Approval: 16-05-2023
Duration: 1 semester
Version: Archive
Comment
Entry requirements
Bachelor’s degree in applied mathematics.
The course can not be followed by students who: have passed MM512 or MM545.
The course can not be followed by students who: have passed MM512 or MM545.
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 and 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 and 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 in space: arc-length curvature and torsion, the fundamental theorem
- Surfaces in space: 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, Guass’ Theorema Egregium.
- Geodesics on surfaces and the equations describing them.
Literature
Examination regulations
Exam element a)
Timing
Autumn
Tests
Mandatory assignments
EKA
N310052112
Assessment
Second examiner: None
Grading
Pass/Fail
Identification
Full name and SDU username
Language
English
Examination aids
To be announced during the course
ECTS value
1
Exam element b)
Timing
January
Tests
Home-assignment
EKA
N310052102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
English
Examination aids
To be announced during the course
ECTS value
4
Additional information
Examination consists of a Home-assignment efter the course has ended.
The re-exam is changed to an oral exam if there are 9 or fewer students enrolled. The re-exam consists of several sets of questions that will be made available to the students in advance. Each set contains questions of different difficulty levels. At the exam one set will randomly be selected and the student must present the answers to the selected set of questions. The examiners can ask for details on the answers. This part takes roughly 20 minutes. At the end of the exam, the examiners can ask the student questions continuing in the same line or touching upon other topics discussed in the course. Total duration: 30 minutes.
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.
In order to enable students to achieve the learning objectives for the course, the teaching is organised in such a way that there are 58 lectures, class lessons, etc. on a semester.
In order to enable students to achieve the learning objectives for the course, the teaching is organised in such a way that there are 58 lectures, class lessons, etc. on a semester.
These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
- Intro phase (lectures) - 28 hours
- Training phase: 14 hours
The intro phase consists of lectures in which concepts, theories, models and ideas are introduced. The lecturer activates the students through varied and flexible communication. During the training phase, the students convert their academic knowledge into skills, test their skills and penetrate deeper into the material.
Activities during the studyphase:
- preparation of exercises in study groups
- preparation of projects
- contributing to online learning activities related to the course
Teacher responsible
Timetable
Administrative Unit
Team at Educational Law & Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.