MM842: Curves and Surfaces

The Study Board for 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
Level: Master

STADS ID (UVA): N310052101
ECTS value: 5

Date of Approval: 12-03-2025


Duration: 1 semester

Version: Approved - active

Internal Course Code

MM842

Comment

The course is co-read with MM512.

Entry requirements

Bachelor’s degree in applied mathematics.
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, as obtained in the courses MM536, MM533 and MM505.

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.

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

See itslearning for syllabus lists and additional literature references.

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

Duration

48 hours

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

42 hours per semester

Teaching Method

Planned lessons
Total number of planned lessons: 42
Hereof:
Common lessons in classroom/auditorium: 42

The teaching consists of lectures in which concepts, theories, models and ideas are introduced. The lecturer activates the students through varied and flexible communication. During the excersices, the students convert their academic knowledge into skills, test their skills and penetrate deeper into the material.

Other planned teaching activities:
  • preparation of exercises in study groups
  • preparation of projects
  • contributing to online learning activities related to the course

Teacher responsible

Name E-mail Department
Du Pei dpei@imada.sdu.dk Institut for Matematik og Datalogi

Additional teachers

Name E-mail Department City
Adrian Petr adri@sdu.dk

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

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.