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Dansk English

MM533: Mathematical and Numerical Analysis (10 ECTS)

STADS: 13014601

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: zimmermann@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 14-16 U23 6,17,19
Common I Monday 16-18 U1 7
Common I Monday 14-16 U150 8,10
Common I Monday 14-16 U48A 9,15-16
Common I Monday 14-16 U55 11,20
Common I Monday 14-16 U1 12
Common I Monday 08-10 U20 18
Common I Tuesday 14-16 U74 14
Common I Wednesday 08-10 U23 6
Common I Wednesday 12-14 U1 7,14,16
Common I Wednesday 12-14 U23 8,15,19
Common I Wednesday 08-10 U1 9
Common I Wednesday 12-14 U45 10-11,17-18
Common I Wednesday 12-14 U55 12,20
Common I Wednesday 12-16 U1 21
H16 TE Wednesday 14-16 U64 7-12,14,16-17,19-20
H16 TE Thursday 08-10 U156 6,18
H16 TE Thursday 14-16 U154 15
H17 TE Monday 08-10 U31 15,19
H17 TE Monday 08-10 U8 17
H17 TE Thursday 10-12 U64 6-10,16
H17 TE Thursday 10-12 U156 11-12
H17 TE Thursday 10-12 U23A 18,20
H17 TE Friday 14-16 U8 14
M1 TE Tuesday 14-16 U64 6-12,15-20
M1 TE Tuesday 16-18 U155 14
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Comment:
Ubegrænset deltagerantal.

Prerequisites:
None

Academic preconditions:
Students taking the course are expected to:
  • Have knowledge of the contents of MM536
  • Have knowledge of the contents of MM540 or MM505 or acquire this knowledge in parallel to the lecture
 


Course introduction
The aim of the course is to enable the student to solve problems concerning the course topics by means of mathematical and numerical analysis. Formulate the answers (including proofs) in a correct mathematical language. Implement algorithms as computer programs and compute numerical approximations to mathematical problems that don't allow a closed form solution.

The course builds on the knowledge acquired in the courses MM536: Calculus for mathematics and MM505: Linear Algebra or MM540: Mathematical methods for economics and gives an academic basis for further studies in applied mathematics and mathematics that are part of the respective degree programs. More precisely, this includes MM545, MM546, MM547, MM548, MM549.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to analyse the qualitative and quantitative characteristics of a mathematical model
  • Give basic understanding on  how to perform computer based calculations in science,  technology and economy
  • Give knowledge and understanding of basic algorithms
 


Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
  • understand the abstract concepts of topological and metric spaces
  • understand and work with the notions of compactness, continuity and convergence in the settings of topological and metric spaces
  • understand the quantitative aspects of convergence in metric spaces
  • analyse and conduct basic numerical methods for
    • root finding
    • interpolation
    • integration
 


Subject overview
The following main topics are contained in the course:
  •     Euclidian-, metric-, and topological spaces.
  •     Continuity of functions. 
  •     Convergence of sequences and series.
  •     Bisection and secant methods and their convergence. 
  •     Compact sets, Heine-Borel theorem. 
  •     Completeness of Euclidian spaces.
  •     Banach fixed point theorem, norms and contractions.
  •     Linear convergence of fixed point iteration. 
  •     Quadratic convergence of Newton iteration.
  •     Uniform continuity and the Riemann integral.
  •     Interpolation. 
  •     Adaptive Newton-Cotes quadrature.
  •     Gaussian quadrature.
 


Literature
    Meddeles ved kursets start.


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Obligatory assignments, during the course. Pass/fail, internal evaluation by teacher. (0 ECTS).
  2. Written exam. Danish 7-mark scale, external marking. (10 ECTS).


Expected working hours
The teaching method is based on three phase model.
Intro phase: 56 hours
Skills training phase: 28 hours, hereof:
 - Tutorials: 21 hours
 - Laboratory exercises: 7 hours

Educational activities
  • Reading of suggested literature
  • Preparation of exercises in study groups
  • Contributing to online learning activities related to the course
 
Educational form
Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.

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.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.