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Dansk English

MM533: Mathematical and Numerical Analysis (10 ECTS)

STADS: 13010201

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: debrabant@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Tuesday 08-10 U91 40-41
Common I Wednesday 10-12 U131 36
Common I Wednesday 10-12 U53 37,39,45-48,50-51
Common I Wednesday 10-12 U91 49
Common I Thursday 12-14 U91 36-37,39-40,46-51
Common I Thursday 12-14 U71 45
Common I Friday 08-10 U91 41
S1 TE Monday 15-17 U49 40
S1 TE Tuesday 08-10 U30a 36-37,39,45-51
S1 TE Wednesday 10-12 U24 44
S1 TE Thursday 12-14 U30a 38
S1 TE Friday 12-14 U30a 38,41,43
S2 TE Tuesday 12-14 U142 36-41,43-44
S2 TE Wednesday 14-16 U133 45-51
S2 TE Friday 14-16 U142 38
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Revison of timetable:
: Ændret efter ønske og ekstra hold oprettet.

Prerequisites:
None

Academic preconditions:
Calculus in several variables should be known.

Course introduction
Analytical concepts are often based on limits of numerical approximations. The aim of this course is to provide the topological framework for convergence, construct and analyze numerical approximations and discuss the mathematical properties of their limits.

Expected learning outcome
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.

Subject overview
  1. Euclidian-, metric-, and topological spaces.
  2. Continuity of functions. 
  3. Convergence of sequences and series.
  4. Bisection and secant methods and their convergence. 
  5. Compact sets, Heine-Borel theorem. 
  6. Completeness of Euclidian spaces.
  7. Banach fixed point theorem, norms and contractions.
  8. Linear convergence of fixed point iteration. 
  9. Quadratic convergence of Newton iteration.
  10. Uniform continuity and the Riemann integral. 
  11. Adaptive Newton-Cotes quadrature. 
  12. Gaussian quadrature.
Literature
There isn't any litterature for the course at the moment.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
Prerequisite test consisting of mandatory assignments. Pass/fail, internal evaluation by teacher. The assignments have to be passed in order to participate in the written exam.  (13010212)

Assessment and marking:
Written exam. Danish 7 mark scale, external examiner. (13010202)

Reexam in the same exam period or immediately thereafter. The reexam may be a different type than the ordinary exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 56 hours
Skills training phase: 28 hours, hereof:
 - Tutorials: 14 hours
 - Laboratory exercises: 14 hours

Educational activities Study phase: 20 hours

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.