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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: achim@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 16-18 U26a 36
Common I Monday 16-18 U1 37-38,40,48
Common I Monday 16-18 U82 39,41
Common I Monday 10-12 U71 45
Common I Monday 10-12 U47 46,49
Common I Monday 10-12 U1 47
Common I Monday 10-12 U9 50
Common I Monday 10-12 U42 51
Common I Thursday 14-16 U47 36,39-41,46-51
Common I Thursday 14-16 U24 38
Common I Thursday 14-16 U51 45
Common I Friday 14-16 U71 37
H1 TE Monday 14-16 U157 37-41,45-51
H2 TE Wednesday 08-10 U145 37-41
H2 TE Wednesday 08-10 U14 45-51
H3 TE Tuesday 14-16 U147 40
H3 TE Wednesday 12-14 U23a 37-39
H3 TE Wednesday 12-14 U156 41,45,48-51
H3 TE Wednesday 12-14 U14 46
H3 TE Wednesday 12-14 U20 47
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Comment:
Ubegrænset deltagerantal.

H1 er først og fremmest til Mat. Øk studerende.

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
    Meddeles ved kursets start.


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.