2024 Spring 2023 Spring 2022 Spring 2021 Spring 2020 Spring 2019 Spring 2018 Spring 2017 Spring 2016 Spring 2015 Spring 2014 Autumn 2013 Autumn 2012 Autumn
Show the courses of study containg this course Se overgangsordninger
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: debrabant@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 10-12 U20 5-6,9,11,14-15,17-19,21
Common I Monday 12-14 U20 10
Common I Monday 12-14 U55 16
Common I Wednesday 12-14 U20 5-6,9-11,13-14,16-18,20-21
Common I Wednesday 12-14 U140 19
Common I Thursday 10-12 U140 13,20
Common I Friday 10-12 U47 22 KD
M1 TE Monday 12-14 U56 5-7,9,11,14,18-19
M1 TE Monday 12-14 U155 15,17
M1 TE Monday 12-14 U14 21
M1 TE Tuesday 08-10 U56 10
M1 TE Wednesday 12-14 U155 7
M1 TE Thursday 12-14 U14 13,20
M2 TE Monday 14-16 U51 15
M2 TE Wednesday 10-12 U56 5-7,9-11,14,17-18
M2 TE Wednesday 10-12 U24 19
M2 TE Wednesday 10-12 U154 21
M2 TE Thursday 08-10 U14 7,13,20
O1 TE Tuesday 10-12 U142 5
O1 TE Tuesday 10-12 U155 6-7,9-11,14-15,17-19,21
O1 TE Thursday 14-16 U14 7,13,20
Show entire timetable
 Show personal time table for this course.

Comment:
Ubegrænset deltagerantal.

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
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

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.