MM533: Mathematical and Numerical Analysis (10 ECTS)
STADS: 13008401Level
Bachelor course
Teaching period
The course is offered in the autumn semester.
1st and 2nd quarter
Teacher responsible
No responsible teachers found, contact the department if necessary
Timetable
| Group | Type | Day | Time | Classroom | Weeks | Comment |
|---|---|---|---|---|---|---|
| Common | I | Monday | 12-14 | U24 | 35-36,38-41 | |
| Common | I | Monday | 10-12 | U23a | 45-51 | |
| Common | I | Wednesday | 14-16 | U23a | 35-36,38-41 | |
| Common | I | Wednesday | 14-16 | U144 | 45,47 | |
| Common | I | Wednesday | 14-16 | U62 | 46,48,50 | |
| Common | I | Wednesday | 14-16 | U23a | 49 | |
| Common | I | Wednesday | 14-16 | U150 | 51 | |
| Common | I | Thursday | 10-12 | U142 | 35 | |
| S1 | TE | Monday | 12-14 | U24 | 37 | |
| S1 | TE | Tuesday | 12-14 | U23a | 49-51 | |
| S1 | TE | Friday | 08-10 | U23a | 36-39,41 | |
| S1 | TE | Friday | 08-10 | U89a | 40 | |
| S1 | TE | Friday | 12-14 | U14 | 45-48 |
Show personal time table for this course.
Comment:
Ubegrænset deltagerantal. 1.+2. kvartal.
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. Euklidian-, 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 Euklidian 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 quadratur.
Literature
- Meddeles ved kursets start.
Website
This course uses e-learn (blackboard).
Prerequisites for participating in the exam
None
Assessment and marking:
a) Written exam. Danish 7 mark scale, external examiner.
b) Mandatory assignments. Pass/fail, internal evaluation by teacher. (0 ECTS)
Re-exam after 4th quarter
The re-exam may be a different type than the ordinary exam.
Expected working hours
The teaching method is based on three phase model.
Forelæsninger: 56 timer
Eksaminatorietimer: 14 timer
Laboratorieøvelser: 14 timer
Educational activities
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.
