2015 Autumn 2015 Spring 2014 Spring 2013 Spring
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Dansk English

MM534: Differential Equations, Computing and Modeling (10 ECTS)

STADS: 13008501

Level
Bachelor course

Teaching period
The course is offered in the spring semester.
3rd and 4th quarter

Teacher responsible
Email: debrabant@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 08-10 U150 05,07-09,11
Common I Monday 08-10 U66 18-20
Common I Tuesday 08-10 U49e 15
Common I Tuesday 08-10 U62 16
Common I Tuesday 16-18 U66 17
Common I Wednesday 12-14 U150 06,10
Common I Wednesday 12-14 U17 19
Common I Wednesday 12-14 U14 21
Common I Thursday 10-12 U147 15
Common I Thursday 10-12 U62 16-18,20-21
Common I Friday 08-10 U91 06-11
S1 TE Wednesday 16-18 IMADAs terminalrum 15-21
S1 TE Friday 14-16 U24 05-11
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Comment:
Fælles undervisning med MM507 i 3.kvartal og MM531 i 4 kvartal.
Ubegrænset deltagerantal. 3. + 4. kvartal.

Prerequisites:
None

Academic preconditions:
Linear Algebra, Mathematical and Numerical Analysis should be known.

Course introduction
To introduce modeling of problems from science and engineering by ordinary differential equations. To analyse and solve these equations both by analytic tools (when appropriate) and by computational methods.

Expected learning outcome
  1. Formulate a differential equation as a model for a simple problem.
  2. Solve differential equations by analytical and numerical methods taught in the course.
  3. Find steady states and analyze the assymptotic behaviour of simple systems of differential equations.
  4. Construct, implement and analyse numerical methods to compute (approximate) solutions to differential equations.
  5. Give an oral presentation and answer supplementary questions on the course syllabus and the problems solved in mandatory assignments.
Subject overview
1.1. First order differential equations and mathematical models.
1.2. Slope fields and initial value problems.
1.3. Euler's approximation.
1.4. Existence and uniqueness, Picard-Lindelöf theorem (as application of fixed point theorem).
1.5. Gronwalls Lemma and the convergence of Euler's method.
1.6. Analytic tools: integrating factors, separation of variables, and exact equations.
2.1. Second order Linear equations: fundamental solutions, the solution space.
2.2. The Wronskian, Abel's theorem.
2.3. Forced vibrations and resonance.
2.4. Analytic tools: undetermined coefficients and the variation of parameters
3. Numerical methods: (embedded) Runge-Kutta methods and adaptivity.
4. Stiffness, implicit methods, A-stability.
5.1. Introduction to Ito-SDEs: Ito integral, Ito process, Ito formula.
5.2 Numerical methods for SDEs: Euler-Mayurama and Milstein methods, weak and strong convergence. 

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
None

Assessment and marking:
a) Oral exam. Danish 7 mark scale, internal examiner. (5 ECTS)

b) Mandatory assignments. Pass/fail, internal evaluation by teacher. A positive evaluation (pass mark) of the mandatory assignments is a pre-requisite for the oral exam. (5 ECTS)

Re-exam after 2nd 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
Laboratorietimer: 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.