MM531: Differential Equations II
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300003102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Bachelor
STADS ID (UVA): N300003101
ECTS value: 5
Date of Approval: 25-04-2019
Duration: 1 semester
Version: Archive
Comment
13008201 (former UVA) is identical with this course description.
This course is co-read with MM831 og MM547.
Entry requirements
Academic preconditions
Studerende, der følger kurset, forventes at:
- Have kendskab til begrebet af en funktion, reelle og komplekse tal, differentiering og integration af funktioner af en og flere variable, vektor calculus, Konvergens af følger, Newton’s metode.
- Være bekendt med: systemer af lineære ligninger, matricer, determinanter, vektorrum, skalar produkt og ortogonalitet, lineære transformationer, egenvektorer og egenværdier, diagonalisering, polynomier, stokastiske variable, normalfordelingen
- Have kendskab til at implementere algoritmer som computer programmer og beregne numeriske approksimationer til matematiske problemer som ikke kan løses eksakt.
Course introduction
The purpose of the course is to analyse and solve ordinary differential equations by computational methods.
The course builds on the knowledge acquired in the courses MM536 (Calculus for Mathematics), MM533 (Mathematical and Numerical Analysis), MM538 (Algebra and Linear Algebra), MM507 (Differential equations) / first half of MM545 (Differential equations and geometry).
The course gives an academic basis for a Bachelor Project in several core areas of Natural Sciences.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to :
- handle complex and development-oriented situations in study and work contexts.
- Give skills to:
- analyse practical and theoretical problems with the help of numerical simulation based on a suitable mathematical model
- describe and evaluate sources of error for the modelling and calculation of a given problem
- justify relevant models for analysis and solution and choose between them
- Give knowledge and understanding of:
- Mathematical modelling and numerical analysis in science and engineering
- reflection on theories, methods and practices in the field of applied mathematics.
Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:
- Construct, implement and analyse numerical methods to compute (approximate) solutions to differential equations.
- Give an oral presentation and answer supplementary questions on the course syllabus.
Content
The following main topics are contained in the course:
- Numerical methods: (embedded) Runge-Kutta methods and adaptivity.
- Stiffness, implicit methods, A-stability.
- Introduction to Ito-SDEs: Ito integral, Ito process, Ito formula.
- Numerical methods for SDEs: Euler-Maruyama and Milstein methods, weak and strong convergence.
Literature
Examination regulations
Exam element a)
Timing
January
Tests
Oral exam
EKA
N300003102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Student Identification Card
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
5
Additional information
Reexamination in the same exam period or immediately thereafter. The re-exam may be a different type than the ordinary exam.
Indicative number of lessons
Teaching Method
Activities during the study phase:
- preparation of exercises in study groups
- preparation of projects
- contributing to online learning activities related to the course