MM507: Differential Equations (5 ECTS)

STADS: 13000701

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: dellamor@cp3.dias.sdu.dk

Timetable
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Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM545 Ordinære differentialligninger og geometri.

Prerequisites:
None

Academic preconditions:
Linear algebra, Mathematical and numerical analysis should be known.

Course introduction
To introduce modelling of problems from science and engineering by ordinary differential equations and to analyse and solve these equations

Qualifications
Having completed the course successfully, the student can be expected to

• analyze and organize a domain or a situation with reference to mathematical modeling
• recognize problems which can be modeled by differential equations
• “read” the qualitative properties described by a model
• construct a mathematical model for a concrete problem
• find solutions analytical or numerical to ordinary differential equations by application of anappropriate tool
• to relate the solutions to the original problem

Expected learning outcome
At the end of the course the student should be able to:
1. formulate a differential equation as a model for a simple problem
2. solve differential equations by methods taught in the course
3. find steady states and analyse the asymptotic behaviour  of simple systems of differential equations

Subject overview
1.1. First order differential equations and mathematical models.
1.2. Slope fields andinitial 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. Systems of first order linear differential equations, and linear higher order differential equations: fundamental solutions, the solution space.
2.2. The Wronskian, Abel's theorem.
2.3. Analytic tools: undetermined coefficients and the variation of parameters.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Required assignments, pass/fail, internal evaluation by teacher.

Reexamination in the same exam period or immediately thereafter.
The re-exam may differ from the ordinary exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours, hereof:
 - Tutorials: 7 hours
 - Laboratory exercises: 7 hours

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.