Vår 2014

MAT-2200 Differential Equations - 10 stp

The course is administrated by

Institutt for matematikk og statistikk

Type of course

The course is mandatory in the Master's degree program in industrial mathematics, and is included in the Bachelor's degree program in mathematics and statistics. It may also be taken independent of study program.

Course overlap

MA-221 Ordinary differential equations 6 stp

Course contents

This course covers the elementary theory of ordinary and partial differential equations. It is useful to all science students. Covers equations of the first order, systems of linear equations, series solutions, numerical methods for ordinary differential equations, separation of variables for partial differential equations and Fourier series.

Admission requirements

Generell studiekompetanse + REALFA + MAT-1003 Calkulus 3 and MAT-1004 Linear algebra or equal .

Søknadskode 9336.

Objective of the course

After the course the student should be able to

Solve first order linear and certain types of non-linear differential equations.
Classify stability of equilibrium for first order differential equations with parameters.
Know existence/uniqueness theorem for initial value problem of differential equations.
Know the concept of linearly independent solutions and particular solutions of n?th order linear differential equations and be able to superpose solutions.
Solve linear differential equations with power series around ordinary points.
Classify linar and almost linear autonomous systems of differential equations with stability of equilibrium.
Solve systems of linear differential equations with constant coeffisients.
Make face portraits and direction fields for aotonomous systems in dimenstion 2.
Know basic theory for Fourier series and use this to solve differential equations..
Use the merthod of separtation of variables on simple partial diferential equations with boundary and initial value conditions that lead to development of Fourier series.
Use Sturm-Liouville eigenvalue theory on standard problems from separation of variables.

Language of instruction

The language of instruction and the syllabus is English. Examination questions will be given in English, but may be answered either in English or a Scandinavian language.

Teaching methods

Lectures: 40 h
Coursework: 30 h

Assessment

Written final exam of 4 hours duration, counting 100 %.

Assessment scale: Letter grades A-F.

Re-sit examination:
Students having failed the last ordinary examination are offered a re-sit examination early in the following semester, if the course is compulsory in their study programme.

Postponed examination:
Students with valid grounds for absence will be offered a postponed examination early in the following semester.

Ordinary examination in the teaching free semester (early exam):
A new ordinary examination will be arranged provided that it already will be given a postponed or a re-sit exam for the course.

For further details see:
- Utfyllende bestemmelser for eksamener ved Fakultet for naturvitenskap og teknologi (only in Norwegian)
- Regulations for examinations at the University of Tromsø

Coursework requirements
A passing grade is required on the mandatory homework sets for permission to take the exam.

Date for examination

One written 06.06.2014

The date for the exam can be changed. The final date will be announced at your faculty early in May and early in November.