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### Vår 2019

# MAT-2200 Differential Equations - 10 stp

## The course is administrated by

## Type of course

## Course overlap

## Course contents

## Application deadline

## Admission requirements

Applicants from Nordic countries: Generell studiekompetanse og følgende spesielle opptakskrav:

Matematikk R1 + R2 og i tillegg enten:

- Fysikk 1 + 2 eller
- Kjemi 1+ 2 eller
- Biologi 1 + 2 eller
- Informasjonsteknologi 1 + 2 eller
- Geofag 1 + 2 eller
- Teknologi og forskningslære 1 + 2

International applicants: Higher Education Entrance Qualification and certified language requirements in English. It is a requirement that students have some prior knowledge of biology and ecology, chemistry and mathematics (Participants must have taken introductory level university courses, and achieved pass grades, in these subjects).

A list of the requirements for the Higher Education Entrance Qualification in Norway can be found on the Norwegian Agency for Quality Assurance in Education website - nokut.no

Recommended prerequsites is MAT-1003 Calkulus 3 and MAT-1004 Linear algebra or equal.

Application code is 9336.

## Objective of the course

- 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 autonomous systems in dimenstion 2.
- Know basic theory for Fourier series and use this to solve differential equations..
- Use the method 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

## Teaching methods

## 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.

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

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

## Recommended reading/syllabus

**Syllabus for MAT-2200 Differential Equations, spring 2019 **

UiT The Arctic University of Norway, Department of Mathematics and Statistics

**Textbook:** Edwards, Penney, and Calvis. Differential Equations and Boundary Value Problems: Computing and Modeling (5th Edition, Global Edition). Pearson 2015.

Syllabus:

Chapter 1: The whole.

Chapter 2: 2.2, 2.4, 2.5.

Chapter 3: 3.1, 3.2, 3.3, 3.5, 3.6.

Chapter 4: 4.1, 4.3.

Chapter 5: All except 5.3.

Chapter 6: 6.1, 6.2.

Chapter 7: Omitted.

Chapter 8: 8.1, 8.2.

Chapter 9: The whole.

Chapter 10: 10.1

**Materials allowed during final examination:**

Rottmann's tables

Two A4-sheets (both sides) of own handwritten notes

Approved calculator.