spring 2019

## MAT-2200 Differential Equations - 10 stp

## 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.

## 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.## 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 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.

## 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

Written test 31.05.2019The date for the exam can be changed. The final date will be announced in the StudentWeb early in May and early in November.

## Recommended reading/syllabus

Pensumliste for MAT-2200 Differential Equations## 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.