spring 2019
MAT2200 Differential Equations  10 ECTS
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 MAT1003 Calkulus 3 and MAT1004 Linear algebra or equal.
Application code is 9336.
Course content
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.Objectives of the course
After the course the student should be able to Solve first order linear and certain types of nonlinear 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 nth 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 SturmLiouville eigenvalue theory on standard problems from separation of variables.
Assessment
Written final exam of 4 hours duration, counting 100 %.
Assessment scale: Letter grades AF.
Resit examination: Students having failed the last ordinary examination are offered a resit 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.
Recommended reading/syllabus
Syllabus for MAT2200 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 A4sheets (both sides) of own handwritten notes
Approved calculator.
 About the course
 Campus: Tromsø 
 ECTS: 10
 Course code: MAT2200
 Responsible unit
 Institutt for matematikk og statistikk
 Kontaktpersoner
