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# 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 study program Mathematics and Finance - bachelor, and is included in the  programs Mathematics and Statistics - bachelor and Applied Physics and Mathematics - master (5-years). 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.

Applicants from Nordic countries: 1 June for the autumn semester and 1 December for the spring semester. Applicants from outside the Nordic countries: 1 October for the spring semester and 15 April for the autumn semester.

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. 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

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.

## 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 %.