# Ordinary Differential Equations I

5 credits

Syllabus, Bachelor's level, 1MA032

A revised version of the syllabus is available.
Code
1MA032
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 15 March 2007
Responsible department
Department of Mathematics

## Entry requirements

Several Variable Calculus, Linear Algebra II

## Learning outcomes

In order to pass the course (grade 3) the student should be able to

• give an account of important concepts and definitions in the area of the course;

• exemplify and interpret important concepts in specific cases;

• formulate important results and theorems covered by the course;

• describe the main features of the proofs of important theorems;

• express problems from relevant areas of applications in a mathematical form suitable for further analysis;

• use the theory, methods and techniques of the course to solve mathematical problems;

• present mathematical arguments to others.

Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.

## Content

Linear differential equations of order n, exact solutions, theorems of existence and uniqueness, power series solutions, systems of differential equations, nonlinear systems, classification of fixpoints, phase portraits, numerical solution methods.

## Instruction

Lectures and problem solving sessions.

## Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.