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
Grading system: Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
Finalised by: The Faculty Board of Science and Technology, 12 December 2011
Responsible department: Department of Mathematics

Entry requirements

Linear Algebra II. Several Variable Calculus or Geometry and Analysis III.

Learning outcomes

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

be able to give an account of basic concepts and definitions for differential equations;

know methods for obtaining exact solutions for linear homogeneous and non-homogeneous differential equations;

know how to find and classify fix points;

be familiar with results on existence and uniqueness of solutions;

know how to apply elementary power series techniques;

be able to describe some simple numerical solution techniques and be familiar with mathematical software for differential equations;

be able to use above mentioned techniques for systems of linear differential equations;

master elementary techniques for qualitative studies of non-linear systems of differential equations;

be able to present mathematical arguments to others.

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.