Ordinary Differential Equations II

5 credits

Syllabus, Master's level, 1MA052

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA052
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 3 November 2008
Responsible department: Department of Mathematics

Entry requirements

120 credit points including Ordinary Differential Equations I, Complex Analysis, general course, or corresponding courses

Learning outcomes

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

master the theory for systems of first order linear differential equations (determine fix points and periodic orbits and their stability properties);

be able to formulate, prove and apply existence and uniqueness theorems (Picard's method and Peano's theorem);

know the elementary theory of differential inequalities and its applications;

be able to use power series techniques for solutions of differential equations;

be able to formulate, prove and apply the theorem about the dependence of the solutions on initial data and parameters;

be familiar with properties of non-linear systems (invariant sets, stability properties);

master elementary techniques for boundary value problems (Sturm–Liouville theory);

be able to describe simple numerical solution methods.

Content

Existence and uniqueness proofs for solutions of ordinary differential equations, first order differential equations, systems of differential equations, non-linear system, dependence on parameters and initial data, numerical solution methods, power series solutions, differential inequalities, boundary value problems, Sturm–Liouville theory, non-linear system, stability, phase portrait.

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.