Ordinary Differential Equations II
5 credits
Syllabus, Bachelor's level, 1MA208
A revised version of the syllabus is available.
- Code
- 1MA208
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G2F
- Grading system
- Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
- Finalised by
- The Faculty Board of Science and Technology, 8 March 2012
- Responsible department
- Department of Mathematics
Entry requirements
60 credits in Mathematics including Ordinary Differential Equations I and Complex Analysis.
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 examination at the end of the course.