Aims

The course is designed to give basic knowledge of techniques for solving ordinary differential

equations and of their general properties as well as of the use of ordinary differential

equations as mathematical models. The course shall also provide the student with numerical

and manipulative skills in using the concepts introduced. Symbolic Algebra Programs may be

used in the course.

Content

Existence and uniqueness of solutions, dependence on initial values. Solvable types of

differential equations, integrating factors, variation of constants, the Wronski determinant.

Linear systems, fundamental matrix, exponential of a matrix. Non-linear systems, phase

space, critical points, stability and asymptotic stability, linearisation, Liapunov functions.

Introduction to the calculus of variations.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course. Hand-in assignments and oral examination

may be given during the course.