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;
• use methods for obtaining exact solutions for linear homogeneous and non-homogeneous differential equations;
• find and classify fix points;
• give an account of results on existence and uniqueness of solutions;
• apply elementary power series techniques;
• describe some simple numerical solution techniques and be familiar with mathematical software for differential equations;
• use above mentioned techniques for systems of linear differential equations;
• use elementary techniques for qualitative studies of non-linear systems of differential equations;
• 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 examination at the end of the course combined with assignments given during the course.