Objectives:

The course introduces the theory and solution methods for ordinary and partial differential equations.

Contents:

Solution methods for scalar and linear systems of differential equations, and stability of nonj-linear systems. The course also includes solution of different partial differential equations by means of Fourier series.

On completion of the course the student should have the following learning outcomes defined in terms of knowledge and skills, and general competence:

Knowledge and skills

The student has the ability to:

• Identify and solve first-order differential equations that are separable, linear or exact.
• Identify different processes that are described by one or more differential equations.
• Explain the theory of existence and uniqueness for second-order differential equations , and master solution methods in special cases.
• Use methods from linear algebra to solve linear systems and give a quantitative description of the solution curves in the phase plane.
• Find critical points for first-order non-linear systems and classify their stability properties.
• Work with simple predator-prey models.
• Use separation of variables and Fourier series to solve the wave equation and the hear equation.

General competence

The student has a good command of the theory behind the above methods

Written examination: 5 hours

Available aids: None