Lectures cover the most important parts of each topic. After this, the students are given exercises on the same topics. The exercises are intended to help students practice calculation technique, understand methods and ideas as well as be able to apply the subject to technical-physical problems. Projects based on MATLAB will be an important part of the course.

MATH250 deals with the following topics:

• Modeling. Derivation of partial differential equations like the  Laplace equation, the diffusion equation and the wave equation from fundamental principles (balance laws) as conservation of mass, charge, particle number, momentum, energy
• Analytical methods. Analytical solution methods for linear partial differential equations: Separation of variables, Hilbert - space theory, Sturm - Liouville theory, Fourier series.
• Numercal methods and simulation. Numerical solution of partial differential equations by means of difference methods. Usage of the program package PYTHON or MATLAB.

Students are to learn the basic theory of partial differential equations. They are to become capable of using this theory for solving problems in biology, geomatics, physics and technology.

After completing the course, the students should master the following topics: conservation laws, classification of partial differential equations, the wave equation, diffusion equations, the Laplace equation, separation of variable techniques, Sturm-Liouville theory, Fourier series and Fourier transform techniques, difference methods.

Students are to be able to use:

• relevant methods and techniques with emphasis on practical applications
• the computer programme PYTHON or MATLAB for solving and visualising problems that are part of the course
• They should also be able to make and analyse simple mathematical models.