MATH250 Partial Differential Equations and Models

MATH250 deals with three aspects of partial differential equations (PDEs):

• Modeling. Derivation of PDEs like the transport equation, the Laplace equation, the diffusion equation and the wave equation, from fundamental principles (balance laws). Examples of fundamental principles are conservation of mass, charge, particle number, momentum, energy.
• Analytical methods. How do we solve PDEs? The course contains an introduction to analytical methods for linear PDEs: Separation of variables, Hilbert-space theory, Sturm-Liouville theory, Fourier series and characteristics.
• Numerical methods and simulation. Almost all PDEs that describe phenomena we observe in real life can not be solved by using analytical methods. To be able to study phenomena described by such PDEs, numerical methods can be used to find approximate solutions. The course includes an introduction to two numerical methods: difference methods and element methods. Implementation by using a programming language of your choice.

Knowledge: When the course is completed, the student will have learned concepts, methods and techniques related to the course content.

Skills: Students shall:

• be capable of using relevant methods and techniques when encountering PDEs.
• know how to use a programming language in order to solve and visualize simple PDEs.
• be able to derive and analyze simple mathematical models in the form of PDEs.

General competence: Students will be capable of using the theory for solving problems in biology, geomatics, physics and other technology fields.