Partial differential equations
Partial Differential Equations is a large subject with a history that goes back to Newton and Leibnitz. Many mathematical models involve functions that have the property that the value in a point depends on its value in a neighborhood of the point. Dependencies like these can be modeled with a partial differential equation. Famous examples are Newton’s second law, Laplace's equation, Schrödinger’s equation and Einstein’s equations
About the group
The PDE group at department of mathematics has a strong connection to the "Centre of Mathematics for Applications". The research concerns linear and non-linear partial differential equations, often in relation to models in very different disciplines like oil extraction, finance or astrophysics. See the research plan for more details. The group is also currently interested in mathematical biology.
The group currently has five fulltime employees and varying number of PhD students, Post Docs and guest researchers. The PDE group has extensive international contacts.
The group is responsible in particular for the following courses:
MAT3360 "Introduction to Partial Differential Equations". This is the introductory PDE course. It treats basic existence and uniqueness results as well as some numerical methods.
MAT4301 "Partial differential Equations". This course is a continuation of MAT3360. Here you will learn more classical theory and techniques for PDEs in \(n\) dimensions.
MAT4305 "Partial differential equations and Sobolev spaces I", a third course in PDEs which also contains an introduction to Sobolev spaces and their role in the modern theory of PDEs.
MAT4315 "Partial differential equations and Sobolev spaces II", the next course in PDEs. The exact content can vary, but usually covers calculus of variations, time dependent problems and Galerkin approximations.
MAT4380 "Non-linear partial differential equations". A course given when sufficient interest and resources are available.
MAT-IN9240 "Numerical analysis of PDEs". A course given when sufficient interest and resources are available.
The group is involved in the master program "Mathematics", programme option "Mathematics for Applications", specialization Partial Differential Equations.