Partial differential equations
Partial Differential Equations is a large subject with a history that goes back to Newton and Leibniz. 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 partial differential equations. Well-known examples include Schrödinger's equation in quantum mechanics, the Navier–Stokes equations in fluid mechanics, and Einstein's equations in general relativity theory.
Are you interested in writing a master thesis with a researcher in this group? Check out this list of previous master theses written with CM members.
About the group
The PDE group does research on both linear and non-linear partial differential equations, often in relation to models in very different disciplines like astrophysics, fluid dynamics, oil extraction and finance. The group is also currently interested in mathematical biology. The research is both oriented toward analysis and numerical methods for partial differential equations.
The group currently has four full time employees and a varying number of PhD students, postdocs 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, but may be taken independently 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 continuation of MAT4305. 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.