MA00CW41 Introduction to Partial Differential Equations (5 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Grading scale:
0-5
Description
A case study of Laplace's equation: gravitational/electric potentials, variational formulation. Explicit solutions in simple geometries; point charges and Poisson problems. Mean value pricinple, Maximum principle, Harnack's inequality. Conformal invariance and related solution methods.
Shorter studies of selected topics: the wave equation and Fourier transform; Sobolev spaces, weak solutions and general elliptic PDE theory; Finite element method.
Learning outcomes
After a completed course the student will:
-understand the importance of partial differential equations in applied and theoretical mathematics;
-know the basic theoretical questions (existence, uniqueness, stability, regularity) in PDEs and their theory in the case of the Laplace and elliptic PDEs;
-know the rudiments of various solution methods: kernel methods, Fourier series, finite element numerics.
Additional information
A new course (2026).
Shared with UTU. Materials prepared in English. Teaching language may be Swedish in case there are only Swedish-speakers taking the course.
Description of prerequisites
BSc level courses in: multivariate calculus, analysis, matrices/linear algebra. General BSc level mathematical maturity required.