Svensk version

The course is taught together with the course MATP36 Partial Differential Equations at the division of Mathematics at the Faculty of Science. More information about MATP36.

What is the course about?

Partial differential equations are widely used for mathematical modelling in science and engineering. At LTH, the course FMAN55 Applied Mathematics provides an introduction to the subject.

Such an introductory course focuses largely on finding explicit solutions to problems in relatively simple geometries, using methods such as separation of variables and Fourier analysis. In an advanced course, the emphasis shifts from explicit computation to the underlying mathematical structure. Using tools from functional analysis and methods such as energy estimates, we study fundamental questions: Do solutions exist? Are they unique? What properties do they have? How do they depend on the data?

This approach allows us to go beyond simple geometries and to study inhomogeneous and nonlinear problems for which explicit solution formulas cannot be found. Once existence, uniqueness and, preferably, continuous dependence on the data have been established, one can turn to methods for computing approximate solutions, as in FMNN45 Numerical Analysis of Partial Differential Equations.

The course thus uses more advanced mathematical tools than in previous courses to draw rigorous conclusions about models governed by partial differential equations.

Syllabus - Study period - Course literature LTH.se