**Welcome to the course tma372/MMG800.**

This is a first course on partial differential equations PDEs intended for students following math and computation oriented studies in master programs at Chalmers and the University of Gothenburg, the International Mathematics Master Program, students in "Teknisk Matematik"(=TM), E3 students at Chalmers, as well as PhD students in computational/applied math and applied sciences and engineering. Students from other disciplines who are not following these programs are welcome to register for the course and encouraged to contact the instructor to get an approproaite follow-up scheme, if necessary.

*Contents:* The course covers topics as:
Approximating solutions to various PDEs (ODEs)
using the Finite Element Method, Polynomial Interpolation, Quadrature rules,
and the
solution of large, sparse linear system of equations. Stability and
convergence analysis, error estimates
in *a priori* and *a posteriori* settings.
Reisz representation and Lax-Milgram theorems,
Application of finite element methods to problems of dynamical systems,
heat conduction, wave
propagation, convection-diffusion-reaction, etc.

Compulsary home assignments contain both analytic approaches as well as coding aspects, ranging from iterative algorithms to problems involving complex multiphysics programing.

Following the course, actively, you should gain some modeling skills relevant to the PDE of your own field of interest, knowledge on weak/variational formulation, and a great deal of finite element analysis consisting of both theoretical aspects as stability and convergence of approximate solutions, as well as numerical analysis and implementations.

The course consists of 36 lecture hours, 20 exercise hours and gives 7.5 points. The course code is for engineering schools (students registered at Chalmers): tma372, and for students registered in GU: MMG800. See also course description:

**course description/PM.**