The course gives an overview of the theory of partial differential equations (PDEs).
The course can be divided into two main parts. The first part treats the Laplace-, heat- and wave- equation whichrepresent model examples of linear elliptic, parabolic and hyperbolic PDEs. Furthermore, first-order non-linear problemsand explicit solution techniques (e.g. transform methods, fundamental solutions, Green's function, scale invariance) areconsidered. The second part of the course covers weak solutions for second-order equations. Sobolev spaces areintroduced and studied. The existence, uniqueness and regularity in these spaces is discussed and the properties ofsolutions is studied.
The course requires 90 ECTS of which 22,5 ECTS is within Mathematical Analysis including a course in Multivariable Calculus and Differential Equations minimum 7,5 ECTS and a course in Linear Algebra minimum 7,5 ECTS. Proficiency in English equivalent to the level required for basic eligibility for higher studies. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.