Main Field of Study and progress level:
Mathematics: Second cycle, has only first-cycle course/s as entry requirements
Computational Science and Engineering: Second cycle, has only first-cycle course/s as entry requirements
Grading scale: TH teknisk betygsskala
Responsible department: Department of Mathematics and Mathematical Statistics
Contents
During this course we further develop the theory of elliptic, parabolic and hyperbolic partial differential equations. The course consists of two parts. The first part treats classical solutions to initial and boundary value problems for the Laplace, heat and wave operators. In addition, first order nonlinear problems and the Cauchy-Kovalevskaya theorem are studied and a variety of useful tools are introduced, such as Fourier transform methods and special ansatzes (separation of variables, scaling invariant methods). The second part of the course treats weak solutions to initial and boundary value problems for elliptic, parabolic and hyperbolic operator of second order. Sobolev spaces are defined and studied and, in particular, issues of existence, uniqueness and regularity are treated in the Sobolev setting. Moreover, properties of the solutions and different solution methods are investigated.
Required Knowledge
Required knowledge: Differential Equations for Engineers (5MA005) and Multi Variable Calculus (5MA010).
Proficiency in English equivalent to Swedish upper secondary course English A (IELTS (Academic) with a minimum overall score of 5.5 and no individual score below 5.0. TOEFL PBT
(Paper-based Test) with a minimum total score of 530 and a minimum TWE score of 4. TOEFL iBT (Internet-based Test) with a minimum total score of 72 and a minimum score of 17 on the Writing Section).
Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
Literature
The literature list is not available through the web.
Please contact the faculty.
