Entry requirements

120 credits including 90 credits in mathematics. Participation in Real Analysis. Participation in Integration Theory or read in parallel. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• solve non-linear equations of the first order with the method of characteristics;
• account for Sobolev spaces and basic properties of Sobolev functions;
• account for basic properties of solutions to Laplace's equation, the heat equation and the wave equation;
• account for applications of Sobolev spaces in regularity theory for elliptic partial differential equations;

Content

The method of characteristics and non-linear equations of the first order. Distributions and Sobolev spaces, extension and trace theorems. The Sobolev inequalities and theorems concerning compactness. The Laplace equation. The heat equation. The wave equation. Applications of Sobolev spaces in the theory of partial differential equations. Existence and uniqueness of weak solutions to elliptic equations of second order.

Instruction

Lectures.

Assessment

Written assignments during the course combined with an oral follow-up examination at the end of the course (10 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other regulations

The course cannot be included in the same degree as Partial Differential Equations, advanced course.