# Syllabus for Partial Differential Equations

Partiella differentialekvationer

## Syllabus

• 10 credits
• Course code: 1MA216
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Mathematics A1N
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2012-03-08
• Established by:
• Revised: 2022-02-11
• Revised by: The Faculty Board of Science and Technology
• Applies from: Autumn 2022
• Entry requirements:

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

• Responsible department: Department of Mathematics

## 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.

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 directives

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

Applies from: Autumn 2022

Some titles may be available electronically through the University library.

• Evans, Lawrence C. Partial differential equations

2nd ed.: Providence, R.I.: American Mathematical Society, 2010

Find in the library

Mandatory