Partial Differential Equations
Syllabus, Master's level, 1MA216
- Code
- 1MA216
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N, Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 11 February 2022
- Responsible department
- Department of Mathematics
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.
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 directives
The course cannot be included in the same degree as Partial Differential Equations, advanced course.
Reading list
- Reading list valid from Autumn 2022, version 2
- Reading list valid from Autumn 2022, version 1
- Reading list valid from Autumn 2019
- Reading list valid from Spring 2019
- Reading list valid from Autumn 2016
- Reading list valid from Autumn 2015
- Reading list valid from Autumn 2013
- Reading list valid from Autumn 2012, version 3
- Reading list valid from Autumn 2012, version 2
- Reading list valid from Autumn 2012, version 1