MATP31 Distribution Theory is an optional course for a Master of Science degree in mathematics. The course was given with the course code MATP31 for the first time in the spring semester of 2021. The previous course code is MATP11.

Course description

The course gives an introduction to Distribution Theory, which is an important tool for the theory of partial differential equations. All functions are not differentiable. One of the purposes of distribution theory is to deal with this problem. It also turns out that results from Fourier analysis are more satisfactory in the distribution theoretical twist. Distribution theory is an important tool in the theory of partial differential equations and thus essential for e.g. theoretical physics. Research on partial differential equations has a strong global position in Lund. The course treats: fundamentals of distribution theory, test functions, the concept of distributions, distributions with compact support, operations on distributions, convolution, homogenous distributions and the Fourier transform.

Teaching
The teaching consists of lectures and seminars. Lecturer is Erik Wahlén.

The lectures are held on Wednesdays, 13.15-15.00 and the seminars immediately after from 15.15-16.00. Both are in 332A. There's no seminar the first week.

See the following page for a detailed schedule of what we will cover each week. See also the link to TimeEdit below.

Plan of lectures and seminars.

Assessment
The course is assessed through a written and an oral examination. The oral examination may only be taken by those students who pass the written examination.

List of formulas for the written exam.

Exam 2023-05-23

Answers to the exam 2023-05-23

Exam 2023-08-21

Answers from the exam 2023-08-21

Course literature
J. J. Duistermaat, J. A. C. Kolk, Distributions, Theory and Applications, Springer, 2010, e-book

We will follow this book closely, so you won't need any other literature. However, if you are interested in other literature, I can e.g. recommend R. S. Strichartz, A Guide to Distribution Theory and Fourier Transforms, which is pretty light reading but isn't always as rigorous and complete as Duistermaat & Kolk.

I can also recommend G. Friedlander & M. Joshi, Introduction to the Theory of Distributions (which is a concise and rigorous book) and L. Hörmander, Linear Partial Differential Operators I (which is very complete, but a bit challenging as a first book on distribution theory).

Review of the course and old exams

Review questions

Exam May 2017

Exam Aug 2019

Answers to Exam Aug 2019

Note that there is a typo in the answers to the exam from Aug 2019. There should be a plus sign in the second factor in 2a, rather than a minus sign.

Schedule
The schedule is available in the TimeEdit schedule tool.

Official Course Description

Student Influence and Course Evaluation

General information about student influence can be found on the link below:

Information for students on student influence, work environment, complaints and study support at the Faculty of Science.pdf

Course representative: Abhijeet Vats

Checklist – what does a course representative do.pdf

Course evaluation 2023

Please fill out the course evaluation using this link. The evaluation is open until Friday June 9. The survey and analysis will be announced in Canvas.

Results from previous course evaluation

Course evaluation, Spring 2021