MMA130 Theory of Distributions Spring 21

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This page contains the program of the course: lectures, exercise sessions and computer labs. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

Program

The schedule of the course is in TimeEdit.

We'll meet 3 times a week over Zoom; Mondays 13.15-15.00, Tuesdays 10.00-11.45, and Thursdays 13.15-15.00. The first meeting is on Monday January 1, 2021.
The meetings will consist of lectures and exercise sessions.

As literature we will use Hasse Carlsson's "Lecture notes on Distributions", which can be found on Hasse's webpage.

Preliminary schedule 

Week Chapters Contents
v. 3 1-3 general introduction, test functions, def of distributions, operations on distributions
v. 4 4-6 finite parts, fundamental solutions of some PDE's, support of a distribution
v. 5 7-8 convergence and convolution of distributions
v. 6 9-10 fundamental solutions, Fourier transform
v. 7 11-12 the Fourier transform and convolutions
v. 8 13-14 Paley-Wiener's theorem, existence of fundamental solutions
v. 9 15-17 fundamental solutions of elliptic differential operators, Fourier series
Applications

 

 


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Recommended exercises

H=Hörmander's book; HC=Hasse Carlsson's lecture notes

Week Exercises
v.3  HC: 1.2, 1.4, 2.2, 2.3, 2.7; H: 3.1.7
v.4  HC: 3.1, 3.2, 4.2; H: 3.1.1, 3.1.14, 3.1.20a, b, c
v.5  HC: 5.5; H: 3.1.20d,e,f, 3.3.9, 3.3.11, 2.5a
v.6  HC: 8.7; H: 2.6a, 2.16, 4.2.1, 4.2.2, 4.2.3, 4.2.4
v.7

 HC: 4.4, 12.5 (with alpha not an integer); H: 7.1.6, 7.1.9, 7.1.10, 7.1.11, 7.1.18
v.8  HC: 12.7, 14.1

 

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Computer labs

 

Reference literature:

  1. Learning MATLAB, Tobin A. Driscoll. Provides a brief introduction to Matlab to the one who already knows computer programming. Available as e-book from Chalmers library.
  2. Physical Modeling in MATLAB 3/E, Allen B. Downey
    The book is free to download from the web. The book gives an introduction for those who have not programmed before. It covers basic MATLAB programming with a focus on modeling and simulation of physical systems.

 

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Course summary:

Date Details Due