MATS 230 Partial differerential equations, fall 2021, 9 cr

tekijä: Mikko Johannes Parviainen Viimeisin muutos keskiviikko 15. syyskuuta 2021, 01.36


Exercise points are denoted to TIM system 

First lecture: 6.9.2021, 14.1516.00, MaD381


A partial differential equation (PDE) is an equation involving an unknown function of two or more variables, and its partial derivatives. Partial differential equations have numerous applications to geometry, stochastics, mathematical finance, physics and image processing.

This course gives an introduction to PDEs. We derive representation formulas for linear equations, and deal with in particular the transport, Laplace, heat and wave equations. Typical questions that arise in the theory of PDEs are existence, uniqueness, stability, and regularity. At the end of the course we look at some examples of solving PDEs numerically using Matlab software.

This is first of the three PDE couses (others being MATS340 Osittaisdifferentiaaliyhtälöt 2 and MATS424 Viscosity theory) lectured at the math department. 


Lectures Monday 14.1516.00 at MaD381 and Tuesday 10.15-12.00 at MaD 202. 

Exercises Tuesday 8.30-10.00 at MaD259, starting at 14.9 (except the last two exercises which are at a computer classroom).

Lectures and exercises:  Jarkko Siltakoski, MaD250,


See the lecture note in the Material folder. It will be updated as the course progresses. Videos that cover the material will also be available after the lectures.

  1. week: Introduction of PDEs, derivation of transport equation, classifications of PDEs, Examples: minimal surface equation.
  2. week: Linear first order equations, method of characteristics, transport equation. Introduction to Laplace's equation.

Completion mode

Course exam and exercises, or alternatively final exam.

In the exercises, the exercises are denoted on the list, and one of the students works out the exercise on the board. You get points from exercises to the course exam according to the following:

35% exercises -> 1 point
85% exercises -> 6 points

If you cannot get to an exercise session, then you can return scanned exercises using this webpage or by sending them to the email address

Two last exercises are computer exercises using Matlab, which are to be returned and each exercise is graded on 0-1 scale. Participation gives you 2 points.


Bachelor level courses in mathematics are recommended, at the minimum in particular Vector calculus 2 or equivalent.  

Exam days

Course exam on 8.12.2021


Exercises appear in the Material folder during the course.


The course follows a lecture note that is updated as the lectures progress (see Material folder) and is mainly based on the beginning of 'Evans: Partial Differential Equations'.

Additional reading

  • E. DiBenedetto: Partial differential equations
  • W. Strauss: Partial differential equations. An introduction.
  • J. Kinnunen: Partial differential equations