MS-C1350: Partial Differential Equations
| Course name | Partial Differential Equations |
|---|---|
| Course code | MS-C1350 |
| Abbreviation | PDE, Some may use ODY (Osittaisdifferentiaalyhtälöt) |
| Period | I-II |
| Lecturer | Riikka Korte |
Description
Introduction to differential equations which utilise partial derivatives with a focus on equations which model harmonicity, heat diffusion and wave movement. Main motivation for having the course is preparing the physics major students for the electromagnetic field theory course (NBE-C2102). The placement is relatively early in the suggested study plan from the school.
Course material
Official material
Lecture notes by Juha Kinnunen (https://sites.google.com/view/jkkinnun/lecture-notes?authuser=0). Lecture notes are very high quality but tedious to read if one is not proficient in reading such text. IMPORTANT: PLEASE READ THROUGH CHAPTER 7, NOTATIONS AND TOOLS.
Course iterations have lecture slides formulated based on the above lecture notes by the lecturer.
Extra material
- 3Blue1Brown - https://www.3blue1brown.com/lessons/pdes (Only a single video)
- Paul’s online math notes - https://tutorial.math.lamar.edu/classes/de/intropde.aspx
A course Telegram has been used for multiple iterations which has been considered immensely useful between the students.
Contents and workload
Be prepared to do work for this course. This is often the “first proper math course” and is often considered to be difficult. Teamwork with other students, including older students, helps immensely.
Overall workload
Weekly contents
| Week | Topics |
|---|---|
| 1-2 | PDE definitions (Laplace, heat, wave), Function spaces ($L^p$, continuously differentiable), Fourier series, change of variables - Goes over some generally used tools and definitions useful throughout the course. Workload is generally fine but change of variable exercises may be more difficult to understand and thus cause some headache. |
| 3-4 | Separation of variables, Boundary and initial value problems - Goes through a more proper approach of solving certain type of PDEs. Relatively manageable workload, includes a lot of mechanical calculations. |
| 5-6 | Fourier transforms, Convolutions, Approximations of the identity, PDEs in upper-half spaces - Goes through important tools of higher dimensional PDEs. Some of the exercises start to be relatively arbitrary (= more likely to be hard to understand) and thus the workload is perceived to be relatively high compared to the previous weeks. If you get the planar wave exercise, it is supposed to be a wave in the sense it solves the wave equation over some plane. |
| 7-8 | Laplace and Poisson equation, Harmonic functions, Green’s function, Gauss-Green theorem - Delves deep into harmonic functions and theory around Laplace/Poisson equations. This is where the course turns a lot more into applying mathematical theory than just mechanical performance, and the workload jumps sharply. Do not take this warning as a joke but do not overly fear this round either. Ask for help and help each other out. |
| 9-10 | Heat equation, Heat equation in a bounded (space-time cylindrical) domain - Delves deep into theory behind the heat equation and its variants. Workload is a massive drop from round 4 but there are still exercises which require good theoretical understanding so the workload is still notable. |
| 11-12 | Wave equation in 1-3 dimensions, Non-homogeneous wave equations - Delves deep into theory behind the wave equation and its variants. A bit higher workload than round 5, mostly due to often having a bit longer exercises. |
Practicalities
Graded 1-5. Completed by lectures, exercises and course exam OR exam only.
Exercises consist of:
- 11 prelecture MyCourses quizzes (10%)
- 6 assignments (25%)
- 2 extra assignment sheets which can be used to compensate missing points from the previous two categories. Random exercises (1-2) from each assignment sheet are graded more thoroughly.
The exam constitutes for 65% of the total grade and is the only technically mandatory part.
Related courses
Official prerequisites
Additional prerequisites
More like this
Trivia
- The course has a sticker pack made from different screen shots from the lecture notes.
- The course was originally only held in the first period with the same amount of exercises.
- Often considered to be the most difficult bachelor’s level mathematics course. Thus, it is often given as an option to anyone asking for easy credits.
- One of the rare English courses to have Finnish assignments as additional material.
- The course exam is often very similar to the returned assignments. Careful consideration and understanding the assignments is recommended.
- Has little actual PDE solving procedures due to having the goal of going over the necessary prerequisite theory for other courses.
- Often considered as a “vuosikurssikokemus” where a lot of people struggle with the course and success is found through teamwork.
Timestamp
Based on the 2026 version.