TMA4305 Partial Differential Equations - Fall 2025
Messages
- The exam and a solution can be found on the previous exams page!
- Formula sheet: The final version has been uploaded (20.11.2025)
- Exam:
- The exam is a digital school exam with hand drawings, i.e., the problems are only shown to you on screen in Inspera, while you submit your handwritten answers on paper especially suited for scanning. You have to bring your own laptop with the safe exam browser installed and a charger.
- In case you never had a digital exam, where you write on paper: Digital school exam and Handwritten answers
- All problems have the same code.
- You are only allowed to write with blue or black ballpoint pens.
- Support material code C: Specified printed and hand-written support material is allowed. A specific basic calculator is allowed.
- You are not allowed to bring printed or hand-written support material with you, but a formula sheet will be provided together with the exam problems.
- This formula sheet will be attached to the exam problems: Formula sheet.
- Note: In the unlikely event that a mistake in the exam problems is spotted during the exam, you won't be informed.
- Formula sheet: The dominated convergence theorem has been added.
- 2. reference group meeting: Tuesday 28.10, 16:00
- If you have any remarks, request, complaints etc. regarding this course, contact the lecturer or the reference group.
- Contact information: further down under reference group
- Formula sheet:
- A first version has been published in the exam section further down.
- 1. reference group meeting:
- A summary can be found further down under reference group.
- The lectures are moved to Simastuen (Room 656, Sentralbygg 2)!
- Welcome to TMA4305 Partial Differential Equations!
- 1st lecture: Monday 18.8
- 1st exercise class: Thursday 28.8
- These pages will be updated regularly throughout the whole semester. As a consequence Blackboard will be used as little as possible, i.e., for important or urgent announcements or other information that does not need to be visible to the entire world.
General information
Lecturer
- Office 1150, Sentralbygg 2
- Office hours: Monday 14:00-15:00
Lectures
- Monday 10:00-12:00 Simastuen (Room 656, Sentralbygg 2)
- Tuesday 12:00-14:00 Simastuen (Room 656, Sentralbygg 2)
Exercises
- Thursday 10:00-11:00 R60
- A problem set will be given each week.
- The problem sets will be supervised in the exercise class. They are part of the curriculum, but are not required to be handed in.
- In general the exercise class is the right place to
- get help with the problem sets
- discuss and ask questions about the material covered in the course
Books and reading material
- Main book: David Borthwick: Introduction to Partial Differential Equations.
- A current list of errata is available here
- Note that you can get the PDF from Springerlink (you must be inside the NTNU network, either physically or via VPN, to get it).
- I might supplement this book with a few notes and material from other sources.
- Some other good PDE books include:
- P. Olver: Introduction to partial differential equations , Springer.
- S. Salsa: Partial Differential Equations in Action, Springer.
- L. C. Evans: Partial differential equations, AMS.
- If you want to know more about Lebesgue spaces:
- S. Axler: Measure, Integration & Real Analysis, Springer.
Tentative curriculum
From Borthwick's book (see further below for bibliographic detail) – but note that the introductory sections on model problems for the various equations are for information only; you are not expected to have detailed knowledge of these models or how they are derived.
- Ch 1 (self study)
- Ch 2 (background material for much of the book)
- Ch 3
- Ch 4
- Ch 6
- Ch 7 background material, no proofs
- Ch 9
- Ch 10
- Ch 11
- Ch 12
In addition:
- The exercises
- Notes by Harald Hanche-Olsen
- First order quasilinear equations: A5 for the screen, A4 for printing
- Weak maximum principle for the heat equation: A5 for the screen, A4 for printing
- Harmonicfunctionology: A5 for the screen, A4 for printing
- Notes by Katrin Grunert, which can be found on the Lecture plan / topics page.
- Chapter 4.4 in P. Olver: Introduction to partial differential equations, Springer.
Note: The notes and the material from other sources might overlap with Borthwick's book.
Reference group
- If you have any remarks, request, complaints etc. regarding this course, contact the lecturer or the reference group.
Exam
- Dato: 05.12.2025, 09:00
- School exam, 4 hours
- Support material code C: Specified printed and hand-written support material is allowed. A specific basic calculator is allowed.
- No printed or hand-written support material is allowed, but a formula sheet will be provided together with the exam.
- This formula sheet will be attached to the exam problems: Formula sheet.
- The exam will be given only in English. Students are free to answer in Norwegian or English.