TMA4165 - Differential Equations and Dynamical Systems Spring 2023

General Info


  • Re-sit examination:
    • Date: Friday 18.8
    • The exam will be a standard oral exam, where you answer questions for about 40 min. Paper and black/whiteboard will be available.
    • I will contact those signed up for the exam via email in week 29.
  • Exam (updated 5.6.)
    • I handed in the grades today.
    • The exam and a solution can be found on the previous exams page.
    • The grading guidelines (also called sensur veiledning) can be found on BB.
  • The Faculty of Information Technology and Electrical Engineering (IE) is sending out a questionnaire-based student evaluation for courses taught at IE. Please help us to improve our teaching by answering this survey in the course TMA4165 Differential Equations and Dynamical Systems
    • The survey closes on May 5. (You answer anonymously, but need to log in with Feide for safety reasons.)"
  • 3rd reference group meeting: At the beginning of the last lecture.
  • Last lecture: Mattelab
    • Unless you have suggestions for certain exercises, exam problems, etc, you would like to have a look at together. If so send an email at the latest on Thursday 20.4..
  • Exercise class 17.4:
    • Devoted to answering questions concerning the posted solution of the project or your solution.
    • Exercise sheet 10 will be discussed on 24.4.
  • The project: A solution is posted on the exercise / project page.
  • 2nd reference group meeting: 9.3
    • If you have any remarks, request, complaints, suggestions contact the reference group.
  • We are well aware of the TMA4165 exercise class being at the same time as the TMA4180 lecture.
    • We asked timeplanen several times to reschedule either the TMA4180 lecture or the TMA4165 exercise class, but without success.
    • For us, i.e. the TMA4165 team, it is nearly impossible to find a time slot which suits all students taking the course as well as a free lecture hall, since there are various study programs involved.
    • See the exercise page for updated information.
  • 1st lecture: Monday 1/9: KJL4 08:00-10:00
  • 1st exercise class: Monday 1/16

General information

The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasises the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modelling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods.

In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

- Wikipedia: read the full article here.


  • Luca Galimberti (week 2-9)
  • Office: 1002, Sentralbygg 2
  • Office hours: Friday, 16:00 - 17:00 (Please write me a message in advance)
  • Katrin Grunert (week 10-17)
  • Office: 1150, Sentralbygg 2
  • Office hours: by appointment


  • Monday 08:00-10:00
    • week 1-3: KJL4
    • week 4-17: H2
  • Tuesday 08:00-10:00
    • week 1-3: H3
    • week 4-17: H2

Exercise assistant


  • Monday 15:00-17:00, K5
  • A problem set will be given every week.
  • The problems 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
  • A project will be given at some point of the semester. You need to get this project approved to be eligible for the exam.

Books and reading material

  • D.G. Schaeffer & J.W. Cain: Ordinary Differential Equations: Basic and Beyond.
    • Note that you can get the PDF from Springerlink (you must be inside the NTNU network, either physically or via VPN, to get it).
    • Chapter 7.11 on index theory can be downloaded from here.

Further reading:

Tentative curriculum

  • Material covered in the lectures (cf. lecture plan / topics)
  • Exercises
  • Project

Reference group

Name Email

Add at the end of the email adresses.


  • School exam.
  • Date and time: 30.5.2023, 15:00
  • Support material code D: No printed or hand-written support material is allowed. A specific basic calculator is allowed.
  • If the course is taught in English, the exam will be given only in English. Students are free to answer in Norwegian or English.
  • Compulsory assignment: You need to get the project approved to be eligible for the exam.
    • If you have fulfilled the project requirement a previous semester, you do not have to do so again. If you want confirmation that you have a registered approval from a previous semester, you need to contact Studentservice.
2023-07-13, Katrin Grunert