TMA4165 - Differential Equations and Dynamical Systems Spring 2024

The webpage for spring 2025: here

The main focus of this course is the study of systems of ordinary differential equations. While the solutions of some well-known families of equations and systems can be computed explicitly, this is not true in general. Instead one tries to understand how possible solutions will behave, without knowing an exact expression for the solutions. Questions that we will address are:

• Does a given system have at least one solution? If so, is there exactly one solution?
• Which influence has a slight change of a parameter or the initial data on the solution?
• If a system has a constant solutions, will solutions starting close by approach this constant solution in the long run or not?
• Is it possible to find out if a given system has at least one periodic solution? If so, what can be said about the period?
• Is it possible to sketch solutions without computing them explicitly?
• ….

For more details see either the Course description or the tentative curriculum below.

• Katrin Grunert
• Office: 1150, Sentralbygg 2
• Office hours: Thursday 13:00-14:00 and by appointment

• Monday 15:00-17:00, H1
• Thursday 14:00-16:00, F2

The lectures will not be recorded.

• Friday 10:000-12:00, R9
• A problem set will be given every week.
• The problems sets will be supervised and discussed 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

• Main book:
  • L. Perko: Differential Equations and Dynamical Systems.
  • Note that you can get the PDF from Springerlink.
• Supplementary sections (see tentative curriculum):
  • D.G. Schaeffer & J.W. Cain: Ordinary Differential Equations: Basic and Beyond.
    • Note that you can get the PDF from Springerlink.
    • Chapter 7.11 on index theory can be downloaded from here.
  • G. Teschl: Ordinary Differential Equations and Dynamical Systems
    • Note that you can get a PDF version for personal use only from here.

Further reading:

• H. Logemann and E.P. Ryan: Ordinary Differential Equations - Analysis, Qualitative Theory and Control, Springer Undergraduate Mathematics Series, Springer, London, 2014.
• I.R. Shafarevich and A.O. Remizov: Linear Algebra and Geometry, Springer-Verlag, Berlin Heidelberg, 2013. (Covers e.g. Jordan normal forms in detail.)
• G. Teschl: Ordinary Differential Equations and Dynamical Systems, Graduate Studies in Mathematics, Volume 140, Amer. Math. Soc., Providence, 2012. (Covers e.g. Hartman-Grobman in detail.)

Note: This is a tentative curriculum. That means we might not cover all the sections listed below and / or I might supplement with a few notes and material from other sources. See the lecture plan / topics page for details.

• Perko:
  • Chapter 1
  • Chapter 2
  • Chapter 3
• Schaeffer and Cain:
  • Section 4.4
  • Section 6.7
  • Section 7.1.1
• Teschl:
  • Sections 10.1-10.2
  • Sections 11.1-11.5
• Exercises

• A reference group should be created. Check here: https://i.ntnu.no/wiki/-/wiki/English/Reference+groups+-+quality+assurance+of+education
• If you have any remarks, request, complaints etc. regarding this course, contact the lecturer or the reference group.

• School exam.
• Date and time: 14.5.2024, 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.