Agenda, Semester Week 13

\(n\)^th Order Differential Equations and Systems hereof

In this final week of the course we will treat linear differential equations with constant coefficients of higher order, in particular of order 2. With these we are embracing a larger category of differential equations that can describe physical systems spreading from mechanical vibrations to electric radio circuits and more. The best part is that we already have learned all the necessary tools for this study. Such higher-order differential equations can be rewritten to systems of differential equations of order 1, so our theory about such systems can be used to investigate \(n\)’th order linear differential equations with constant coefficients. For \(n=2\) in particular we will describe how one solves the homogeneous case.

Key Terms

Linear \(n\)’th order differential equations with constant coefficients. Initial-value conditions. Particular solutions. General solution for \(n=2\).

Preparation and Syllabus

This week will cover Sections 13.3 from Chapter 13 in [the textbook]. Note that Section 13.4 in this chapter is not a part of our syllabus.

Exercises

Exercises for Long Day. A SymPy test in Möbius for Python module 4 will take place 15:30-17:00 on Long Day.

The Short Day this final week is dedicated to exam training. The usual lecture at 13:00 will be replaced by a Q&A hour (lasting expectedly up to 1½ hours). At the exercise session, go to the website to the past exam problems via the menu and choose the May 2025 exam set to work on. There will be no Weekly Test this Short Day.