Program, 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 equation with constant coefficients. Initial conditions. Particular solution. General solution for \(n=2\).

Preparation and Syllabus

This week will cover Sections 12.3 and 12.4 from Chapter [12 - Systems of linear ordinary differential equations of order one with constant coefficients].

Exercises

Exercises for Long Day.

The Short Day this week (originally scheduled for Theme 4) will be dedicated to exam training. Firstly, an extraordinary lecture will be held from 13:00 lasting until about 14:30 — we will work through the HW4 solution in the first half of the lecture; the rest of the lecture will be a Q&A session, where students may bring questions to any part of the syllabus. At the exercise session after the lecture, go to the past exam problems via the menu and choose the May 2024 exam set to work on. There will be no Weekly Test this Short Day.