Mathematics Seminar - Cagri Karakurt, Bogazici University, Istanbul

Title: Differential Equations and Harmonic Oscillators

Abstract:

This is a sample lecture on non-homogeneous second-order linear differential equations with constant coefficients. The learning outcomes are as follows. At the end of the lecture, the students will:

1. Understand the structure of the general solution, y = y_c + y_p.
2. Be able to derive the complementary solution, y_c, using the characteristic equation.
3. Learn how to determine a particular solution, y_p, using the method of undetermined coefficients. Specifically, they will develop an intuition for correctly selecting a trial function based on the non-homogeneous term and the complementary part of the equation.
4. Witness an application of these concepts in a problem arising from physics: determining the equation of motion of a driven harmonic oscillator.