Brief Introduction to the Theory of Parametric Resonance

In these lecture notes, we present a basic mathematical theory of parametric resonance. This includes the Floquet stability theory for periodic systems of linear differential equations and its implications for nonlinear stability. As applications to mechanical systems, we consider a pendulum with a moving support. In the end we discuss other applications in physics. We refer the reader for further studies to the books [1, 2, 6].