Gewone Differentiaalvergelijkingen

This course is about ordinary differential equations (ODE). For first order ODE we will treat linear, separable, and exact equations. We will prove existence and uniqueness of solutions, using Picard iterations. For second order ODE we will introduce the concepts of a Wronskian and a fundamental solution, as well as introduce the method of reduction of order. We will learn how to solve constant coefficient linear ODEs using the methods of variation of parameters and judicious guessing for finding particular solutions. Moreover, we will treat power series solutions, the method of Frobenius for equations with singular points and the method of solving ODE using the Laplace transform. We will treat higher order ODE as well as systems of linear ODE, using the eigenvalue-eigenvector method for finding solutions. We will also cover qualitative theory of ODE, in particular stability of solutions and equilibria, invariant sets, the Hartman-Grobman linearisation theorem and phase portraits of linear systems.