Mathematics: Ordinary Differential Equations 1

<p>Ordinary differential equations are one of the most important mathematical tools within the natural sciences. They can be used to describe anything from population dynamics to quantum mechanics. The overarching goal of the course is for the students to aquire knowledge about the fundamental concepts and methods in the theory of ordinary differential equations, and to be able to apply these to solve and analyze relevant problems in the subject.</p><p>The course treats:</p> <ul> <li>Existence and uniqueness of solutions to initial value problems for systems of ordinary differential equations.</li> <li>Approximation of solutions and continuous dependence on parameters.</li> <li>Linear systems with variable and constant coefficients. Fundamental matrices and the matrix exponential function.</li> <li>Autonomous systems. Phase portraits. Stability theory. Periodic solutions.</li> <li>Applications in other sciences.</li> </ul>