MATH 303 — ODE and Dynamical Systems (DKU)

Overview

MATH 303 is a required course for DKU students in the major Applied Mathematics and Computational Science and elective for students in other majors.

Course Description

Differential equations and dynamical systems are essential mathematical tools for modeling a large variety of phenomena. They are used in Physics, Chemistry, Biology, Ecology, Finance, Sociology, and beyond, to describe various processes. However, differential equations in most cases cannot be solved and we need to use qualitative methods in order to understand such processes. In this course we will do two things. First, we will see how to solve some first-order differential equations and linear differential equations. The fact that such differential equations can be solved makes them very special. Second, we will consider nonlinear differential equations. In general, these cannot be solved, and therefore we will need to qualitatively understand the behavior of the solutions, without actually finding them. To achieve this, we will combine our knowledge of the solutions of linear differential equations with other theoretical results from the theory of dynamical systems. This course uses results from single- and multi-variable Calculus and from Linear Algebra and it is a prime example of how such results can be applied in more complicated contexts with a wide range of applications in other scientific domains.