Some Tools Developed in Math 4
In math 4 we will learn what a system of ordinary differential equations
is and gain an understanding of the
fundamental
results about how to solve and understand such systems.
We will examine many interesting examples
like the Lokta-Volterra equations, linear systems of
equations, and a detailed look into some basic differential equations
like the
logistic equation. Mathematical topics such as the
stability analysis of equilibrium solutions and the basics bifurcation
theory will be explored via graphical techniques such as
simulation and
phases plane analysis as well as by
an exploration of some of the fundamental
mathematical results arising in these theories, like the
linearization theorem, the
characterization
of linear systems, and the use of various linear algebra
tools that arise in this context (include some matrix algebra and
eigenvalue analysis). Below you see a phase
portrait related to the Lokta-Volterra equations, equations that
arise when attempting model the relationship between predator and
prey.
