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The goal of this website is to introduce the idea of mathematical modeling using a system of differential equations. It intends to familiarize readers with the behaviour of a linear system, and to introduce the reader to the idea of steady states and the stability of steady states for systems.

To understand the content, the reader should be comfortable working with ordinary differential equations and linear algebra.

This module was written by Gerda de Vries and Cole Zmurchok for CRYSTAL-Alberta.

Content adapted from Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, by Steven H. Strogatz, Perseus Books, 1994 and A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Tools, by G. de Vries et al, SIAM 2006.

An interested reader may wish to explore Romeo & Juliet - A System of Discrete-Time Equations. The discrete-time equation module is akin to this; however, it explores the problem in discrete instead of continuous time.