MAT 516 - Math Biology

Units: 3
When Offered: Spring (even years)
The study of difference equations to model different biological phenomena. An introduction to concepts of the qualitative theory of differential equations such as steady-state solutions, stability and linearization, Phase-Plane methods and nullclines, classifying stability characteristics, global and local behavior, limit cycles, oscillations, and the Poincaré-Bendixson theorem. An introduction to linear difference equations and how to solve these analytically while understanding the behavior of solutions. Students will learn how analyze the qualitative behavior of solutions for nonlinear difference equations via linearization. The study of steady states, stability criteria and cobwebbing and other numerical resources to solve difference equations.