Math 463 provides an introduction to the use of continuous differential equations in the biological and biomedical sciences. In this course, mathematical models are developed, analyzed and numerically simulated in order to investigate mechanisms underlying specific ecological, cellular and molecular processes. The goals of this course are: (1) Critical understanding of the use of a variety of dynamical systems methods in biology and (2) Exposure to computational techniques that are required to study ordinary differential equations that arise in mathematical biology. By the end of this course students are able to derive, interpret, solve, understand, discuss, and critique ordinary differential equation models of biological systems.
Here is what Lindsey Ades, who took the course in Fall 2017 had to say about her experience:
“Your course last semester has been one of my favorite courses that I have taken at the University of Michigan and I attribute a lot of that passion, as well as my success in the class, to your teaching. I really enjoyed learning from you.”
Math 563 – Advanced Mathematical Methods of the Biological Sciences
This course focuses on the derivation, analysis, and simulation of partial differential equations (PDEs) that model specific phenomena in molecular, cellular, and population biology. A goal of this course is to understand how the underlying spatial variability in natural systems influences motion and behavior. Mathematical topics covered include derivation of relevant PDEs from first principles; reduction of PDEs to ODEs under steady state, quasi-steady state, and traveling wave assumptions; analytical and numerical solution techniques for PDEs and concepts of spatial stability and instability. These concepts will be introduced within the setting of classical and current problems in the biological and the biomedical sciences such as cell motion, transport of biological substances, tumor growth, invasion, epidemiology and biological pattern formation. Above all, this course aims to enhance the interdisciplinary training of advanced undergraduate and graduate students from mathematics and other disciplines by introducing fundamental properties of partial differential equations in the context of interesting biological phenomena.