Instructor: Forger

Thus, Thurs 10-11:30

3 Credits

Background and Goals: From sleeping patterns, heartbeats, locomotion and firefly flashing to the treatment of cancer, diabetes and neurological disorders, oscillations are of great importance in biology and medicine.  Mathematical modeling and analysis are needed to understand what causes these oscillations to emerge, properties of their period and amplitude and how they synchronize to signals from other oscillators or from the external world.   The goal of this course will be to teach students how to take real biological data, convert it to a system of equations and simulate and/or analyze these equations.

Content: The course will provide an overview of biological problems (including demonstrations) and modeling techniques. Models will typically use ordinary differential equations. Mathematical techniques introduced in this course include 1) the method of averaging 2) harmonic balance 3) Fourier techniques 4) entrainment and coupling of oscillators 4) phase plane analysis and 5) various techniques from the theory of dynamical systems.  Emphasis will be placed on primary sources (papers from the literature) particularly those in the biological sciences.  Consideration will be given in the problem sets and course project to interdisciplinary student backgrounds.  Teamwork will be encouraged.