Math 232 - Introduction to Dynamical Systems for Biologists

• Prerequisites: Math 221 or 211
• Frequency: Irregular
• Student Body: This course is meant for students in the biological sciences
• Credits: 3. (N-I)
• Recent Texts: Calculus for Biology and Medicine (Neuhauser), Understanding Nonlinear Dynamics (Kaplan and Glass)
• Past Instructors: Christopher Raymond
• Background and Goals: Biology is a vast subject, but a common feature of many areas of biology over the past several decades has been the rapidly increasing importance of mathematics. Math 231 and Math 232 are companion courses covering two types of mathematical models important in biology: probabilistic (math 231) and deterministic (math 232). These are mathematics classes, but with a view towards biology and biological applications of the mathematical theory to be covered . We will discuss how to derive such models for various applications, mainly chosen from biology. We will show how to find exact solutions for certain special types of equations and how to get qualitative information about the solutions of such equations when we are unable to solve them exactly. This may include the use of computer programs such as Maple or Matlab.
• Alternatives: n/a
• Subsequent Courses: n/a

Content coverage:

• Differential and difference equations
• Exponential, Logistic, Gompertz growth models: bacteria, rabbits, cancer cells, etc.; effects due to delayed responses;
• Population Dynamics: sharks and fish, lynxes and rabbits, etc.; effects due to harvesting;
• Oscillations in biological systems;
• Waves in biological systems;
• Infectious diseases and epidemics;
• Deterministic models for population genetics;