…and it is probably time to start posting in the blog again.
Here is web page for the course in Mathematical Biology, which turned into a course on geometric theory of ODE and Dynamical systems, so a better title for the course would be “A mathematical language for models in biology.” The original plan was too ambitious and I did not cover two last bullets:
- Evolutionary game theory. Classical game theory, Nash equilibria. Evolutionary game theory and the replicator equation. Biological application: How do altruists appear?
- Modeling the space heterogeneities. Random walk and diffusion equation. Traveling wave solutions. Reaction-diffusion systems. Biological application: How big does an island have to be to support a population?
Probably it is a good idea to have a reading course on this subject and finish the lecture notes, which definitely require a lot of polishing.
One more class in ODE is over, here is the latest web page. I updated lecture notes and hopefully now they contain much less typos and errors. The goal is to add a very limited number of topics, which are very important, quite interesting, and usually are not covered during the lectures due to time limitations, to give students an opportunity to have some additional reading. Topics that I have in mind are
- Convolution for the Laplace transform and Duhamel’s formula
- Treating periodic functions with Laplace transform
- Delta-function and Green’s function
- Applications of the systems of linear ODE in electric circuits
- System of masses on springs and separation of variables
- Short exposition of further topics in ODE
Finally, next semester I am teaching graduate ODE.
Mathematical Biology 