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Math 590: Advanced Applied Mathematics

### Course Description

The course will focus on problems from mathematical biology.

The mathematical biology sources will be Peskin and Hoppenstaedt's
"Mathematics in Medicine and the Life Sciences" and Murray's
"Mathematical Biology". The course will start with a crash course in
nonlinear ODEs and bifurcation theory using Jordan & Smith's
"Nonlinear Ordinary Differential Equations". Additional references
would be Hirsch & Smale and Guckenheimer & Holmes. We will consider
population dynamics, biological oscillators, reaction-diffusion
equations, chemotaxis, biological waves, spatial pattern formation,
and epidemiology. Students will be introduced to matlab and will use
it to perform computational experiments.
Class meets TuTh, 3:00 -- 4:20.

### Prerequisites

Freshman Calc, Sophomore Calc, Real Analysis. Additional courses on
ODEs and PDEs would be appreciated, but not demanded.

Homework due Thursday September 24.

Homework due Thursday October 1.

a maple worksheet showing how to do perturbation expansions

Homework due Thursday October 8.

Solutions to chapter 5 homework

Crash course in matlab

Homework due Tuesday October 20.

Making figure 7.4

Homework due Tuesday October 27.

Homework due Thursday November 5.

Homework due Tuesday November 17.

Homework due Thursday December 10.