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Content

Course Catalog 





Amath 504 is intended as either the third course in the Amath 422-423-504 mathematical biology sequence


or as a standalone course in advanced aspects of mathematical biology.



The primary focus of the course is on spatial models in biology.





Topics to be covered include:

  • 
the formulation of spatially structured models,

  • 
reaction-diffusion equations,

  • 
steady-state solutions,

  • 
models of spread,

  • 
traveling waves of invasion,

  • 
the spread of rabies,

  • 
integrodifference equations,

  • 
PDEs in stochastic problems,

  • 
random movement: the diffusion equation revisited,

  • 
reaction-diffusion models for chemical reactions,

  • 
the Smoluchowski theory of diffusion-controlled reactions,

  • 
Brownian motion and stochastic differential equations,

  • 
and Kramers theory and evolutionary stochastic dynamics.