Date  Lecture 
Presentation 
1/19(R)  Introduction 

1/24(T)  Review of calculus, review of basic population models  
1/26(R)  Dimensions, Derivation of reactiondiffusion equations 

1/31(T)  Chemical mixing problem, boundary conditions 

2/2(R)  Separation of variables 

2/7(T)  Smoothering effect of diffusion 

2/9(R)  Steady states, Critical patch 
1. (P. Dunlap) Diffusion equation from Brownian motion 
2/14(T)  Point source, fundamental solution  2. (M. Zuk) Fourier transform in diffusion equation and music 
2/16(R)  Traveling wave solution of Fisher equation  3. (R. Carpenter) Fisher's 1937 paper 
2/21(T)  4. (D. LaMontagne) Derive animal
aggreration
model of Turchin 5. (D. Grady) Solution of porous media equation 

2/23(R)  Biological invasion 
6. (P. Lucey) Skellam's 1953 paper 
2/28(T)  7. (F. Hirata) Derive analytic solution
of diffusive logistic equation with
point source 8. (L. Osborne) Analytic solution of traveling wave solution of diffusive logistic equation 9. (T. Little) Exact solution of population model with densitydependent migration and Allee effect 

3/2(R)  10. (C. Brittin) Eigenfunctions of
Laplacian
for balls in 2d and 3d 11. (D. Bigelow) Harvesting of bottomdwelling creatures 

3/412 
Spring Break, no class on 3/7, 3/9 

3/14(T) 
no class, professor goes to a meeting  
3/16(R) 
no class, professor goes to a meeting 
date 
lecture 
presentation 
3/21(T)  Numerical solution of diffusion equation takehome test due 5pm 

3/23(R)  Perturbation and bifurcation  
3/28(T)  Global bifurcation and period of pendulum 

3/30(R)  Reactiondiffusion systems, phase plane analysis 

4/5(T)  Turing bifurcation  
4/7(R)  Sample presentation: reactiondiffusion equation with
convection 
Junping Shi 
4/12(T)  Patterns of
animal coat 

4/14(R)  Epidemics or chemotaxis models 

4/19(T) 
Derive
and solve BlackScholes PDE
in finance. (P. Dunlap) Tumour modeling (M. Zuk) 

4/21(R)  FitzHughNagumo
equation (P. Lucey) Traveling wave in epidemic models (D. Grady) Wave type solutions for Fisher equation in higher dimension. (F. Hirata) 

4/26(T) 
Regular and irregular patterns
in semiarid vegetation (D.
LaMontagne) Diversity of vegetation patterns and desertification (T. Little) Invasion and the evolution of speed in Australian cane toads (D. Bigelow) 

4/28(R) 
Synchronization in
reactiondiffusion models of neural
conduction. (L. Osborne) Autocatalytic chemical reactions (R. Carpenter) Nonlocal logistic equation (C. Brittin) 

4/29(F) 
project
paper due 5pm 

4/305/9 
no final exam 