Math 490 lecture, presentation schedule
Instructor: Prof. Junping Shi
Jones 122, 221-2030,

Date Lecture
1/19(R) Introduction

1/24(T) Review of calculus, review of basic population models
1/26(R) Dimensions, Derivation of reaction-diffusion 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
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
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 density-dependent migration and Allee effect
10. (C. Brittin) Eigenfunctions of Laplacian for balls in 2-d and 3-d
11. (D. Bigelow) Harvesting of bottom-dwelling creatures
Spring Break, no class on 3/7, 3/9

no class, professor goes to a meeting
no class, professor goes to a meeting

3/21(T) Numerical solution of diffusion equation
take-home test due 5pm

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

3/30(R) Reaction-diffusion systems, phase plane analysis

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

4/14(R) Epidemics or chemotaxis models

Derive and solve Black-Scholes PDE in finance. (P. Dunlap)
Tumour modeling (M. Zuk)

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

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)

Synchronization in reaction-diffusion models of neural conduction. (L. Osborne)
Autocatalytic chemical reactions (R. Carpenter)
Non-local logistic equation  (C. Brittin)

project paper due 5pm

no final exam