Syllabus and Course schedule

Textbook: A Course in Mathematical Biology , de Vries et. al., SIAM 2006

References

• Essential Mathematical Biology by Nicholas F. Britton, Springer
• Mathematical Biology I, II, by J.D. Murray, Springer
• Mathematical Model in Biology by Leah Edelstein-Keshet, SIAM
• Introduction to the Mathematics of Medical Imaging, C. L. Epstein, Prentice Hall

Homework #1 Due Feb. 16th. 2007 (Submit your homework as an electronic file.)

Homework #2 Due Feb. 23rd 2007 (Submit your homework as an electronic file.)

Homework #3 Due Mar. 16th 2007 (Submit your homework as an electronic file.)

Homework #4 Due April 20th 2007 (Submit your homework as an electronic file.)

Homework #5: This homework is optional. If you have time, do this homework. If not, you may want to skip this homework. Instead, focus on your final project. For those who want to do this homework, I attached the ca1.m and ca4.m.

Example #1: Population growth of Paramecium aurelia in isolation using the discrete logistic model.

Model Equation: X(n+1) = r(1-x(n)/K)x(n)

p1.m (model plot), data.m (experimental data)

Cobwebbing and Linear Stability Analysis, Feb. 6 2007

Example #1: Experimental data for the change in population density and its polynomial approximation

p2.m (data plot and the 2nd order approximation)

p3.m (Cobwebbing for the discrete logistic model. You need to input the parametere k and the saturation level (or carrying capacity).)

p4.m (Cobwebbing for the discrete logistic model. For different population growth model (3rd order polynomial-like curve).)

p5.m (Cobwebbing for the discrete logistic model with the normalized population.)

p52.m (Feigenbaum Diagram)

Latex example file: mylatex.tex

Systems of Discrete-Time Series, Feb. 13 2007

Example #1: Love affairs: Romeo and Juliet

p6.m (Two by Two system)

Host-Parasitoid Model, Feb. 22 2007

Example #1: Nicholson and Bailey Model

p7.m (a,k,c, H[0] = 50, P[0] = 10)

Example #2: The Beddington Model

p9.m (a,r,c,K, H[0] = 50, P[0] = 10)

Pattern formation, Mar. 13 2007

Example #1: Turing instability

turing.m (Two chemical reaction, 1D model)

Example #2: 2D pattern formation

enzyme.m (Two dimensional model)

Stochastic Process, Apr. 12, 2007

Example #1: 2D Random Walk

brown.m

position.m

brown2.m (2 components with different diffusion coefficients)

position2.m

Example #1: 1D/2D Cellular Automata

ca1.m (1D CA)

ca4.m (Greenberg-Hastings Automata)

Medical image reconstruction, May. 15, 2007

Example #1: Recontruction of the Fourier 1D image containing the Gibbs oscillations.

iprm.m