Web Page for Math 414
TEXTBOOK: "A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods," de Vries, Hillen, Lewis, Muller, Schonfisch, SIAM, 2006.
Assignment 1 (due 2/8), Problems 1.4.1, 1.4.2 (some code to get you started), 2.4.5.
Assignment 2 (due 2/18), Problems 2.4.2, 2.4.9 (for this modify ParameciumAurelia.m, nonlin_ls.m), 2.4.14, and hand in code that generates output from the difference equation you developed in 2.4.14(b).
Assignment 3 (due 3/1), Problems 2.4.13 and also write a small piece of code that generates the solution for the parameter values given in (b); 2.4.18; and write code that generates the output in Figures 2.21 and 2.22.
Assignment 4 (due 3/11)
Problems 3.9.2, 3.9.3
Problem 3.9.4 and add part (d) use MATLAB's ode45 to solve each of the three ODEs and use the solutions to support your arguments in parts (b) and (c).
Problem 3.9.12 and add part (c), use ode45 to solve the systems in part (a) and (b) with realistic values of parameters chosen so that the differences in the models are apparent.
Assignment 7 (due 4/19)
Fit the model (10.2-3) p. 268 to the last two columns of data given in Table 9.9, p. 248. Use lsqnonlin. You may start with PAureliaPcaudatumContinuous.m, logistic_resid.m, logisticODE.m but at least as useful is LynxHare_fit.m. Hand in a listing of your code, which should plot the data and fitted model. Also sketch a plot of the phase plane diagram for the fitted values, and verify your sketch using pplane6.
Assignment 8 (due 5/1)
Example 1, week 1, Paramecium Aurelia, crude model fit & nonlinear fit.
Example 2, week 2, logistic difference equation for generating Fig 2.10.
Example 3, week 3, love affair, system of two difference equations, for generating Fig 2.19.
Example 4, week 4, phase plane/vector field MATLAB function, for Chapter 3.
Example 5, week 5, third order Taylor series method for solving an ODE, for Chapter 3.
Example 6, week 6, MATLAB's ode45 for solving the logistic ODE. You will also need this right hand side function for logistic ODE.
Example 7, week 7, nonlinear least squares data fitting: example 1 (NonlinDemo.m, expfun_resid.m, sample_plot.m), example 2 (LynxHare_fit.m, lynxhare_resid.m, lynxhare_rhs.m).