Matlab files for Math 448 Spring 2006

MATLAB CODES FOR SELECTED EXAMPLES
"Mathematical Modeling", 3rd edition, by Mark Meershcaert

(last updated 12/04/2006)

Example 1.1 (Pig Problem)

contains sensitivity to both r and g

HTML version pig1.html
Matlab code pig1.m

Example 2.1 (Color TV Problem)

HTML version colorTV1.html
Matlab code colorTV1.m

Example 2.2 (Color TV Problem with constraints)

contains sensitivity to both parameter a and constraint value c

HTML version lagrange.html
Matlab code lagrange.m

Example 3.1 (Pig Problem with nonlinear growth assumption)

contains Newton's Method for solving equations of the type F(x)=0

HTML version NonlinearPig.html
Matlab code NonlinearPig.m

Example 3.2 (Facility Location Problem)

contains Random Search Method to solve systems F(x1,x2)=0, G(x1,x2)=0

HTML version Facility.html
Matlab code Facility.m (movie source)

Example 3.3 (Lawn Chair Problem)

contains Newton's Method for solving systems F(x1,x2)=0, G(x1,x2)=0

HTML version LawnChair.html
Matlab code LawnChair.m

Example 3.4 (Farm Problem)

contains Linear Programming (Large Scale Method and SIMPLEX method)

HTML version Farm1.html
Matlab code Farm1.m

Matlab codes for plotting solutions of dynamical systems
(courtesy of John Polking, Rice University, free download at http://math.rice.edu/~dfield/)

Plotting Direction Fields (for 1D Dynamical Systems) dfield.m
Phase Portraits (for 2D) pplane7.m
ODE Solver (for 2+ dimensions) odesolve.m

Example 4.2 (Whales Problem)

contains the code for plotting direction fields in Matlab
For phase portraits, use the interactive code pplane7.m

HTML version Whales.html
Matlab code Whales.m

Example 4.3 (Docking Problem)

Requires a separate file dockfun.m (see the note in the code)

HTML version Docking.html
Matlab code Docking.m

Example 5.1 (Tree Problem)

contains the code for the Eigenvalue Method for Continuous-Time Dynamical Systems

HTML version TreeEigenvalue.html
Matlab code TreeEigenvalue.m

Example 5.2 (Docking Problem Revisited)

contains the code for the Eigenvalue Method for Discrete-Time Dynamical Systems

HTML version DockingEigenvalue.html
Matlab code DockingEigenvalue.m

Pontryagin Maximum Principle

Contains the statement and an outline on how to apply the Maximum principle PDF

Landing Probe on Mars Problem PDF
Insects as Optimizers Problem PDF
Ferry Problem PDF
Harvesting for Profit Problem PDF

Example 6.1 (War Problem)

contains stability analysis for discrete dynamical systems performed via repeated simulations

HTML version war.html
Matlab code war.m

Example 6.2 (Euler Method for Whale problem)

contains Euler Method applied to the 2x2 system given by the Whale Problem

HTML version whaleseuler.html
Matlab code whaleseuler.m

Example 6.3 (Euler Method for RLC circuit problem)

contains Euler Method applied to the 2x2 system given by the RLC circuit Problem

HTML version RLCeuler.html
Matlab code RLCeuler.m

Logistic Map - Chaotic behavior

contains the plot of the bifurcation diagram for the limit set of the logistic map f(x)=ax(1-x)

HTML version perioddoubling.html
Matlab code perioddoubling.m
Interactive Java web applet - Period Doubling Map

Example 6.4 (Chaos in the discretized whale problem)

HTML version whaleschaos.html
Matlab code whaleschaos.m

Markov Chain Example

Google's PageRank (pages 23-31) part of Cleve Moler's "Numerical Computing with MATLAB" book
The m-files needed for PageRank example can be downloaded here.