## Maple and Excel examples for MA 314 (see also examples for MA 164H)

·  Mortgage of a house ( .xls) An Excel example to numerically solve the mortgage problem. Analytic solution is given here.

·  Digoxine example ( .xls) An Excel example to numerically find how to administer medicine problem.

·  Dynamic systems behavior ( .xls) An Excel example describing different behavior of a dynamical system.

·  Car Rental example ( .xls) An application of dynamical systems to Inventory  Distribution for a Car Rental Company.

·  Competitive Hunter example ( .xls) Sensitivity Analysis for the Owls-Hawks Model.

·  Predator-Prey system ( .xls) An Excel example describing Rabbits-Wolves system (compare with the continuous model).

·  Curve Fitting (.htp , .mws) In this example we construct models that fit a given data using the Chebyshev and the Least Squares technique. Then the data is plotted together with the corresponding solution. The models illustrated are linear model y=Ax+B, and power model y=Ax2.

·  Curve Interpolation (.htp , .mws) In this example we construct Lagrange interpolation polynomial for a given data.

·  Divided Differences behavior ( .xls) An Excel example which uses divided differences to study polynomial data.

·  Spline Interpolation (.htp , .mws) In this example we consider interpolation for a given data using natural cubic splines. We also compare polynomial and spline interpolation.

·  Area and volume ( .htp , .mws) Here we model deterministic behavior using simulation. Area and volume are found using Monte Carlo methods.

·  Heads/Tails game simulation ( .htp , .mws) A short Maple program, which simulates the throw of a coin game.

·  Unfair die simulation ( .htp , .mws) The throw of an unfair die is simulated using a short Maple program.

·  Let's make a deal ( .htp , .mws) The gameshow "Let's make a deal" is considered.

·  Harbour simulation ( .htp , .mws) In this problem we simulate the arrival and the unloading of four ships in a harbor. The inter arrival times are assumed to be uniformly distributed between 15 and  145 minutes and the unloading times between 45 and 90 minutes. The output provides the average and the maximum harbor and waiting times, as well as the percentage that the unloading facility was idle.

·  Linear programming ( .htp , .mws) Here we apply Maple to solve geometrically Linear Program with two decision variables.

·  Linear programming ( .xls) Here we apply Excel to solve algebraically Linear Program with two decision variables.

·  Maximum Flow Problem ( .xls) Here we apply Linear Programming to the maximum Flow Example on Figure 8.24.

·  0-1 Matrix Problem ( .xls) Here we apply Linear Programming to the 0-1 Matrix Example on p. 307 (Max Flow problem Figure 8.18).