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

· __Mortgage____ of a house__ ( **.xls**)
An Excel example to numerically solve the mortgage problem.

· __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.

· __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=Ax^{2}.

· __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.