Maple Examples for MA 314
Curve
Fitting (via Chebyshev and Least Squares Criteria)
In this example we construct different
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}.
In this example using a certain data
(say n data points) we construct the polynomial of degree at most
n1
that interpolates this data. Then we plot the polynomial and the data points.
In this example using a certain data
(say n data points) we construct the cubic spline (degree at most
3) that interpolates this data. Then we plot the spline function and the
data points.
Monte
Carlo Simulation (Monte Carlo Simulation of Toss of a Coin and Roll
of an Unfair Die Experiments)
The first example simulates the toss
of a fair coin experiment to determine the probability of Heads or Tails.
The second example deals with the roll of an unfair die with probability
distribution of the outputs as follows;
Output

1

2

3

4

5

6

Probability

1/10

1/10

2/10

3/10

2/10

1/10

To simulate this experiment we choose
a random number in [0,1] and assign to this experiment outcome 1 if the
result is in [0,0.1] subinterval, 2  if in [0.1,0.2], 3  if in [0.2,0.4],
4  if in [0.4,0.7], 5  if in [0.7,0.9], and 6  if in [0.9,1.0].
Harbor
Simulation (Solution queuing problems using simulation techniques)
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.