||To expand using Binomial Theorem the binomial (ax+b)^n, with a, b, n,
||You will be prompted for values of a, b, and n. The program will then
display the expanded polynomial.
||The polynomial is stored in M1 in vector form.
|This calculates a normal approximation to a large binomial distribution
||You will be prompted for the number of Bernoulli trials, the probability
of a positive outcome, whether the number of positive outcomes is <,
>, <= or >= the given target, and the target (the given number of
|Uses the Newton-Raphson Method to find a root of an equation given a
||Run the aplet.
After the instruction message box, enter the equation in F1(X). If
you wish, you may plot the equation at this stage.
Use VIEWS to select Solve Equation... You will be
prompted for an initial guess, and the aplet will iterate the equation
until it either encounters a mathematical error, or the iteration
converges on a root (to 8 decimal places), or 30 iterations are carried
out without convergence.
If no errors are encountered, the aplet's NUM view will be
displayed with all intermediate values of X. If the aplet encounters an
error, the HOME screen will be displayed. Press NUM to view
the iteration's progress up to the point of the error.
The four columns in NUM are as follows:
X: The current guess
F1(X): The function at the
F2(x): The derivitave of the
equation at the
F3(X): The next guess
Press VIEWS and select New Function to enter another
equation, or press SYMB to view the current equation, derivative,
and next guess equation.
1. Unlike the rest of this collection, this IS
an aplet and should be loaded from the LIB view.
2. I've also written a Newton-Raphson aplet. Mine
is intended as a teaching tool and is very visual. Quin's is intended as a
||Generates a transformation matrix given geometric transformations
||You will be prompted initially for the number of translations required.
You can then select the translations, in the order
that they are applied, to be reflections, shears, rotations, or dilations
(scaling operations). For each translation you
may be required to supply additional information.
|The resulting matrix is stored in M9. The 'Rotation'
uses the current HOME angle setting
||Finds a transformation matrix given two points and their images.
||You will be prompted for a point, it's image, another point, and it's
image. This is useful for questions like:
A(x1, y1)->A'(x2, y2)
B(x3, y3)->B'(x4, y4)
What matrix will transform A to A' and B to B'?
|Some point combinations cannot be described with a linear transformation
matrix, and so this program cannot solve them.
The points are entered as complex numbers (x, y). The resulting matrix
is stored in M3.
||Demonstrates the effect of a translation matrix on a user-defined shape.
||The main menu consists of four options, Define Shape, Transform,
Set Axes, and Exit.
Define Shape: This allows the user to define a shape to be
drawn. By default this is a 2x2 square with vertices at (-1, -1), (1, -1),
(1, 1), and (-1, 1).
Transform: This draw the axis and the initial shape. Press any
key to continue. The shape is then drawn after the transformation has been
applied, so the two shapes can be compared. Press any key to
Set Axes: This allows the axis ranges to be changed from inside
|This program calls another program
'DrawAxes', which MUST be on your calculator before running
|Prob. from Z-Score
||Replace the "Cumulative Probabilities For The Normal
Distribution" table in the SEA Tables Book.
||You will be prompted for a z-score, and the direction of the
area [P(Z<=z) or P(Z>=z)]. The program will display the
|This is covered in the Prob Distributions
aplet in my collection. (CC)
|Z-score from Prob.
||Provide an inverse function for the 'Prob. from Z-score' program.
||You will be prompted for a probability (between 0 and 1). The area under
the curve y=erf(X), representing this probability, can be to the left of
the Z-score in question, to the right, or centered. The Z-score will then
be displayed. Press any key.
||This is covered in the Prob Distributions
aplet in my collection. (CC)
|Linear System Solver
||To solve an NxN system of linear equations
||You will be prompted for the number of variables. Then each equation is
input in vector form.
ax + by + ... = c
dx + ey + ... = f
is entered as
[a, b, ..., c] ENTER
[d, e, ..., f] ENTER
The value of each variable is displayed, in the order used in the
equations. In the example, the results would be x=, y=, etc.