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Wesley B. Loewer's
Plotting Programs
version 1.12
(C) 1991, Wesley B. Loewer
Manual Updated: May 18, 1992
Page 2
Table of Contents
Topic Page
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Latest Version . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Common Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Saving & Retrieving . . . . . . . . . . . . . . . . . . . . . . 5
PCX Format . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Plotting & Zooming . . . . . . . . . . . . . . . . . . . . . . . 6
Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Two Dimensional Function Plotter . . . . . . . . . . . . . . . . . . 10
Conic Section Plotter . . . . . . . . . . . . . . . . . . . . . . . . ?
Derivative Plotter . . . . . . . . . . . . . . . . . . . . . . . . . 13
Relation Plotter . . . . . . . . . . . . . . . . . . . . . . . . . . ?
Bifurcation Plotter . . . . . . . . . . . . . . . . . . . . . . . . . 14
Data Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . ?
Revision History . . . . . . . . . . . . . . . . . . . . . . . . . . 18
In Closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Plotting Programs
Page 3
Introduction:
These plotting programs were designed to help students understand graphs
a little better by allowing them to quickly plot a graph to see what the
function looks like. Often, students get bogged down in button pushing
and point-by-point plotting and fail to grasp the real significance
behind the graph. The goal of these programs is to eliminate the busy
work of plotting, freeing the student to proceed to higher level
thinking.
Speaking of free, that's one of the nice things about these programs.
(See the end of this file for the conditions in which this program may
be used without charge.) These may not be the best plotting programs
that you can find, but you can't beat them for the price. I have tried
to include as many features that I thought students and teachers could
actually use. Please distribute to anyone who can use it.
Latest Version:
The latest version of "WL Plot" can be found at
Data Warp Premium BBS
(713) 355-6107
Spring, TX
"WL Plot" is distributed as WLPLT???.ZIP, where the ??? represents the
version number. When passing "WL Plot" along to others, please
distribute all the files and documentation. Currently, the ZIP contains
the following files:
wlplot.exe func.exe conic.exe
deriv.exe relat.exe cfit.exe
bifurc.exe helvb.fon wlplot.doc + sample files
Hardware:
You will need an IBM-compatible computer with DOS version 3.0 or later.
(It will probably work with an earlier version but it has not been
tested.) You will also need some sort of graphics capability, either
CGA, EGA, MCGA, VGA, or Hercules graphics adapters (except for the Curve
Fitting program). A mouse is useful but not necessary.
Plotting Programs
Page 4
Getting Started:
Start the program by typing "wlplot" at the DOS prompt. The user will
be presented with the following choices.
Assortment of Plotting Programs
1) Functions
Plots functions in Cartesian, Polar, or Parametric form.
2) Conic Sections
Plots parabolas, circles, ellipses, and hyperbolas.
3) Derivatives
Plots functions along with 1st and 2nd derivatives.
4) Relation Plotter
A somewhat slow but extremely useful plotter for graphing relations
that are not necessarily functions. It's also good for those
situations where you just cannot solve for y.
5) Bifurcations
A bifurcation fractal plotter. Shows period doubling and
demonstrates concepts such as Chaos and the Feigenbaum number. To
see an example, try the population equation r*p*(1-p) with initial
value=0.5, x min=1, x max=4, y min=0, y max=1, with r as the
independent variable and p as the dependent. It's slow so be
patient.
6) Curve Fitting
Fits a line or curve to a set of data points. Uses linear,
logarithmic, exponential, power, and up to 9th degree polynomial
models. This program can run without a graphics adapter card.
Graphics is not needed to calculate the coefficients of the best
fit line or curve (such as slope and intercept). Graphics
capability is needed, however, if the curve is to be displayed on
the screen or printed. Up the 1500 data points are allowed.
0) Exit
Exits the program.
The individual programs listed may be loaded either from "wlplot" as
shown above or from the DOS command line. This was done so that 360K
floppy based users could still use the programs on separate disks. Each
of these plotting programs are explained in detail below. All the
programs share a similar user interface. When a program first starts, a
menu appears on the screen with several groups of options listed
together. To move from one group to another, you can use the following
keys:
Function key (ex. <F3>) - moves to a particular group
<TAB> - moves to the next group
<SHIFT><TAB> - move to the previous group
To move to different options within a group, use the up and down arrow
keys. If you have a mouse, simply point the mouse arrow to the desired
selection and click the left mouse button. A ">" will appear at the
Plotting Programs
Page 5
left of the selected option. There are four different types of options
on the menu screen. Each type is explained below with an example.
Toggle type The option is turned on or off by pressing the
space bar, the return key, or clicking on the
option with the left mouse button. If an X
appears in the parenthesis, the option is turned
on.
Example:
(X) Grid The grid is turned on.
Example:
( ) Grid The grid is turned off.
Choice type A list of choices is presented. A choice is
selected by pressing the space bar, the return
key, or clicking on the choice with the left mouse
button.
Example:
( ) Cartesian The list presented on the left can only have one
( ) Polar choice between them. In this case, the Polar
(*) Parametric graph is selected, so the graph cannot be
Cartesian or Parametric.
Example:
(2) Cartesian The Cartesian type graph has been selected. The
( ) Polar "2" indicates that 2 equations will be
( ) Parametric simultaneously plotted. A "1" would indicate a
single equation would be plotted.
Action type Selecting an action option causes something
immediately to be done. An action is activated by
pressing the space bar, the return key, or
clicking the left mouse button.
Example:
Save Saves current equations and settings to disk.
Dialogue type The program expects a response from you, such as a
value or an equation.
Example: The user is expected to enter in a function such
y() = as "sin(x)"
Example: The user is expected to enter a number such as
x min = "-2.5"
Common Features:
A number of features are common to several of the plotting programs.
These common are discussed below.
Saving & Retrieving:
When a save or retrieve action is selected, the main menu is cleared and
another screen appears at the top of the screen prompting you for a file
name to use to save the data. You can type in a file name, or if you
have a mouse, double click on a file name listed. You do not have to
put an extension on your file names. (For example, the file name
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Page 6
"abcd.efg" has the extension is ".efg".) A default extension will be
appended to filenames which do not have an explicit extension.
PCX Format:
The PCX format is a graphics format commonly used by other software,
such as painting, word processing, and desk-top publishing programs.
Therefore, graphs saved with the "Save-PCX" option can be imported into
these other programs. The filename extension for PCX files is ".pcx".
Variables:
These programs can use up to 10 variables at a time. To indicate which
variable is to be the horizontal independent variable, move to that
variable in the "<F5> Variables" menu and enter an "i" or an "h". The
message "<independent variable>" will then appear. Some programs allow
you to declare a variable as the vertical dependent variable by entering
a "d" or "v". To get rid of old variables, select the "Purge Unused
Variables" option.
Plotting & Zooming:
While the graph is being plotted, hitting any key will stop the plotting
procedure. After plotting is finished, an arrow will appear. This
arrow can be move around by either the arrow keys or a mouse. Pressing
the space bar will cause the X & Y coordinates of the arrow tip to be
shown in the lower left hand corner of the screen. You can zoom in to
define a new plotting area by placing the cursor at the desired
location. To define the left, right, top, or bottom edges, press the
'l', 'r', 't', or 'b' keys respectively. The <F1> key or the <LEFT
MOUSE BUTTON> is a short-cut for the bottom left hand corner of the
plotting area, and pressing the <F2> key or the <RIGHT MOUSE BUTTON> is
a short-cut for the top right hand corner of the plotting area. A
rectangle will appear to show what area you have define. Pressing the
<ENTER> key, the <ESC> key, or <BOTH MOUSE BUTTONS> will cause the graph
to be replotted with the new zoomed in screen coordinates. Pressing the
<CTRL-ENTER> or <CTRL-BOTH MOUSE BUTTONS> causes the graph to zoom out,
making the image smaller. If zooming has not taken place, the program
returns to the main menu.
Printing:
To print a graph directly to a printer, DOS's GRAPHICS utility must be
loaded before starting the plotting menu. When you have a graph that
you would like printed, press the <SHIFT><PrtSc> key (or just <PrntScrn>
key on enhanced keyboards). See your DOS manual for details of the
GRAPHICS command. Note that DOS version 3.3 and earlier can only print
CGA mode graphics while version 4.0 and later can print EGA and VGA
graphics as well. You can force the plotting program to use CGA mode
graphics by starting the program with "wlplot cga". This allows you to
print the screen, even if your DOS version is prior to 4.0, even if you
have a VGA card. You can also print a screen by saving it to a file by
selecting "Save-PCX" and then importing the PCX file into a painting or
word processing program. This allows you to merge plots with other
graphics into a document. (See "PCX Format" on page 6 of this
document.)
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Page 7
Functions:
The following functions are known to the program:
Constants:
pi 3.141592653589793
e 2.718281828459045
Binary functions:
add x+y
subtract x-y
multiply x*y or 2x
divide x/y
exponentiation x^y
modulus x mod y or mod(x,y)
combination comb(n,r)
permutation perm(n,r)
maximum max(x,y)
minimum min(x,y)
Unary functions:
negation -x or neg(x)
inverse inv(x)
square root sqrt(x)
square sq(x)
round round(x)
ceiling ceil(x) round up
floor floor(x) round down
integer int(x) truncate decimal
fractional frac(x)
absolute value abs(x)
sign sign(x)
factorial n! or fact(n)
is value real? isreal(x)
Trigonometry functions: (in radians)
sine sin(x)
inverse sine asin(x) or arcsin(x)
cosine cos(x)
inverse cosine acos(x) or arccos(x)
tangent tan(x)
inverse tan atan(x) or arctan(x)
inverse tan2 atan2(x,y) or arctan2(x,y)
cotangent cot(x)
inverse cot acot(x) or arccot(x)
secant sec(x)
inverse sec asec(x) or arcsec(x)
cosecant csc(x)
inverse csc acsc(x) or arccsc(x)
rad to deg raddeg(x)
deg to rad degrad(x)
Plotting Programs
Page 8
Logarithm related functions:
natural log ln(x)
exponential exp(x)
common log log(x)
antilog alog(x) or antilog(x)
log base n logb(n,x)
hyperbolic sin sinh(x)
inverse sinh asinh(x)
hyperbolic cos cosh(x)
inverse cosh acosh(x)
hyperbolic tan tanh(x)
inverse tanh atanh(x)
Bessel functions:
1st kind, 0 j_0(x)
1st kind, 1 j_1(x)
1st kind, n j_n(n,x)
2nd kind, 0 y_0(x)
2nd kind, 1 y_1(x)
2nd kind, n y_n(n,x)
Trinary Function:
conditional if if(b,t,f)
if b is true then use t, else use f.
ex: if(x>=0,3x,x^2)
The if is probably the single most powerful function here. It allows
the user to perform branching of sorts. Nested if's are allowed. For
example the following pseudo-code
if x < 2
then y = 3x^2
else if x < 5
then y = 6x
else
y = x^2+5
can be coded Algebraically as
if( x<2, 3x^2, if( x<5, 6x, x^2+5))
or in RPN as
x 2 < 3 x sq * x 5 < 6 x * x sq 5 + if if
Boolean Comparisons: (evaluates to 1 if true, 0 if false)
less than a<b
greater than a>b
less than or equal to a<=b
greater than or equal to a>=b
equal to a=b
not equal to a<>b
and a and b or and(a,b)
or a or b or or(a,b)
exclusive or a xor b or xor(a,b)
In numeric comparisons, non-real values cannot be compared except in the
case of "<>" when a real and a non-real are always considered to be not
equal. In boolean comparisons, non-real values are considered false.
This leads to the interesting fact that "sqrt(-1)>0" and "sqrt(-1)<0"
are both considered false, but "not(sqrt(-1)>0)" and "not(sqrt(-1)<0"
are both considered true.
Plotting Programs
Page 9
Stack Functions: (available in RPN mode only)
drop bottom element drop
duplicate bottom element dup
swap bottom two elements swap
recall stack element n n rcl
store in stack element n n sto
roll bottom n elements n roll
n must be a number.
If n is positive the stack rolls down, a negative n rolls up
Functions may be entered in either Algebraic or RPN notation. Although
the Algebraic mode is recommended for general use, RPN mode has been
provided for compatibility with RPN calculators. Also, complicated
equations can often be written more easily in RPN notation. In
Algebraic mode, all standard rules of order of operation are obeyed.
Algebraic Order of Operations:
highest parentheses ()
functions
^
* / mod
+ -
= <>
< <= > >=
and
xor
or
Examples:
Algebraic: a+b*sin(c*(t-d))
RPN: a b c t d - * sin * +
Algebraic (2x-1)(3x^2.5+2) (note: the '*' is optional)
RPN 2 x * 1 - 3 x 2.5 ^ * 2 + *
Algebraic: -1^2 (note: ^ is executed first. The result is -1)
RPN: 1 2 ^ neg
Algebraic: (-1)^2 (note: - is executed first. The result is +1)
RPN: -1 2 ^ or 1 neg 2 ^
Algebraic: -(1-3)^2 (result is -4)
RPN: 1 3 - 2 ^ neg
Algebraic: 2(3(4+sin(.5)))^6 (result is 11778539.8142)
RPN: 2 3 4 .5 sin + * 6 ^ *
Algebraic: max(a,b)
RPN: a b max
Algebraic: if(x>-2 and x<=2, 3x+2, abs(x))
RPN: x -2 > x 2 <= and 3 x * 2 + x abs if
Plotting Programs
Page 10
The following is a list of options used by each of the plotting
programs. The Function Plotter contains most of the options found in
the rest of the programs.
Two Dimensional Function Plotter
<F2> Function:
( ) RPN notation On: RPN, Off: Algebraic
f(x) = The function to be entered.
Example: sin(2x)
<F3> Plot Type:
(1) Cartesian Normal Vertical vs Horizontal Axis. 1 or 2
functions may be plotted at once.
( ) Polar Polar Coordinate System (in radians). 1 or 2
polar functions may be plotted at once.
( ) Parametric Cartesian Coordinate System with both vertical
and horizontal variables are expressed as a
function of yet another variable.
Example: x(t) = sin(t), y(t) = sq(t)
<F4> Plotting Style:
steps = 160 The number of increments to use in plotting the
function.
( ) Show Axis On: Draws the X and Y axis.
Off: No axis and no grid.
(overrides Grid option below)
( ) Grid On: Places a grid on the graph.
Off: No grid.
(overridden by Show Axis option above)
(X) Overlay graph On: Overlays next plot on top of the previous
plot.
Off: Clears the screen between plots.
( ) Log on x axis On: Makes the x/y axis logarithmic.
( ) Log on y axis Off: Uses normal linear scale.
<F5> Plotting Area:
Reset Plotting Area Restores default plotting area.
x min = -10 Allows the values of the plotting area to be
x max = 10 entered manually.
y min = -7.5
y max = 7.5
Plotting Programs
Page 11
<F6> Variables:
Purge Unused Variables Deletes all variables not being used by the
current functions.
x = Numeric value of variables.
a = Example: x = i (for independent variable)
a = 2.5
<F7> Domain:
min = -10 Allows the region of the graph to be different
max = 10 than the x min/max as declared in the "Plotting
Area" section.
(X) domain based on On: Domain changes with x min/max changes made
x min/max in "Plotting Area"
Off: Allows domain to be independent of
plotting area.
<F8> (actions)
Plot Plots the graph. Short cut keys are: <Ctrl-P>
or <Ctrl-Enter> or <Right Mouse Button>
View Displays the last plot. Short cut key is
<Ctrl-V>
Save Saves current equations and settings to disk.
Short cut key is <Ctrl-S>
Retrieve Retrieves previously saved file. Short cut key
is <Ctrl-R>
Save-PCX Saves graph in the PCX format usable by many
graphics programs.
Retrieve-PCX Retrieves a previously saved PCX file.
Quit Leaves the program.
Plotting Programs
Page 12
Conic Section Plotter
<F3> Conic Section
Type:
( ) Vertical Parabola Selects which type of conic section to plot.
( ) Horizontal
Parabola Moving from any of the top six types to the
( ) Circle Standard type will cause the constants to
( ) Ellipse automatically be set so as to regenerate the
( ) Vertical Hyperbola same shape. This process is not reversible
( ) Horizontal since the Standard form does not necessarily
Hyperbola fit any of the other types.
( ) Standard
<F4> Plotting Style:
( ) Focal Points Displays the focal points and asymptotes where
& Asymptotes appropriate on certain conic sections.
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Derivative Plotter
<F4> Plotting Style:
(X) Show Function Determines which derivatives should be shown.
(X) Show 1st The function, its first derivative, and its
Derivative second derivative can be show in any
( ) Show 2nd combination.
Derivative
<F5> Plotting Area:
x min = -10 The vertical range of the function and each
x max = 10 derivative can be set independently of each
f min = -4 other. The horizontal domain is the same for
f max = 4 each plot.
f' min = -4
f' max = 4
f" min = -4
f" max = 4
Plotting Programs
Page 14
Relation Plotter
<F2> Function:
0 = A relation whose value is to be compared to
zero or true/false.
Examples: x^2 + y + abs(x)^y
y < x and y > x^3
<F4> Plotting Style:
Horizontal Resolution= Determines how many pixels to skip in plotting
Vertical Resolution= the relation. Using a resolution = 1 can take
quite a long time. Values up to 10 give
acceptable results.
<F6> Variables:
x = Numeric value of variables. Since the
y = relations plotted are not necessarily
a = functions, both horizontal axis and vertical
axis need to be declared.
Example: x = h (for horizontal variable)
y = v (for vertical variable)
a = 2.5
<F8> Plot A graph is made by using solid shading in areas
where the relation is greater than zero or is
true; light shading in areas where it is less
than zero or is false; and no shading at all
where the relation is not real. The value is
equal to zero where the two shaded areas meet.
Plotting Programs
Page 15
Bifurcation Plotter
<F3> Recursion Loops:
pre-plot loops = 100 Indicates the number of iterations to "throw
away" before the points are to be plotted.
plot loops = 64 Indicates the number of points to plot.
initial value = 0 Indicates the initial value of the independent
variable.
<F8> Plot Plotting with bifurcations is considerably
different than with the normal function
plotter. The dependent variable is described
by a recursive formula, such as z=z^2+c, so
that z is defined in terms of itself. The
dependent variable's initial value is
determined by the "initial value" option. The
right side of the equation is evaluated and
this becomes the new value of the dependent
variable. This is done a number of times as
set by the "pre-plot loops" option before any
plotting is done. Then the values of the
equation are plotted for the next few times as
set by the "plot loops" option.
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Data Curve Fitting
<F2> Data:
Clear Data Points ERASES ALL DATA POINTS!!!
Number of Data Indicates the number of data points up to 1500.
Points = 0 The number may be changed after data points
have been entered. If the number of data
points are increased, the (x,y) values (0,0)
are added to the end of the list.
Edit Data Points The editing window is where the data is
┌───────────────────┐ entered.
│ │ Editing keys:
├─ X ─────── Y ──┤ Enter: accepts the value currently being edited
│ │ Left/Right Arrow: moves left/right within the
│ │ data being edited.
│ │ Up/Down arrow: moves up/down to the another X-Y
│ │ pair
│ │ Tab: moves back and forth between the X and the
│ │ Y data
│ │ Home/End: move to the beginning/end of the data
│ │ being edited
│ │ PageUp/PageDown: moves up/down by one window
│ │ screen
│ │ Ctrl-Home/End: moves to the top or bottom of
└───────────────────┘ the list
Esc: exits the editing session
<F3> Plot Type:
( ) Linear Selects the type of mathematical model to use.
( ) Exponential When a type is selected, an equation showing
( ) Logarithmic the form of the model is shown just below the
( ) Power list of types. If "Best Fit Curve" is
( ) Polynomial selected, all five types are tested and the one
Degree = 2 with the highest R² is used. If "None" is
( ) Best Fit Curve selected, the points are plotted without any
( ) None best fit curve show.
R² = R² is the square of the correlation. A value
of 1 would mean a perfect fit. A value of 0
means no correlation, a result of a line with
zero slope or a randomly distributed points.
<F8>
Save Stores the data and options in a tab delimited
Retrieve ASCII file. This format allows the data to be
entered/retrieved from most spreadsheet
programs.
Plot Information Menu
(X) Automatic x-y On: The next 10 values are set automatically by
Values the program.
Off: The user is responsible for entering
appropriate values. It is recommended
Plotting Programs
Page 17
that the automatic values be calculated
and the user then adjust these manually if
desired.
x min = 0 Determines the range of values to use in the
x max = 7 plot of the data points.
y min = 0
y max = 8
x scale = 1 Determines how much each unit on the graph will
y scale = 1 actually represent.
x scale title: Gives a title descriptive of the scale being
y scale title: used.
x axis interval = 1 Indicates the interval between the hash marks
y axis interval = 0.5 on the axis.
steps = 160 Indicates how many iterations to use in
plotting the curve. This value is not used
when using the linear model.
( ) Grid On: Uses a grid across the graph, Off: No grid.
( ) Log on x axis On: Uses logarithmic scale.
( ) Log on y axis Off: Uses linear scale.
Plot Title: Allows two lines descriptive of what the graph
Plot Subtitle: represents.
x axis title: Describes what the axis is representing.
y axis title: Example: mass
Plot Graph Actually plots the data. Short cut keys are
<Ctrl-P> or <Ctrl-Enter> or <Right Mouse
Button>
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Revision History
1.0 Original Program
1.01 Fixed garbled error messages for certain RPN stack errors.
1.1 Changed the menu program filename from the more descriptive
"plotmenu.exe" to the more rewarding "wlplot.exe." Also changed
the name of the relation plotter from "last.exe" to "relat.exe."
The name of the trinary function "ifte" (if-then-else) was
shortened to "if." The name "ifte" is still legal for the sake of
compatibility.
Changed the method of error trapping to allow better handling of
the if(boolean,true statement,false statement). Now,
if( x<0 , x , sqrt(x) )
is properly evaluated when x<0. Before, both the true and false
statements had to evaluate to a real number in order for the result
to be evaluated. Now, only the final answer of an expression must
evaluate to a real number.
Added the unary function "isreal."
Changed the names of the Bessel functions from j0, j1, jn, y0, y1,
and yn to j_0, j_1, j_n, y_0, y_1, and y_n.
The Relation Plotter was speeded up considerably. It is also
considerably more accurate. This speed and accuracy improvement is
a consequence of having the program automatically reduce the pixel
resolution value at the borders between two regions. The default
resolution was changed from 4 to 1/40th the resolution of the
screen. (Thanks goes to The Stone Soup Group's Fractint for the
"solid guessing" speed up concept.)
The way in which numeric values are converted into boolean values
was changed. Values greater than zero are considered true, while
values less than or equal to zero are false. Also, non-real values
are considered false. Previously, only values equal to zero were
considered false and non-real values were not evaluated at all.
An option to turn the axis on or off has been added. If Show Axis
is turned off, then the function is graphed on a blank screen.
Show Axis overrides the Grid option.
Selecting "Save" now stores the current equation(s) and settings to
a file. Previously, a bit-mapped image was saved to disk along
with some of the settings. Retrieved files must now be
regenerated, but they are a tiny fraction of the size of a bit-
mapped image file.
1.11 Changed maximum equation length from 80 characters to 200.
Now prevents steps=0, which caused "division by zero" problems.
Also now correctly reports large number of steps.
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In the Conic Section program, added the automatic conversion to the
Standard form.
1.12 Fix a bug in the Conic Section plotter that would occasionally
cause the program to abort when trying to plot a Standard Form
equation.
First version to be distributed through Data Warp BBS (see p. 3)
Plotting Programs
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In Closing
A special word of thanks goes to my Physics and Algebra II students who
unknowingly were my beta testers. They are the reason I put these
programs together and made them publicly available.
These programs are intended for use in educational settings only. As a
teacher, my reward comes from knowing that my efforts have been
fruitful. Although donations would be appreciated, the only payment
that I require is that each user send a letter or postcard letting me
know that he/she is using my program. Teachers may send a single letter
with the names (or at least the number) of students using the program
each year. This serves no purpose other than to give the author a pat
on the back and make him feel as though he has contributed to mankind.
If this program should prove useful to someone outside of an educational
setting (such as in a job or even research), a reasonable payment of $25
is required. If anyone is interested in the source code, please contact
me.
Copyright is retained by Wesley B. Loewer.
If you are a teacher and would like to swap ideas on how these programs
can be used in class, or if you are in the Houston area and are
interested in an inservice, feel free to contact me.
Please send any questions, suggestions, and contributions to:
Wesley B. Loewer or Wesley B. Loewer
78 S. Circlewood Glen McCullough High School
The Woodlands, TX 77381 3800 S. Panther Creek Dr.
(713) 292-3449 The Woodlands, TX 77381
(713) 367-1025 ext. 251
Plotting Programs
