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About MPP
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Downloading MPP
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Setting Up and Starting MPP
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Using MPP
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About MPP3D
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Using MPP3D
About MPP (Midshipman's Plotting Package)
This is a very nice little DOS freeware program designed principally
for graphing in two dimensions (for details on features and usage see below).
It's easy to install, learn, and use and it has lots of great features.
And it will run fine on just about any DOS machine (even old 286's...though
a color monitor is a definite plus). A companion program MPP3D (which is
included with the standard distribution) allows one to graph functions
in 3 dimensions as well.
When you first start up MPP you see the opening
information screen (or
"slash
screen"). MPP consists of ten "suites" with varying purposes.
You choose the suite you wish to use from the opening information screen
(i.e. press the "1" key followed by "ENTER" to use suite 1). MPP makes no use of a mouse...all
navigation and operation of the program is accomplished by straightforward
use of the arrow keys, the function keys (the "F1" through "F10" keys at
the top of most keyboards), and other keys on the standard keyboard. The
main function key operations for the program are clearly indicated at the
bottom of the main input screen.
Downloading MPP (Don't want
to hassle with downloading? Then click
here)
MPP is available for download as a "zipped" file via the
Math Archives at University of Tennessee at Knoxville.
The file mpp.zip is in .zip format, so you'll need to have an unzipping
utility to decompress it before you can run MPP. If you don't have
an unzipping utility
click
here.
Setting Up and Starting MPP
When you unzip the file mpp.zip, a directory named MPP will automatically
be set up with appropriately organized files and subdirectories.
In Windows 95, if you unzip the mpp.zip file into the root directory
of your C: drive, you should be able to start up the the program
by opening the MPP folder window and double-clicking the icon for "mpp.exe".
However, if you unzip the original mpp.zip file into a subdirectory
of the C: drive, and try double-clicking the mpp.exe icon, you
may get an error
message like this. You can probably get MPP to start up by just choosing
the "Yes" response to this error message. But if you want to fix this problem,
proceed as follows.
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Open the MPP folder window, right-click on the mpp.exe icon,
drag down to the bottom of the pop-up window and release the mouse to open
the "Properties" dialog box.
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Click on the 2nd "tab" (labelled "Programs"). You should see something
like this
on your screen.
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You need to edit the entries in the 2nd and 3rd fields (labelled "Cmd line"
and "Working") to reflect the correct "folder path" for the mpp.exe
file on your machine. For instance, if I had unzipped the original mpp.zip
file into the directory
C:\Aaron, then the path to the file mpp.exe
would be
C:\Aaron\MPP\mpp.exe. So I would retype C:\Aaron\MPP\mpp.exe
for the "Cmd line" entry and
C:\Aaron\MPP for the "Working"
entry---and my dialog box would look like this
.
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Close the properties box. This should eliminate the error message problem
discussed above.
There is an alternative way to run DOS programs in Windows 95. You
can "open a Dos-Prompt window" as follows. Click the Start button (normally
at bottom left of the screen). In the resulting pop-up menu, drag to "
Programs". In the (perhaps large) pop-up submenu drag to "MS-DOS Prompt".
Your screen should look something like this.
When you release the mouse a blank DOS window will open with a blinking
cursor. Within this window you are in the "command line" environment of
DOS. To run the mpp program, you will need to move into your MPP directory
(i.e. "change directory" using the DOS command "cd"). Once you are in the
MPP directory, simply type "mpp.exe" (or just "mpp") at the DOS prompt
to run the main MPP program. MPP3D comes as a separate program. To run
MPP3D type "mpp3d" (or "mpp3d.exe") at the DOS prompt.
Using MPP
The first (and most commonly used) MPP suite is the main "plotting package"
which is used for graphing real-valued functions of a single real variable.
Each MPP suite has two main "modes": an input mode for typing in
the functions you wish to graph; and a graphics mode for viewing
the graphs. Initially, you're placed in input mode, where you type in your
function(s). In the "plotting package" suite, up to six functions can be
graphed on the same screen in different colors (nice for comparing graphs
of related functions, e.g. shifts and scalings). Functions can be specified
in the common formats: y=f(x), x=f(y), as well as polar and parametric
form. MPP has all the standard elementary functions built in (e.g. root,
trig, exponential and log functions, etc.), as well as number of less common
ones for a program of it size and type (e.g. Gamma function, Bessel functions,
Heaviside function, Greatest Integer function, the "k-th derivative" (of
a previously input) function, for k=1,2). To see a complete list of all
available functions and their "syntax/usage" within MPP, press "cntrl-f"
while in "input mode". There is also an "options screen" (accessed by pressing
"cntrl-o" from the "input mode") where you can configure things like monitor
and printer info, and select or deselect whether a coordinate grid (rectangular
or polar) should be superimposed on the graphics screen.
To view your graphs, you move into graphics mode by simply pressing
the "F9" function key. (For easy reference, the operations provided by
all the function keys are clearly indicated at the bottom of the "input
mode" screen.) After a moment of quiet comtemplation (i.e. computing),
MPP renders your graphs on screen.
MPP generally produces nice graphs. But it does often have problems
dealing gracefully with vertical asymptotes. If MPP stops abruptly in the
middle of drawing a graph, check to see that you haven't inadverently asked
it to divide by zero at the x value where graphing halted! If you're trying
to get MPP to graph a function over, say, the interval [-1,5] having a
vertical asymptote at, say x=3, then one way to do it is to "break the
graph into pieces". That is, graph the left half separately from "xmin=-1"
to "xmax=2.99" and the right half from "xmin=3.01" to "xmax=5". Another
approach to dealing with vertical asymptotes is to adjust the "step size"
for the graph (the "step size" option appears to the right of your "xmin"
and "xmax" specifications, below the field where you type in the formula
for the function). The "step size" is the increment between sampled input
points which MPP uses to construct points on your graph. Thus if you graph
a function over the interval [-3,4] with step size=.01, MPP will calculate
the values of your function at x=-3.00,-2.99,-2.98,...,3.98,3.99,4.00 and
join all the resulting (consecutive) points by line segments. (Try setting
step size = 1.0 and see what happens to your graphs!). Sometimes the step
size can be chosen to avoid sampling the function at input values leading
to "division by zero". But be aware that this will lead to a "spurious
line segment" appearing where the vertical asymptote belongs.
In addition to its graphing capabilities, MPP does have some rudimentary
"text insertion" capabilities for labeling items in "graphics mode" (press
"h" for a help screen to explore the possibilities). To print your graph,
just press "p" in graphics mode. (But first you'll want to configure MPP
for your printer in the "options screen"...recall, you get to that screen
by pressing "cntrl-o" from "input mode".)
While many users will spend most of there "MPP time" using the "plotting
package", there are also nine other "suites" which allow you to explore
various Calculus topics.
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For Math 110A (Calculus I) there are
MPP "suites" which allow you to:
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animate the process of "a sequence
of secant lines approaching a tangent line" which underlies the geometric
interpretation of the limit definition of the
derivative;
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graph implicitly defined functions (i.e. graph equations of the
form F(x,y)=0) and their tangent lines;
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find "roots of functions" (i.e. solutions of f(x)=0) using Newton's
Method and other methods;
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For Math 110B (Calculus II) there are
MPP "suites" which allow you to:
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plot graphs in polar
coordinates and view these graphs with a polar coordinate background
grid;
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plot parametric curves;
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explore various concepts related to sequences and series;
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compute numerical approximations for single variable integrals using
either upper, lower, midpoint, trapezoidal, or "simpson" sums. This suite
will graph the integrands along with the associated rectangular (or trapezoidal
or parabola capped) boxes corresponding to the user provided step-size
for the sum;
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For Math 110C (Calculus III) there
are MPP suites which allow you to:
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graph families of level curves for a function of two variables (i.e.
graph f(x,y)=c for various c values);
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plot vector fields in 2 dimensions;
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compute double and triple integrals numerically.
As mentioned before, MPP has 10 suites altogether. Check 'em out when you're
ready.
About MPP3D
In addition to the main program described above, MPP also comes with a
companion program called MPP3D which allows one to graph surfaces and curves
in 3 dimensions. Surfaces may be specified in various formats: z=f(x,y),
y=g(x,z), x=h(y,z), as well as in cylindrical and spherical coordinates,
or in general parametric form. You can also plot space curves of the form
( x(t), y(t), z(t) ) for t varying in a specified interval. And there is
a nice, easy to use, feature which allows you to "visually" rotate the
underlying coordinate frame (using the arrow keys) and redraw a surface
from a new viewing angle.
Using MPP3D
To run MPP3D, enter the MPP subdirectory and type "mpp3d" (or "mpp3d.exe")
at the DOS prompt. After the program loads, you will find yourself in the
input
mode screen for MPP3D. Here you can type in the min and max coordinate
values for your "viewing box". Pressing the F2 function key moves
your cursor to the input field for specifying the surface or curve you
wish to graph. The default setting is for entering z=f(x,y), but
by pressing the F6 function key you are presented with a list of
alternate formats such as: y=g(x,z), x=h(y,z), cylindrical or spherical
coordinates, general parametric form, or a parametrized curve. The last
thing to do in input mode is type in the intervals over which you wish
the independent variables (or parameters) to vary, then you're ready to
press the F9 key to display the graph.
MPP3D will take a bit of time to compute and then present your graph.
You are now in graphics mode. Here you can press the "r" on your
keyboard to bring up a bold colored "xyz-axes frame" which can be
rotated in all directions (using the arrow keys on the keyboard) so as
to change the viewing angle of your surface. When you have found the frame
orientation you wish to view from, press the return key and MPP3D will
recompute the image and present it to you.
Overall MPP is really a great little program. I recommend it highly.
Enjoy!
