This file contains abstracts for a collection of 26 math programs that are written and maintained by John Kennedy in the Mathematics Department at Santa Monica College. The programs are for IBM compatible computers and are used by the students in the Math Lab at SMC. These programs may also be of interest to high school students and math teachers at almost any level.

Depending on your installed hardware/software/browser, this file is approximately 35 pages long when printed. If you intend to read it all you may wish to consider printing it rather than browsing it all on-line. You can also save this file and then browse it locally. The first 9 sections listed in the outline below contain preliminary information. The 10th section is the heart of this document. 

The following is a brief list of all the programs. By clicking on a program name in the second column you can go to a more detailed abstract of the corresponding program. JKGRAPH and JKMATRIX and PARAM3DSF are the three most popular programs and cover most of the basic math curriculum for graphing 2D functions and performing matrix computations and graphing 3D surfaces. Almost everyone should be interested in downloading at least these three programs.
 

Abstract #	Program Name	Brief One-Line Description of the Program:
1.	JKGRAPH	General 2D function graphing/analysis; polar, parametric, implicit, infinite series, integrals & related calculus.
2.	JKCFIT	Curve fitting with 4 basic function types; good for students enrolled in a science laboratory.
3.	POLYFIT	Curve fitting using polynomials up to degree 10. Companion program to JKCFIT.
4.	JKDIFEQ	Graphs slope field for 1st-order differential equations; Euler & Runge-Kutta algorithms.
5.	LPG	Linear Programming Graphs in 2D; solves, graphs, easily creates intricate 2D linear inequality systems.
6.	JKPROB	Pascal's Triangle & Pi approximation via probability; Galton Board & Buffon's needles.
7.	COMBO	Combinations and permutations; actual list and set creation; multisets; binary strings; multinomial coefficients.
8.	JKMONEY	Financial calculator. Loans; amortization schedules; annuities, interest earning schedules, account depletion.
9.	JKTRI	Solves triangle problems using Laws of Sines and Cosines; handles 19 different cases; draws solutions to scale.
10.	TRIGFUN	Visual display of trigonometric functions and their relationship to the unit circle. Degrees and radians modes.
11.	KOCH	Koch Snowflake; Hilbert Curve; Mandlebrot Set; Pythagorean Tree; harmonograms; other artistic figures.
12.	POLYHEDRA	A program for printing paper models of 3D regular polyhedra.
13.	JKTURING	Simulates a Turing machine and a Finite State Machine; it's user programmable.
14.	RPNPC	Reverse Polish Notation Programmable Calculator; simulates assembly language; stack architecture; debugger.
15.	SENTCALC	Sentential calculus; truth tables, tautology testing; Polish notation and Karnaugh maps.
16.	JKFINITEFIELDS	Finite fields & groups. Matrix & polynomial algebra with modular arithmetic; sets of basis vectors; Galois fields.
17.	JKCURVE3D	Graphs 3D parametric curves; tangent, normal, binormal trace modes; osculating circle; curvature; arclength.
18.	JKSURF3D	Graphs 3D surfaces; Z=F(X,Y); normal vectors; surface trace modes; level curves; double integrals; areas, volumes.
19.	VFIELDS	Graphs 3D vector fields, curves, surfaces; calculates line and surface integrals (work, flux, other applications).
20.	PARAM3DSF	Graphs 3D parametric surfaces; Mobius strip, Klein bottle, knots; tube mode; other intricate 3D surfaces; calculates surface area.
21.	JKTHANOI	Towers of Hanoi game that illustrates the power of a recursive algorithm; manual and automatic modes.
22.	JKNLINE	Creates number line graphs; solutions to 1-variable inequalities; includes labels and size scaling.
23.	JKXPRES	Extended precision calculator; exact numbers up to 20,000 digits long; combinations, factorials, permutations.
24.	JKITERATE	Combines recursive sequences with special function evaluations; generates special tables.
25.	JKMATRIX	Row operation algorithms for matrices; Simplex, determinants, inverses, bases, eigenvectors, Markov chains.
26.	JKCALC	General purpose calculator; fractions; binary integers; complex #'s; factors polynomials; continued fractions.

First see the Packages section to determine which *.ZIP file to download for each individual program.   Then see  Download Information to actually retrieve the corresponding ZIP file.

An outline for this ABSTRACTS document consists of the following 11 sections:
1. Update and Version Information.
2. The Background & Knowledge Required To Use These Programs.
3. The Hardware and Software Required To Use These Programs.
4. About The Windows 95/98/ME/XP/NT/2000/Windows 7 32-Bit Programs.
5. Available Formats and Installation
6. How To Acquire The Programs.
7. Further Information
8. This Collection Versus Commercial Programs
9. File Types & Tutorial & Additional Help & Documentation Information
10. The Program Abstracts
11. An Index Of All The Files.

1.Update and Version Information.

This document file: ABSTRACTS.HTM 185,635 02/14/2010 06:05 PM

These programs are periodically updated to make improvements and add new features (and sometimes to correct bugs!). The line before each paragraph description gives the latest filename information about the most recent version of the program as of the time this ABSTRACTS.HTM file was last made or saved. This information includes the file size in bytes and the date and time of the most recent update. Each 32-bit Windows program also has version specific information in the format Version M.m.R.B where M.m are the Major and minor version numbers, R is release number and B is the build number. If you already have a version of one or more of these programs you may wish to compare your file version with the version information in the abstracts list. Within any program you are running, there should be a Help menu item named About that tells you the current version numbers for that program.
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2.The Background & Knowledge Required To Use The Programs In This Collection.
The programs described below have been designed to be used by people with little or no computer background.  All of these programs contain self-documenting help screens and the more complex programs are accompanied by tutorial lessons designed specifically for first-time users.  The mathematical background required to use these programs depends on the nature of each individual program.  However, each program is designed to be a learning tool to help motivate an interest in mathematics and computer science, so users may benefit from trying a program even if they do not fully exploit all of the program's capabilities.
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3.The Hardware and Software Required To Use The Programs
These programs have been developed over a number of years and continue to evolve over generations of various hardware and operating systems versions. The collection includes 32-bit WINDOWS-95/98/ME/XP/NT/2000/Windows 7 programs. A printer is optional for a few programs if you want to produce hard copy output.
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4.About The Windows-95/98/ME/XP/NT/2000/Windows 7 32-Bit Programs.
All WINDOWS programs are exclusively 32-bit applications  that are native to all of WINDOWS-95/98/ME/XP/NT/2000/Windows 7. If you have a 64-bit Windows operating system, these programs should run without any changes. 

The minimum recommended screen resolution is 1024x768. It is possible to use super VGA 800x600 but this is not recommended. Of course resolutions higher than 1024x768 can also be used.

Depending on the version of the WINDOWS operating system that you have, the look and feel of the WINDOWS user interface can be changed through how you make the settings for the appearance of the display. In any version of WINDOWS, but especially in WINDOWS XP, you can right click any open area of the desktop to bring up a menu item and select the PROPERTIES of the display. If you then click on the APPEARANCE tab you can select a desktop SCHEME. Your choice of SCHEME affects the size and colors of window title bars and borders and fonts and icons.

These math programs were developed using the WINDOWS STANDARD SCHEME. If you use the WINDOWS XP SCHEME that is the default for WINDOWS XP, then your displays may look noticeably different from the screen shots that appear in our help files. The differences can include, but are not limited to, discoloring of background elements and spacing of controls in some dialogs. For the most part, these differences should only be cosmetic and should not affect the actual operation of the programs, even though they are irritating for the author. You are hereby warned that not all WINDOWS are created equal. We are all at the mercy of how Microsft changes its WINDOWS standard.
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5.Available Formats and Installation.
The programs are made available free to anyone with Internet access.  Program groups or subcollections are called packages and are available only in ZIP files. See Download Information to begin the download of a particular ZIP file package. After downloading a ZIP file you will need to unzip that file before you can use the programs it contains. If you are not familiar with unzipping ZIP files then you should go to any popular download web site like www.yahoo.com and look for and download a free program called WINZIP. Better yet, ask a friend who knows about ZIP files to help you.

At the time of this writing there are 26 programs that have been grouped into eight ZIP file packages. The eight ZIP file packages are named JK32W?.ZIP, where ? is a single digit ranging between 1 and 8.

The contents of each ZIP file package is shown across each row in the table below. Individual programs are identified by their abstract number and name. Just click on any program name to go directly to a detailed abstract of that program.

ZIP Filename	Contained Programs >>>
JK32W1.ZIP	1. JKGRAPH
JK32W2.ZIP	2. JKCFIT	3. POLYFIT	4. JKDIFEQ
JK32W3.ZIP	5. LPG	6. JKPROB	7. COMBO	8. JKMONEY
JK32W4.ZIP	9. JKTRI	10. TRIGFUN	11. KOCH	12. POLYHEDRA
JK32W5.ZIP	13. JKTURING	14. RPNPC	15. SENTCALC	16. JKFINITEFIELDS
JK32W6.ZIP	17. JKCURVE3D	18. JKSURF3D	19. VFIELDS	20. PARAM3DSF
JK32W7.ZIP	21. JKTHANOI	22. JKNLINE	23. JKXPRES	24. JKITERATE
JK32W8.ZIP	25. JKMATRIX	26. JKCALC

 Outline   Program List     Download Information

The reason for having multiple ZIP files is so that the entire collection can be split into several reasonably sized logical groups for downloading.  As the program collection expands, the file groupings or subcollection packages may also change.

If you have a pure ZIP file then all you need do is unzip the contents into any directory. In particular, under WINDOWS-95/98/ME/XP/NT/2000/Windows 7, there are no entries written to any registry. Installation couldn't be any easier. To uninstall all the files for any system, all you need do is delete all the files in the corresponding subdirectory. Relative path information is included within each ZIP file and if you use that information when unzipping then each of the 26 programs will be placed in separate subdirectories under a main directory named JKPROGS. For instance, all the files associated with the JKGRAPH program will be placed in JKPROGS\JKGRAPH and all files associated with the JKMATRIX program will be placed in JKPROGS\JKMATRIX. The names used for each program subdirectory are the same as in the above table.

If you have just received and installed one or more packages of files then you probably have a subset of the entire collection.  You will just have to compare your installed files with the list in section 11 below to determine which files you have and which files you are missing. 

Each package contains a README.TXT file that is what you are now reading in HTML format. README.TXT is the same in all packages and in all ZIP files.  When installing a new package you can safely overwrite any older README.TXT file as the new package should contain either the same, or a more up-to-date README.TXT file.
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6.How To Acquire The Programs
The only way to acquire the programs is over the Internet.  Point your Internet browser to the location:

 John Kennedy's Downloadable Software (http://homepage.smc.edu/kennedy_john)

and follow the links to the downloadable software.

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7.Further Information
Any technical questions or comments about any of these programs may be referred to the author by any of several means including Internet e-mail, voice telephone or snailmail.

John Kennedy
Mathematics Department
Santa Monica College
1900 Pico Blvd.
Santa Monica, CA  90405

Voice Mail: (310) 434-4721  (24 hrs.)
e-mail:  rkennedy@ix.netcom.com

The author cannot return long distance phone calls.  Sorry, but the idea is that the cost should be free to the author first, and free as much as possible after that to you!  The author is not in the business of selling software or the business of providing service.

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8.This Collection Versus Commercial Programs
The development of the programs in this collection began many years ago when there was very little math software available.  At present, there are major commercial packages that have outstanding mathematical capabilities.  The major names include MATLAB, MAPLE, MATHEMATICA, MACSYMA, THEORIST, and DERIVE. All of these commercial programs were developed by and for professional mathematicians and literally millions of dollars of research has been spent either directly or indirectly in their development.

The cost of these commercial programs is not only beyond most student budgets, many teachers and schools can't afford them either.  Just like the first shirt-pocket calculators that initially cost hundreds of dollars, the price of commercial math software will steadily decline.  In the not-too-distant future everyone will be able to buy all the capability in MATHEMATICA for less than $20.  But we aren't there yet.

In addition to the price obstacle, most commercial software was not designed for classroom demonstrations nor for student experimentation.  The capability of most commercial math software goes way beyond the level of student use.  If you have ever tried to develop instructional demonstrations with any of the commercial programs you are already aware of and understand the problem.  The programs were not specifically designed for performing demonstrations with animations.  The programming capability might lead the novice teacher into thinking they could use the program in the classroom to demonstrate anything. But a great deal of effort must usually be expended to make even a modest educational demonstration, and even then the result may only be marginally satisfactory.

Students (and teachers) who use commercial programs require a significant amount of time to develop proficiency in their use.  Such an effort is worthwhile for those who will continue to use the software outside of school. It is also worthwhile to learn how to write programs using one of the commercial scripting languages.  Developing a programming skill in MATHEMATICA is most rewarding.  But most students do not consider themselves in the category of mathematical programmers and will never learn to program directly in the languages used by these packages.

While the user interfaces are continually improving, none of the major commercial programs are particularly well-suited for first-time beginners who only need to learn and perform relatively simple tasks.  Unlike most word processing programs that have standard feature sets and work in similar ways, commercial math programs vary widely in their syntax and input/output.  Many programs still have command line interfaces even though they claim to work with the WINDOWS operating system.  The major commercial programs are truly amazingly powerful, but in some ways they are still primitive.

The software described below has two advantages over commercial software.

   1. Cost (it is free; however it does have to be copied and distributed)

   2. It is made for teachers and students where the end goal is learning and discovering.  It is for first-time beginning users.  Many of the programs contain demonstrations and/or animations that illustrate the mathematical concepts and techniques that students should be learning.

These same two advantages are disadvantages if you want state of the art math software.  The software described below probably has limited use outside of a learning environment.  Buy the professional stuff when you need programmable state of the art large-capacity high-speed numeric or symbolic algorithms. Otherwise, kindly accept some exposure to this educational software as preparation for more robust software that may be in your future.
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9.File Types & Tutorial & Additional Help & Documentation Information
Files of the type *.EXE are executable program files. 

Files of the type *.PDF are program help files. This collection uses PDF files for its context sensitive help system. PDF stands for Portable Document File and is supported by using a free program named Adobe Acrobat Reader. If you don't have this program installed on your machine you should visit www.adobe.com and download and install their free Acrobat Reader program. Instructions are available under each Help menu.

Other files of the type *.TXT contain examples that are used with a particular program. These text files may also be imported into any ASCII text editor (like Notepad) for reading and or printing, but they can also be loaded by the program that created them. See the index of all the files to determine the *.EXE program that is associated with a given *.TXT file.
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10.The Program Abstracts

1. JKGRAPH.EXE  1,830,912  02/14/2010  1:14 PM  Version 4.89.4.199
The program called JKGRAPH is used to graph and analyze 2-dimensional function curves that can be made using standard rectangular functions or polar or parametric functions. In addition to five standard types of function curves, JKGRAPH also has facilites for working with infinite series, Fourier series, and functions given in the implicit form f(x,y)=0. The five standard function types include rectangular functions in the form Y=F(X), polar functions in the form R=F(@), parametric functions in the form X=F(T) and Y=G(T), polar parametrized functions in the form R=F(T) and @=G(T) and finally rectangular functions in the form X=F(Y). You can view any rectangular portion of the XY-plane and you can easily perform zooming operations. You can control individual graph curve attributes including colors and line thickness. You can also select from among 8 different background grids that include combinations of the standard XY-axes, polar-coordinate axes, and an XY-lattice grid. You can copy any graph to the WINDOWS clipboard in a color bitmap format in which you specify both the size of the graph in inches and the resolution in terms of the number of pixels per inch. You can also create WINDOWS enhanced metafiles for importing into other Windows applications. Within each function group you can work with two independent curves or you can link the two curves and then perform special operations such as finding points of intersection or integrating to find the area between two curves. JKGRAPH provides four trace modes with the names Coordinate Trace Mode, Graph Trace Mode, Tangent Line Trace Mode, and Normal Line Trace Mode. Regardless of the current function type, in each mode you can drag the mouse cursor across the screen and dynamically see graphic elements related to the trace position. JKGRAPH can also perform special animated actions on function curves. You can automatically find maxima/minima points or automatically find intersection points between two curves. You can also use the program to automatically find points of inflection, even on polar or parametric curves. For both Y=F(X) and X=F(Y) function curves you can apply either Newton’s Method or the Method of Successive Bisections to find the x or y intercepts. Both methods can show an animated action and can generate tables of values. There is also a special dialog box for estimating the differential dy at any point on the graph of Y=F(X) or X=F(Y). The program uses a Chebyshev polynomial approximation to aid in computing the derivative. You can also apply several integration techniques to any curve. For both types of rectangular functions there are 11 different integration methods that include lower, upper and midpoint Riemann sums, the Trapezoid Rule, Simpson’s Rule, Gaussian Quadrature, the Romberg Algorithm, arc length and surface area and volumes using either disks or washers or cylindrical shells. The program draws 3D-objects to simulate disks, shells, and washers. The program can integrate both with respect to X or Y. For polar and parametric function types you can calculate areas and arc length. JKGRAPH can also automatically graph the derivative or inverse of any function curve and it can automatically graph the anti-derivative curve. It even does anti-derivative curves when the function type is a polar, parametric, polar parametrized or X=F(Y) curve. It can also make a series of varying related curves using a special graphing parameter. It also has a feature that allows you to analyze any decimal answer and helps determine the pure mathematical nature of that answer. This program can also work with any general infinite series and has special functions related to computing and graphing a function defined by a power series. It can automatically graph the term by term differentiated or integrated power series. This program also has a special dialog box for working with Fourier series that are a special kind of infinite series. JKGRAPH can add extra drawing elements to a graph that include isolated points, lines, and labels. It can also graph implicit functions in the form f(x,y)=0. This program can save the state of all function curves and graph parameters and all other values in an ordinary text file. This text file can then later be opened to re-load or re-create the entire environment or state of the program. In fact, the text file can be edited, and once the format is understood, you can create entirely new functions and graph domains by just editing the text. This feature provides a fast but convenient way to create various examples that can be quickly loaded and run. You can also setup a slide show to display a series of function graphs. The slide show can run in either an automaic or a manual mode. The file SlideListJKGraph.txt can be used as a slide show file. JKGRAPH comes with 103 text file example functions in other files named Fourier021.txt, FourierNegOne.txt, FourierSQWave.txt, FourierTri.txt, ImplicitAbsPiriForm.txt, ImplicitAgnesi.txt, ImplicitAround.txt, ImplicitBadTooth.txt, ImplicitBells.txt, ImplicitBernoulliLemniscate.txt, ImplicitBiFolium.txt, ImplicitCassiniOval.txt, ImplicitCircle.txt, ImplicitConchoid.txt, ImplicitDescartesFolium.txt, ImplicitDiamonds.txt, ImplicitDoubleCusp.txt, ImplicitEggs.txt, ImplicitFig8Island.txt, ImplicitFilledSpokes.txt, ImplicitFingers.txt, ImplicitHyperbolas.txt, ImplicitHypocycloid.txt, ImplicitIslands.txt, ImplicitKisses.txt, ImplicitLandscapes.txt, ImplicitLines24.txt, ImplicitLituus.txt, ImplicitMultigraphLines.txt, ImplicitNicomedesConchoid.txt, ImplicitOddAround.txt, ImplicitOddity.txt, ImplicitOsculation.txt, ImplicitParallelLines.txt, ImplicitPiriForm.txt, ImplicitSpider.txt, ImplicitSpreading.txt, ImplicitSquares.txt, ImplicitStrophoidH.txt, ImplicitStrophoidV.txt, ImplicitSunBurst.txt, ImplicitUnsymmetric.txt, ImplicitWild1.txt, ImplicitWild2.txt, ImplicitWild3.txt, ImplicitWitch.txt, ImplicitY2XAndX2Y.txt, ImplicitYingYang.txt, Param1.txt, Param3.txt, Param3X3.txt, Param4.txt, ParamCrazy.txt, ParamCurlyQ.txt, ParamFigure8.txt, ParamFish.txt, ParamLongBow.txt, ParamSpiral.txt, ParamStrophoids.txt, ParamTearDrop1.txt, ParamTearDrop2.txt, ParamTriangle.txt, ParamUrchin.txt, ParamWraps.txt, PolarCochleoid.txt, PolarEars.txt, PolarEyes.txt, PolarFish.txt, PolarNut.txt, PolarRose.txt, PolarRound.txt, PolarStar.txt, PolPmBalloonCurve.txt, PolPmCurvingCurve.txt, PolPmSpiral.txt, SeriesAltHarm.txt, SeriesCosh.txt, SeriesCosine.txt, SeriesE2X.txt, SeriesNSqr.txt, SeriesSine.txt, SeriesSinh.txt, SeriesSQWave.txt, SlideListJKGraph.txt, YFXDefaultFuns.txt, YFXDenseSpeckles.txt, YFXGreatestInteger.txt, YFXMaxS2C.txt, YFXMin32X.txt, YFXMultiBand.txt, YFXMultiGExample.txt, YFXSine01.txt, YFXSine03.txt, YFXSine05.txt, YFXSine07.txt, YFXSine09.txt, YFXSine11.txt, YFXSine13.txt, YFXSine15.txt, YFXSine17.txt, YFXSine19.txt, YFXSqrtLn.txt, YFXWGlass.txt, and YFXX2Up3.txt. There is a tutorial help file named HelpJKGraphTut.pdf as well as a quick start help file that is named HelpJKGraphQSB.pdf. Two other help files deal with special topics and dialog boxes and are called HelpJKGraphDialogs.pdf and HelpJKGraphST.pdf. Normally JKGRAPH.EXE, HelpJKGraphDialogs.pdf, and HelpJKGraphST.pdf and HelpJKGraphQSB.pdf, and HelpJKGraphTut.pdf must must all reside in the same subdirectory. JKGRAPH is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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2. JKCFIT.EXE  970,240  02/14/2010  1:40 PM  Version 2.76.4.156
The JKCFIT program is designed to perform curve fits to data.  Thus this program is a statistical program that can be used to analyze data and discover a functional relationship between two variables.  The program can employ any one of four kinds of regression functions that include linear functions, exponential functions, logarithmic functions, and power functions.  The user can select any particular function or they can let the program automatically choose the function of best fit for the given data.  Once a curve has been fit to the data the user can predict new points along the curve.  The program employs a recursive process for accumulating statistical sums that provides more accurate than usual statistics.  The program makes easy entry and editing of data.  The program can graph a scatter diagram of the data and it can graph the fitted function curve that passes through the data.  The graphing features include an XY-plane window, scalable axes, a Coordinate Trace Mode, a Graph Trace Mode and zooming features.  All of the data and/or statistics may be saved to or read from disk files, or printed on a printer, or copied to the WINDOWS clipboard. The two files JKCFCHILD.TXT and JKCFSAMPLE.TXT contain sample data. This program has context sensitive help in the file HelpJKCFitST.pdf. There is even an auxiliary help file HelpJKCFitTut.pdf that is a tutorial for first-time users.  Normally the 5 files JKCFIT.EXE, HelpJKCFitST.pdf, JKCFCHILD.TXT, JKCFSAMPLE.TXT, and HelpJKCFitTut.pdf must reside in the same subdirectory. JKCFIT is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.  See also the program listed below named POLYFIT.EXE that is a companion program to JKCFIT that specializes in performing higher-degree polynomial curve fits.
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3. POLYFIT.EXE  940,544  02/14/2010  1:28 PM  Version 3.12.4.125
The POLYFIT program is a companion program to the program JKCFIT.  This program specializes in performing polynomial curve fits to data.  The polynomials may be of any degree between 1 and 10.  This program performs two kinds of fit; the first is called an Exact Point fit and this means the program can generate the Legendre interpolating polynomial that goes through each data point exactly.  The second type of fit is a standard least squares curve fit.  Except for the fact that this program specializes in higher degree polynomials, the operation and feature set is identical to that of the JKCFIT program. The two files PFEXAMPLE1.TXT and PFEXAMPLE2.TXT contain sample data. This program has context sensitive help in the file HelpPolyFitST.pdf. There is even an auxiliary help file HelpPolyFitTut.pdf that is a tutorial for first-time users.  Normally the 5 files POLYFIT.EXE, HelpPolyFitST.pdf, PFEXAMPLE1.TXT, PFEXAMPLE2.TXT, and HelpPolyFitTut.pdf must reside in the same subdirectory. POLYFIT is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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4. JKDIFEQ.EXE  1,139,200  02/14/2010  1:39 PM  Version 3.3.4.319
The JKDIFEQ program is designed to graph and solve first order differential equations. The program can make the graph of the direction field that is associated with the differential equation. It also dynamically shows the solution graph to an initial value problem that can be overlaid on the direction field. This provides an insightful view of the family of solution curves and demonstrates how solutions are sensitive to the initial conditions. The graphing features include an XY-plane window, scalable axes, a Coordinate Trace Mode, a Function Trace Mode and zooming features. The numerical methods for solutions to initial value problems include the standard Euler and modified Euler methods as well as a 4th order Runge-Kutta method. Solutions to initial value problems can be animated using a single-step mode that graphically demonstrates the convergence process. A table of all the step points can also be made. You can also setup a slide show to display a series of slope fields. The slide show can run in either an automaic or a manual mode. The file SlideListJKDiffEq.txt can be used as a slide show file. This program includes 12 other text files named DiffEqAutonomous1.txt, DiffEqAutonomous2.txt, DiffEqCircles.txt, DiffEqCrazyImplicit.txt, DiffEqDefault.txt, DiffEqRandom.txt, DiffEqSagPattern.txt, DiffEqSwirlPattern.txt, DiffEqSwirls.txt, DiffEqXDivY.txt, DiffEqXTimesY.txt, and DiffEqYDivX.txt that can be loaded into the program as sample differential equations to be studied. There is a tutorial help file named HelpJKDifEqTut.pdf in addition to the dialogs help file named HelpJKDifEqDialogs.pdf and the special topics help file named HelpJKDifEqST.pdf. JKDIFEQ is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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5. LPG.EXE  1,214,464  02/14/2010  1:45 PM  Version 1.74.4.81
The LPG program graphs systems of 2-dimensional linear inequalities and can be used to solve linear programming problems in 2 variables. LPG stands for Linear Programming Graphs. The program can also be used to create systems of linear inequalities that have nice solutions. There is both an objective function trace mode and a linear constraint trace mode that visually aid in demonstrating the nature of the solutions. This program can be used to create graphs as bitmaps or metafiles that can be incorporated into other Windows programs. This program also makes it easy to enter and edit problems and to save problems and quickly load examples. There is also a tutorial help file named HelpLPGTut.pdf in addition to two help files named HelpLPGDialogs.pdf and HelpLPGST.pdf. LPG is a 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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6. JKPROB.EXE  613,376  02/14/2010  1:49 PM  Version 2.51.1.42
The program called JKPROB is a WINDOWS program that really consists of two separate applications related to probability.  The first application simulates a GALTON board and the second application simulates BUFFON's Needles.  Each application simulates an animated action and the user can control the speed of animation by setting one of three modes that are called Automatic, Demonstration, and Single Step.  The Automatic mode is the fastest, the Demonstration mode simulates a slow-motion camera and the Single Step mode simulates a stop-action camera.  The GALTON application can be used to show how nature produces the binomial coefficients in Pascal's Triangle.  The BUFFON application shows how the number Pi can be approximated by dropping needles on a floor.  Both applications have context sensitive help in the files HelpJKProbGaltonIH.pdf and HelpJKProbBuffonIH.pdf.  There are also two auxiliary help files HelpJKProbGaltonTut.pdf and HelpJKProbBuffonTut.pdf that are tutorials for first-time users.  Normally the 5 files JKPROB.EXE, HelpJKProbGaltonIH.pdf, HelpJKProbGaltonTut.pdf, HelpJKProbBuffonIH.pdf,, and HelpJKProbBuffonTut.pdf must all reside in the same subdirectory. JKPROB is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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7. COMBO.EXE  708,096  02/14/2010  1:56 PM  Version 1.69.1.108
The COMBO program is a simple program for computing and analyzing both combinations and permutations and related functions. The main use of this program is that it allows you to name the elements in a set of objects and then the program can generate and display all the subsets of size K where you let K be any number. This task is not trivial if you try to do it manually. The program can also generate and display all permutations of all subsets of size K. It can compute what are called multisets, and it can generate strings of binary words with a fixed number of bits that are set. This program can also compute multinomial coefficients. Other related functions include simply calculating the number of combinations or permutations of N elements chosen K at a time or computing the factorial of N or computing the number 2 raised to the Nth power or computing the binary bit patten for the number N. If you need to compute exact large values for either permutations or combinations or factorials that may run into the thousands of digits then you should try the program listed below named JKXPRES. The help file for the COMBO program is named HelpComboIntro.pdf. The COMBO program is a 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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8. JKMONEY.EXE  641,024  02/14/2010  1:59 PM  Version 2.39.1.38
The program called JKMONEY is a WINDOWS financial program that handles the two most common cases of compound interest.  This program works with the 5 standard financial variables n, i, PV, PMT, FV and can handle these in any meaningful combination.  This program can also print interest earning schedules for a lump sum or for a series of periodic constant payments. This program can also compute the amortization schedule for a loan or compute a table of periodic constant withdrawls that will deplete an account.  Tables may be printed on a printer or copied to the WINDOWS clipboard or saved in ASCII text files.  There is a tutorial help file named HelpJKMoneyTut.pdf There is also a general help file named HelpJKMoneyIH.pdf. Normally the 3 files JKMONEY.EXE, HelpJKMoneyTut.pdf, and HelpJKMoneyIH.pdf must all reside in the same subdirectory. JKMONEY is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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9. JKTRI.EXE  671,232  02/14/2010  2:01 PM  Version 2.41.1.35
The program called JKTRI is a WINDOWS program that solves triangle problems involving the Laws of Sines and Cosines.  This program can also generate and test Pythagorean triples.  In a typical triangle type of problem, three known parts of a triangle are entered and the program will calculate the other three parts.  There are 19 possible cases and this program handles all of them, including the ambiguous case of the Law of Sines.  So if two triangles match the given input, this program yields both answers.  This program also draws the triangle solutions to scale in a window.  There is a help file named HelpJKTriIH.pdf and there is a tutorial help file named HelpJKTriTut.pdf that is for first-time users.  Normally the 3 files JKTRI.EXE, HelpJKTriIH.pdf, , and HelpJKTriTut.pdf must all reside in the same subdirectory.  JKTRI is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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10. TRIGFUN.EXE  577,024  02/14/2010  2:04 PM  Version 1.59.1.54
The TRIGFUN program is a simple program for studying the relationships between the six trigonometric functions and the unit circle. This program allows you to select each of the six trigonometric functions in turn and then drag a slider control that moves a point around the unit circle. While the point is being moved, you will see two graphs. The graph on the left shows the unit circle and it shows a colored line segment that relates to the value of the selected trigonometric function for the angle determined by the point on the circumference of the unit circle. The graph on the right shows the same colored segment as the height of the function in the normal graph for that function. The program also displays the exact values for the sixteen special points around the unit circle for each of the six trigonometric functions. Students can use this program to better understand how the trigonometric values relate to parts of the unit circle. The program can work in either degrees or radians modes and displays all special values as exact pure numbers and as decimal approximations. The user can set the colors used in the graphs. Users can also put the program in an automatic animation mode in which the angle gets pushed around the unit circle automatically. Users can control the speed of animation. The help file for this program is named TRIGFUN.HLP that is for first-time users. TRIGFUN is a 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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11. KOCH.EXE  1,078,784  02/14/2010  2:06 PM  Version 3.26.1.101
The purpose of the KOCH program is to generate and display some special mathematical curves.  This program can generate the Koch Snowflake, the Hilbert curve, the Mandelbrot Set, the Pythagorean Tree, harmonograms, and in addition, it can generate some artistic looking pictures based on simple transformations with squares and triangles.  Thus the main content of the program is related to recursive mathematical curves and iterative processes.  In fact, the program generates a recursive grammar to create the drawing instructions that are used to build the Hilbert Curve.  For the Koch Snowflake the program not only displays the successive approximations but it also calculates the perimeter, and the area and the number of sides in the polygon.  The Koch Snowflake is a continuous curve that is nowhere differentiable and has infinite arclength but encloses only a finite area.  For the Hilbert curve this program calculates the number of segments and the total perimeter.  The Hilbert curve completely fills a 2-dimensional area, and is continuous but differentiable nowhere.  This program can also make some very artistic looking curves using hypotrochoids, epitrochoids, peritrochoids, and other curves from the trochoid family. The peritrochoid curve was used in the design of the Wankel rotary engine. The file Trochoids.pdf contains information about curves in the trochoid family. This program has help in the file HelpKoch.pdf>. Normally the three files, KOCH.EXE, HelpKoch.pdf, and TROCHOIDS.PDF must reside in the same subdirectory.  KOCH is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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12. POLYHEDRA.EXE  652,800  02/14/2010  2:08 PM  Version 1.32.1.216
The program called Polyhedra is a simple program for printing on 2D paper, models of 3D regular polyhedra. After cutting and folding and Scotch taping, the user can make 3D paper models of the five regular solids that have the names Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron. Polyhedra comes with a help file named HelpPolyhedra.pdf. Polyhedra is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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13. JKTURING.EXE  565,248  02/14/2010  2:11 PM  Version 2.23.4.70
The JKTURING program is a WINDOWS program that simulates the operation of a Turing Machine and a Finite State Machine. Turing Machines are abstract models of primitive digital computers. In fact, they provide the most fundamental model for all logical computations. Such a machine was conceived by the British mathematician Alan Turing in 1935, long before digital computers became established. Turing also worked on machines to break the secret codes produced by the German Enigma machine in World War II. JKTURING provides a tape with 999 elements, with each position capable of holding a single symbol. This tape capacity should be more than adequate for the demonstration nature of this program. For a genuine Turing Machine, these symbols are only allowed to be the unary digits 0 and 1. However, JKTURING can also employ a richer set of symbols that includes the 94 printable ASCII characters. When used in this mode, JKTURING can be used to model a general Finite State Machine or FSM. In fact, JKTURING is good for modeling both a genuine Turing Machine and a general FSM. Various states can be given general identifier names that contain up to 5 characters. This maintains the primitive nature of FSMs. Programs that comprise the State Transition Table may contain any number of lines. In addition, JKTURING contains an editor so that users may write, edit, and save their Turing Machine programs. You can also vary the speed of animation and can run programs in either an automatic mode or a single-step mode. Five sample demonstration programs are included in the files named JKTDEMO1.TXT, JKTDEMO2.TXT, JKTDEMO3.TXT, JKTDEMO4.TXT, and JKTDEMO5.TXT. This program has context sensitive help in the files HelpJKTuringIntro.pdf and HelpJKTuringTut.pdf. You should install the Adobe Reader program before running JKTuring. Normally all the files must reside in the same subdirectory. JKTURING is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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14. RPNPC.EXE  899,072  02/14/2010  2:16 PM  Version 2.21.1.62
The RPNPC program was designed to simulate a programmable RPN calculator. This calculator/computer provides an integrated programming environment that includes a built-in editor with complete syntax checking. The environment includes an interpreted language that provides full run-time error checking. You can learn to program a computer with this program. Programs you create may be saved to or read from disk files. This program is an excellent tool for learning how a Reverse Polish logic calculator works. It can also be used to simulate a type of assembly language that is simple, yet is rich with features that include conditional comparisons and flag testing, indirect memory addressing, and the ability to make subroutine calls and watch the build-up and break-down of the subroutine return stack. Programs may be executed in an animated mode that shows the internal workings of the machine. You can minimize the animation when speed is desired. The user can also set two time delay factors to control the animation speeds. Included with this program are 5 demonstration program files called PCDEMO1.TXT, PCGCF.TXT, PCPRIMEF.TXT, PCPRIMES.TXT, and PCSUBS.TXT. A sixth text file named PCPROGS.TXT contains explanations about how to use the sample programs and how they work. There is also a tutorial help file named HelpRPNPCTut.pdf that is for first-time users. Another help file is HelpRPNPCIH.pdf. A background paper that discusses some of the history behind Reverse Polish Notation (RPN) is provided in the file RPNBG.pdf. Any of these *.TXT files may be imported into any word processor and/or printed on any printer. The RPNPC program is a 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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15. SENTCALC.EXE  771,584  02/14/2010  2:22 PM  Version 2.18.0.109
The SENTCALC program performs analysis of formulas from the Propositional or Sentential Calculus, a branch of symbolic logic. SENTCALC can be used to perform a complete truth table analysis of propositional formulas of arbitrary complexity. The program can generate all truth-value lines, or generate only the true lines, or generate only the false lines. It can simply test a formula as a tautology. The program can also display the parse tree structure that corresponds to any formula, and it can translate formulas from the common infix notation to Polish notation. In fact the program can also generate both prefix and postfix notations for a formula. This program also generates and displays the Karnaugh Map that is associated with a given formula or truth table that is comprised of 2, 3, or 4 variables. The program also calculates a minimal length formula that generates the same truth table as determined by the Karnaugh Map. Truth tables and formulas can be printed on a printer or saved in text files. This application is still under development. SENTCALC is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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16. JKFINITEFIELDS.EXE  807,424  02/14/2010  2:25 PM  Version 2.41.0.274
The JKFiniteFields program can create both addition and multiplication tables for finite fields of prime order, and it can create rings using modulo n arithmetic. In addition to working with fields and Abelian groups of finite order, it can also perform matrix computations using modulo n arithmetic. The program can add and subtract and multiply matrices where all computations are performed within a finite field. It can row reduce a matrix and calculate sets of basis vectors for both the column space and the row space of a matrix. All matrix computations are performed using only modulo n arithmetic. Tables and matrices may be copied to the Windows clipboard, or they may be printed on a printer or they may be saved in text files. This program also has a Reverse Polish logic calculator for working with polynomials. This program can find all zeros of any polynomial up to degree 14 where the zeros come from the finite field of integers modulo a prime number. It can also add, subtract, multiply, and divide any two polynomials, using modular arithmetic on all the polynomial coefficients. It can easily calculate and show both quotient and remainder polynomials.In addition to all of the above, this program can calculate Galois fields of small order and can make addition and multiplication tables for Galois fields. It can calculate the order of any Galois field element when that field contains about 3,000 or fewer elements. Finally it can also calculate the minimal polynomial for any such element relative to the field of integers modulo the prime characteristic of the Galois field. This program can also construct the non-cyclic finite group that has p(p-1) elements whose operation rule is the composition of linear functions in the form f(x)=mx+b. In this case m must be nonzero and both m and b are integers modulo p where p is the prime modulus of the program. JKFiniteFields is accompanied by one help file named HelpJKFiniteFieldsTut.pdf. JKFiniteFields is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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17. JKCURVE3D.EXE  1,227,264  02/14/2010  3:26 PM  Version 4.19.6.489
The JKCURVE3D program can be used to graph any continuous space curve given in a parametric form in 3-dimensional space. You can view the curve from any position or orientation in space. You can also use your mouse to walk around the curve and to trace points along the curve. This program can also calculate the arclength between any two points on the curve. This program has four trace modes with which you can study the curvature at any point on the curve as well as the tangential and normal components of acceleration. Another trace mode shows the three mutually orthogonal unit vectors that form a local coordinate system at any point on the curve. The system of those three vectors is called the TNB system where T represents the Tangent vector, N represents the Normal vector and B represents the Binormal vector. The plane determined by the N and B vectors is called the normal plane. The plane determined by the T and N vectors is called the osculating plane and the plane determined by the T and B vectors is called the rectifying plane. The fourth trace mode shows the osculating circle as the trace point moves along the curve. In this last mode you can see the dynamics of the osculating circle as it changes its radius and orientation. You can also setup a slide show to display a series of 3D curves. The slide show can run in either an automaic or a manual mode. The file SlideListCV3D.txt can be used as a slide show file. There are 38 example curves contained in other text files named CVAlmostASurface.txt, CVBaseballSeam.txt, CVBicycleSeat.txt, CVBiCylindric.txt, CVChonchoSpiral.txt, CVCycloidFlat.txt, CVCycloidGrowing.txt, CVDefaultGraph.txt, CVEllipticalHelix.txt, CVEllipticalTongue.txt, CVFigure8Knot.txt, CVFourCorners.txt, CVHelix.txt, CVHelixOnCone.txt, CVKingsCrown.txt, CVKnottyMess.txt, CVLissajous1.txt, CVLissajous2.txt, CVLogSpiral.txt, CVOddBitOfWire.txt, CVPigTail.txt, CVRollerCoaster.txt, CVSineAndCube.txt, CVSineAndSquare.txt, CVSineOnCone.txt, CVSineOnSphere.txt, CVSphereCylinderIntersect.txt, CVSpiralSpring.txt, CVToroidalSpiral.txt, CVTorusKnot43.txt, CVTorusKnot52.txt, CVTorusKnot75.txt, CVTrefoilKnot.txt, CVTwistedCubic.txt, CVTwoChairBacks.txt, CVViviani.txt, CVWoblySpring.txt, and CVXAxisHelix.txt. There is a tutorial help file named HelpJKCurve3DTut.pdf for first-time users. There is a help file for dialog boxes named HelpJKCurve3DDialogs.pdf and there is another help file about special topics named HelpJKCurve3DST.pdf. JKCURVE3D is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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18. JKSURF3D.EXE  1,537,536  02/14/2010  3:30 PM  Version 5.24.5.484
The JKSURF3D program can be used to graph a continuous surface given by Z=F(X,Y) in three dimensions and to view that surface from any position or orientation in space. The program can render the surface in several ways that include drawing lines of either constant X or constant Y, drawing an unrendered fishnet view, or rendering a more robust view with hidden lines removed and coloring the surface using a specified color that varies with the intensity of light from a single light source. You can also use your mouse to walk around the surface and to trace points along the surface. This program can also calculate the surface area and the signed volume that lies between the surface and the XY-plane. It can also make a 2D drawing of the level curves for a given surface. You can also run a normal vector anywhere across the surface. You can also setup a slide show to display a series of 3D surfaces. The slide show can run in either an automaic or a manual mode. The file SlideListSF3D.txt can be used as a slide show file. There are 108 example surfaces contained in other text files named SF2Hills1Valley.txt, SFAlmostASaddle.txt, SFAnOddSaddle.txt, SFATopOnAPoint.txt, SFBed.txt, SFBoxHalves.txt, SFBowl.txt, SFBowlWith4Legs.txt, SFBridge.txt, SFBugleHalf.txt, SFButterfly.txt, SFCanyonWalls.txt, SFCarPort.txt, SFClairoutContradiction.txt, SFConocuneus.txt, SFCorrugatedRoof.txt, SFCraterDimple.txt, SFCraterFlat.txt, SFCurlyQ.txt, SFCurvedBlanket.txt, SFCurvedDown.txt, SFDefaultSurface.txt, SFDepression.txt, SFDevilsChair.txt, SFDihedralAngle.txt, SFDihedralVolume.txt, SFDimpledHat.txt, SFDivideByTwo.txt, SFDome.txt, SFEggCarton.txt, SFEvenChannel.txt, SFExpFunnel.txt, SFExponentialBackstop.txt, SFFlatBridge.txt, SFFlatBladeScrewDriver.txt, SFFoldedSurface.txt, SFFountain.txt, SFFourExtremes.txt, SFFourHills.txt, SFFourHumpsAndFlat.txt, SFFourSheets.txt, SFGradientZero.txt, SFHalfLegChair.txt, SFHandkerchief.txt, SFHelmet.txt, SFHillAndHole.txt, SFHillsAndValleys.txt, SFHorizontalChair.txt, SFHumps.txt, SFHyperbola.txt, SFJaggy.txt, SFKnobHill.txt, SFLittleDimple.txt, SFLowerTorus.txt, SFMonkeySaddle.txt, SFMoreBumps.txt, SFNegTunnels.txt, SFOneCover.txt, SFOneHill.txt, SFOneMaxOneMin.txt, SFOperaHouse.txt, SFOriginBadLimit.txt, SFParabolicBlanket.txt, SFPagoda.txt, SFPagodaWithBoundary.txt, SFPikesPeak.txt, SFPlateaus.txt, SFRidges.txt, SFRipples1.txt, SFRipples2.txt, SFRipples3.txt, SFROOF.TXT, SFSaddle.txt, SFScoop.txt, SFSeatWith4Legs.txt, SFSideChair.txt, SFSineHill.txt, SFSlideUpDown.txt, SFSphereCut.txt, SFSpikes.txt, SFSquareBlock.txt, SFSquareHole.txt, SFSquareSineWaves.txt, SFSquatter.txt, SFSwallowTail.txt, SFTent.txt, SFThreeDepressions.txt, SFThreeSnails.txt, SFTrafficCone.txt, SFTriangleHole.txt, SFTrough.txt, SFTunnels.txt, SFTurtleShell.txt, SFTwoByTwo.txt, SFTwoChannels.txt, SFTwoDips.txt, SFTwoHalfFunnels.txt, SFTwoHumpsAndADip.txt, SFTwoPlateaus.txt, SFUnusualSurf.txt, SFUpDownFunnel.txt, SFUpperTorus.txt, SFWarped.txt, SFWavyBlanket.txt, SFWrinkle.txt, SFXYDamped.txt, and SFZeroVolumeExample.txt. There is a tutorial help file named HelpJKSurf3DTut.pdf and two other help files are named HelpJKSurf3DDialogs.pdf and HelpJKSurf3DST.pdf. JKSURF3D is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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19. VFIELDS.EXE  1,121,792  02/14/2010  3:35 PM  Version 2.18.4.285
The VFIELDS program can graph vector fields in 3 dimensions and can also associate either a 3D curve or a 3D surface with the vector field. It can show only those field vectors that lie on the surface or curve or it can show the entire field. This program can then calculate either a line integral or a surface integral. Line integrals can also calculate work along the 3D curve and surface integrals can also calculate the total flux over a surface. The program can save the state of all graph elements and parameter values in an ordinary text file. This text file can then later be opened to re-load or re-create the entire environment or state of the program. The text files can be edited, and once the format is understood, you can create entirely new vector fields by just editing the text. This feature provides a fast but convenient way to create various examples that can be quickly loaded and run. You can also setup a slide show to display a series of vector fields, or 3D surfaces or 3D curves. The slide show can run in either an automaic or a manual mode. The file SlideListVF3D.txt can be used as a slide show file. VFIELDS comes with 48 examples in other text files named AroundAPoleVF.txt, ArchwaySF.txt, BaseballSeamCV.txt, CapSurfaceSF.txt, CircularTornadoVF.txt, ConstantFieldVF.txt, CorkScrewXCV.txt, CorkScrewYCV.txt, CorkScrewZCV.txt, CosineWaveSF.txt, DihedralSurfaceSF.txt, DomeSF.txt, EllipticalTongueCV.txt, FlatRiverVF.txt, FourSheetsSF.txt, HelixCV.txt, HerringBoneVF.txt, HyperbolicTornadoVF.txt, InverseSquareInVF.txt, InverseSquareOutVF.txt, KingsCrownCV.txt, LeftTurnVF.txt, Lissajous1CV.txt, Lissajous2CV.txt, LittleDimpleSF.txt, OpposingVectorsVF.txt, OriginAsASourceVF.txt, ParabolicSF.txt, PlaneSurfaceSF.txt, RandomNormalVF.txt, RandomPosVF.txt, Ripples1SF.txt, RollerCoasterCV.txt, RotatingWheelVF.txt, SaddleSF.txt, SineAndSquareCV.txt, SineOnConeCV.txt, SpiralSpringCV.txt, SpreademVF.txt, TearDropCV.txt, ToroidalSpiralCV.txt, TrefoilKnotCV.txt, TubeOnASphereCV.txt, TurtleShellSF.txt, TwoChairBacksCV.txt, TwoSourcesVF.txt, UndulatingRiverVF.txt, and WoblySpringCV.txt. VFIELDS has a tutorial help file named HelpVFieldsTut.pdf that is for first time users. Another help file with special topics is named HelpVFieldsST.pdf. A third help file concerned with dialog boxes is named HelpVFieldsDialogs.pdf. Normally VFIELDS.EXE, HelpVFIELDSDialogs.pdf, HelpVFIELDSST.pdf and HelpVFIELDSTUT.pdf must reside in the same subdirectory. VFIELDS is a 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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20. PARAM3DSF.EXE  1,446,912  02/14/2010  3:44 PM  Version 4.78.4.303
The program called PARAM3DSF.EXE can graph surfaces in 3 dimensions that are given in a parametric form. X=F(U,V), Y=G(U,V), Z=H(U,V) where U and V are the parameter variables. You can view any surface from any position or orientation in space. The program gives a robust view with hidden lines removed and colors the surface using a specified color that varies with the intensity of light from a single light source. You can render the surface in several ways including drawing lines of constant U or constant V or drawing a wireframe view or drawing a view without surface lines. You can use your mouse to walk over the surface and to trace points along the surface. This program also has a normal vector trace mode that can show a unit normal vector at any point on the surface. This program can also use a third parameter variable to make what are called multi-graphs. Another special feature is the ability to create a tube surface that follows and wraps around and along any 3D parametrized curve path that serves as the center line of the tube surface. Tube types include 1-dimensional strings, 2-dimensional flat ribbons, and 3-dimensional regular n-sided polygons of any fixed-size radius where n=1,2,3,4,5,6,... Tube surfaces can be used to make models of wires, and roller coasters, and various kinds of knots. Two special dialog boxes can be used to quickly make torus knots and Lissajous knots. This program can also calculate the surface area and it can make a slide show of surfaces that can be controlled in either an automatic or a manual mode. The file SlideListPS3D.txt can be used as a slide show file. There are 194 example surfaces contained in other text files named PSAlmostASaddle.txt, PSAlmostMobius.txt, PSAuger.txt, PSBadSnowPlow.txt, PSBallooonKiss.txt, PSBarbequeTongs.txt, PSBigApple.txt, PSBigAppleMultigraph.txt, PSBlackHole.txt, PSBour.txt, PSBowl.txt, PSBoysSurface.txt, PSBreather.txt, PSBreatherOpen.txt, PSButterfly.txt, PSCanCrunched.txt, PSCapsuleMultigraph.txt, PSCatalan.txt, PSCheeseBlockCubed.txt, PSCircularFountain.txt, PSClosedFunnel.txt PSCone.txt, PSCone2Nappes.txt, PSConeMultigraph.txt, PSConeRing.txt, PSConocuneus.txt, PSCornucopia.txt, PSCrossCap.txt, PSCrossOver.txt, PSCruller.txt, PSCutCone.txt, PSCylinderHalf.txt, PSDefaultSurface.txt, PSDini.txt, PSDoubleHelix.txt, PSEllipsoidCut.txt, PSEllipsoidFull.txt, PSEllipticBowl.txt, PSEllipticBowlMultigraph.txt, PSEmptySnailBowl.txt, PSEnneper.txt, PSFangs.txt, PSFigure8.txt, PSFigure8Multigraph.txt, PSFigure8VariableZ.txt, PSFlyingSaucerMultigraph.txt, PSFlyingSaucerMultigraph2.txt, PSFoldedCardboard.txt, PSFoldedSurface.txt, PSFountainOnABase.txt, PSFourQuarterWheels.txt, PSFunnel.txt, PSFunnelMultigraph.txt, PSGergonneLike.txt, PSGradientZero.txt, PSHelicoid.txt, PSHelicoid2.txt, PSHelixTube.txt, PSHelixTube2.txt, PSHelixTubeMultigraph1.txt, PSHelixTubeMultigraph2.txt, PSHelixTubeMultigraph3.txt, PSHelixTubeMultigraph4.txt, PSHenneberg.txt, PSHenneberg2.txt, PSHyperbolicFolds.txt, PSHyperboloid1Sheet.txt, PSHyperboloid2Sheets.txt, PSIgloo.txt, PSInsideWorld.txt, PSInsideWorldMultigraph.txt, PSKalman.txt, PSKleinBottle.txt, PSKuenSurface.txt, PSLampShade.txt, PSLeprechaunHat.txt, PSLogarithmicSplit.txt, PSMobiusStrip.txt, PSMobiusStripDoubleTwist.txt, PSMonkeySaddle.txt, PSNotRegular.txt, PSNutBowl.txt, PSOddShell.txt, PSOpen2Cones.txt, PSOpenBumpySphere2.txt, PSOpenCover.txt, PSOpenIceCreamCone.txt, PSOpenShell, PSOpenVase.txt, PSOrangeCrush.txt, PSPartialShell.txt, PSPartialSphere.txt, PSPartialSphereMultigraph.txt, PSPC2Intersections.txt, PSPCAlmostABowl.txt, PSPCBaseballSeam.txt, PSPCEllipticalTongue.txt, PSPCFigure8Knot.txt, PSPCHelix.txt, PSPCHelixOnCone.txt, PSPCKingsCrown.txt, PSPCKnottyMess.txt, PSPCLissajous1.txt, PSPCLissajous2.txt, PSPCRollerCoaster.txt, PSPCSelfIntersectingTube.txt, PSPCSimpleKnot.txt, PSPCSineOnCone.txt, PSPCSpiralTube.txt, PSPCToroidalSpiral.txt, PSPCTorusKnot43.txt, PSPCTorusKnot52.txt, PSPCTorusKnot75.txt, PSPCTrefoilKnot.txt, PSPCTubeOnASphere.txt, PSPCTwoChairBacks.txt, PSPCVivianiRibbon.txt, PSPill.txt, PSPlateaus.txt, PSPseudoCrossCap.txt, PSPseudoSphere.txt, PSPseudoSphere2.txt, PSPyramid.txt, PSRomanSurface.txt, PSRoof.txt, PSRotatedSineWave.txt, PSSaddle.txt, PSSaddlePartsMultigraph.txt, PSSaddleSquare.txt, PSSelfIntersecting.txt, PSShellHalfHalf.txt, PSShellSelfIntersecting.txt, PSShellSuper.txt, PSShellSuper1.txt, PSShellSuper2.txt, PSSineSurface.txt, PSSnail.txt, PSSnail2.txt, PSSpecialBowl.txt, PSSpecialBowl2.txt, PSSpecialBowlMultigraph.txt, PSSphereAndCylinder.txt, PSSphereBumpy.txt, PSSphereBumpyMultigraph.txt, PSSphereBumpyOpen.txt, PSSphericalRing.txt, PSSpiralRamp.txt, PSSplitBowl.txt, PSSpiralWall.txt, PSStarBase.txt, PSSteinerRoman.txt, PSSteinerRomanPartial.txt, PSSwimmingPool.txt, PSTheBlob.txt, PSTheBlobPartial.txt, PSThreePerpCylinders.txt, PSThreePlanes.txt, PSThreeTogether.txt, PSThruLookingGlass.txt, PSTinRoof.txt, PSTireFull.txt, PSTireSlit.txt, PSTorusElliptic.txt, PSTorusFull.txt, PSTorusHalf.txt, PSTorusHalfMultigraph.txt, PSTorusPartial.txt, PSTorusPartial2.txt, PSTorusPlain.txt, PSTorusThreeIntersecting.txt, PSTorusThreeTouching.txt, PSTorusUmbilic.txt, PSTorusUmbilicInside.txt, PSTrough.txt, PSTroughMultigraph.txt, PSTube.txt, PSTubeMultigraph.txt, PSTubeMultigraph2.txt, PSTubeMultigraph3.txt, PSTubeShrinking.txt, PSTubeTouches.txt, PSTwistedAround.txt, PSTwoCollectors.txt, PSTwoDomes.txt, PSTwoMouths.txt, PSTwoScoops.txt, PSTwoTogether.txt, PSUnevenRing.txt, PSUnusualDome.txt, PSWarpedCone.txt, PSWedge.txt, PSWhitneyUmbrella.txt, PSWirlyBird.txt, and PSWoblySpring.txt. PARAM3DSF has context sensitive help in the files HelpParam3DSFDialogs.pdf and HelpParam3DSFST.pdf.  There is a tutorial file, HelpParam3DSFTut.pdf, that is for first-time users.  Normally PARAM3DSF.EXE, HelpParam3DSFDialogs.pdf, HelpParam3DSFST.pdf and HelpParam3DSFTut.pdf must reside in the same subdirectory. PARAM3DSF is a 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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21. JKTHANOI.EXE  465,408  02/14/2010  3:46 PM  Version 2.18.1.33
The JKTHANOI program is a WINDOWS program that plays the game known as the Towers of Hanoi. This program demonstrates the validity and simplicity of a recursive solution to a complex problem. The main logic in this program is only three lines long! The program can work in both automatic and manual modes. Up to 511 consecutive game moves can be animated with the speed of animation controlled by the user. This program has context sensitive help in the file HelpJKTHanoi.pdf. Normally the two files JKTHANOI.EXE and HelpJKTHanoi.pdf must reside in the same subdirectory. JKTHANOI is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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22. JKNLINE.EXE  634,880  02/14/2010  3:48 PM  Version 2.42.1.40
The program called JKNLINE is a WINDOWS program that is used to make graphic pictures of number lines.  The number lines may contain any kind of interval or isolated points and can be thought of as representing solutions to one-variable inequalities or equations.  The purpose of this program is to make bitmap images or metafiles that can be copied into a scientific word processor or other type of document that requires number line graphs. Number line interval endpoints or isolated points may be open or closed. Intervals are automatically shaded. This program provides relatively fine control over the size, spacing, and placement of each of the graphic elements that make up the number line graph.  You can also use custom fonts and colors for labels and titles.  The final graphic images can be printed on a printer or they can be copied into the WINDOWS clipboard as bitmap images in which you can specify the size and resolution of the image. You can also save the image as a Windows metafile. Usually you will also save the image in a special text file format that only the JKNLINE program can read.  There is on-line help in the file HelpJKNLineIH.pdf.   There is also a tutorial for first-time users in the file HelpJKNlineTut.pdf and there are several example number lines in the files JKNLSMPL.TXT, JKNLX2.TXT, JKNLX3.TXT, JKNLX4.TXT, JKNLX5.TXT, and JKNLTUT.TXT. JKNLINE is a native 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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23. JKXPRES.EXE  518,144  02/14/2010  3:51 PM  Version 2.21.1.81
The JKXPRES program is for performing multiple precision arithmetic with large integers.  This program is useful whenever you need to work with numbers that would overflow the 10-digit capacity of your calculator.  The program works with nonnegative integers with a dynamic range between 1 and 20,000 digits. The special computational algorithms include unusually large factorials, powers, permutations, and combinations.  For example, you can use JKXPRES to compute the exact value of 1000 factorial that is a number 2,568 digits long.  Or you can compute the number of combinations of 3000 objects chosen 1500 at a time that results in a number 902 digits long.  The number 2 raised to the 5,000th power is a number 1,506 digits long.  The need for computing exact values of large integers may seldom arise, but when it does, JKXPRES may satisfy the need.  JKXPRES warns you whenever any calculation would overflow the 20,000 digit capacity of any single number. The program employs a model of a Reverse Polish Logic calculator.  There are multiple overlapping windows.  Each number occupies its own window and can be displayed in any one of three formats.  Numbers may be displayed as long strings of continuous digits.  Digits may also be grouped three at a time separated by commas.  The third format displays a number with 5-digit groups separated by spaces.  A clipboard may be used to copy temporary results.  Numbers may be saved to or read from disk files.  The program will automatically count and display the count of the number of digits in each number.  The program can also be used to automatically compare any two extended precision numbers; a task that would be extremely tedious if done manually.  This program can also count the number of 0-9 digits in a number and also report the distribution percentages of the digits 0-9 that appear in any number. It also has a built-in timer that automatically computes the elapsed time of any calculation. If you need to actually make a list of either the permutations or combinations and the number is relatively small then you should try the program listed above named COMBO. JKXPRES has context sensitive help in the file HelpJKXPresIH.pdf.  There is a tutorial file, HelpJKXPresTut.pdf, that is for first-time users.  JKXPRES is a 32-bit WINDOWS application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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24. JKITERATE.EXE  705,024  02/14/2010  3:53 PM  Version 1.31.0.44
The JKIterate program is used to create special iterative and recursive sequences of real numbers. The program can combine recursive sequences with special function evaluations to create special tables of function values. Applications include the method of constant slope, Newton's Method, and other recursive processes. JKIterate comes with two help files named HelpFormulaHelp.pdf and HelpJKIterate.pdf. JKIterate is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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25. JKMATRIX.EXE  1,060,864  02/14/2010  3:59 PM  Version 7.56.22.10
The JKMatrix program is designed to perform and to teach row operation algorithms on matrices. The program can work in a decimal floating-point mode in which calculations are carried out to 18 significant digits, or it can work in a fraction mode with exact rational arithmetic. The fraction mode is more useful for instructional purposes while the decimal mode is more appropriate for scientific or engineering applications. You can easily switch between fractions and decimals at any time. The program can find complete solutions to systems of linear equations, can compute determinants and inverses of matrices, and solve standard and non-standard Linear Programming problems using the simplex algorithm, and can perform other special algorithms that include the Gram-Schmidt Orthogonalization process, the calculation of eigenvalues and eigenvectors, and the calculation of Markov Chains. The program can calculate sets of basis vectors for the kernel, range, and row space of a matrix. The inter- matrix operations include addition, subtraction, and multiplication of matrices as well as scalar multiplication. The program provides 61 mathematical operators that can be applied to matrix elements. This program provides easy entry and editing of matrices that may be up to 20x20 in size. Matrices may be re-dimensioned and rows and columns can easily be inserted or deleted. Matrices may be saved to and/or read from disk files. Each matrix occupies a window and as many as 9 overlapping windows may be open on the desktop at once. JKMatrix is accompanied by a tutorial help file named HelpJKMatrixTut.pdf, a help file on special topics named HelpJKMatrixST.pdf, and a help file on all dialog boxes named HelpJKMatrixDialogs.pdf. JKMatrix also comes with many example matrix files. JKMatrix is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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26. JKCALC.EXE  809,472  02/14/2010  4:04 PM  Version 2.13.4.22
The program called JKCALC.EXE is a general purpose calculator that works with five basic data types that include real numbers, complex numbers, fractions, integers (with binary logic, base b=2, b=8, b=10, or b=16), and polynomials.  Thus JKCALC.EXE is really five calculators combined into one. The real numbers have between 19 and 20 significant digits with a dynamic range between 3.4 x 10^-4932  and 1.1 x 10^4932.  Real number functions include the basic four +, -, *, /, reciprocals, squares and square roots, powers, nth roots, trigonometric and inverse trigonometric functions (in degrees or radians modes), logarithmic and power functions (base 10 and base e), hyperbolic and inverse hyperbolic functions, factorials, permutations, combinations, prime factorizations of integers, greatest common factor, least common multiple, and the group order of one integer modulo another.  The complex number functions include all of the real number functions for which the analogous operations are well-defined.  Of significance are complex values for nth roots, complex powers, complex logarithms, complex trigonometric and complex inverse trigonometric and complex hyperbolic and complex inverse hyperbolic functions.  In fraction mode you can perform basic operations on fractions that may be displayed in both improper and mixed number form.  There are special functions for working with both simple and general continued fractions.  In the integer mode you can specify the word size in terms of the number of bits per integer.  The word size may be any multiple of 4 up to a maximum width of 32 bits.  Integer display options include binary, octal, decimal, or hexadecimal formats.  Integers may be signed or unsigned.  If signed, integers may be in either 1's or 2's complement format.  In addition to normal arithmetic, there are logical operators that include bitwise NOT, AND, OR, NAND and XOR.  The polynomial mode operators include +,-,* and /. Polynomial division yields both quotient and remainder polynomials.  A special function allows any polynomial with integer coefficients to be completely factored using exact rational linear factors.  Polynomials may be up to degree 25 and are easily entered, edited, and evaluated.  Other special functions include the ability to determine the fixed and periodic parts of any repeating decimal that represents any fraction.  In addition to base 10, repeating decimals may be analyzed and displayed with respect to binary, octal, and hexadecimal formats.  Another special function converts any decimal to a simple continued fraction and displays all the convergent terms as fractions and decimals.  JKCALC.EXE provides all this functionality in a model of a calculator that operates using reverse Polish logic.  Each number (data type) occupies its own window. This program has context sensitive help in the files HelpJKCalcTut.pdf and HelpJKCalcDialogs.pdf and HelpJKCalcST.pdf. Normally JKCALC.EXE and all these help files must reside in the same subdirectory. JKCALC is a 32-bit Windows application for WINDOWS-95/98/ME/XP/NT/2000/Windows 7.
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11.An Index Of All The Files
The following is an alphabetical listing of all 651 files. There are 26 program files. The additional 625 files provide support for help and documentation and examples. The file reference numbers correspond to the above program abstract numbers. If you used the relative path information when you unzipped each ZIP file, then all the files associated with each distinct program will be in a subdirectory with the same name as the program. All files with the same reference number belong to one and only one program and should normally be copied into the unique subdirectory corresponding to each program. The relative starting base path is named JKPROGS.
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