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Program Name:  Derivative
Version:       1.0
Platform:      TI-83 BASIC
               Bill Nagel's Aurora & AShell83 Compatible
Program Size:  1257 bytes
Release Date:  October 25, 1999 - First Public Release
Author:        Mark Fairpo
Author E-mail: fairpo@breathemail.net
Description:   Assists with the derivative, integral and inverse of functions
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1- Setup Instructions
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Send DERI.83G to the calculator.
Run PROGDERI or run Aurora and click DERI.
If you are not using Aurora delete ICONDERI.


2- Welcome to Derivative
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Thanks for picking up Derivative, which is distributed free of charge. It
FEATURES: the Inverse, Derivative, Second Derivative, and Indefinite Integral
or Antiderivative, with respect to X of functions entered in Y1 or Y2.
It plots a bunch of points, identified by 24 boxes or a solid line (INVERSE).
These can be used to verify the correct answer or simply for graphing.
You cannot zoom or trace in Derivative, however it wisely refits your y-axis.

You may use the Fit xyLine option to fit a polynomial function not exceeding
degree 4 to the data. NOTE: Derivative never reduces numbers (for instance,
it displays .6667X for 2/3X and 1X for X), and never puts in the integration
constant C: It is giving you AN INTEGRAL, not a formula for all integrals.

The Fit xyLine option uses your quartic regression model, QuartReg. The
DERIVATIVE and INTEGRAL options use a recurrence of your nDeriv (successively
for the 2nd DERIVATIVE) and fnInt operators, which use the symmetric
difference quotient method and Gauss-Kronrod method respectively, each with
an error tolerance (accuracy) of 1e-5 or 5 digits. So whereas some programs
are internally restricted to polynomials, we avoid any restrictions.


3- An Example of How to Use it
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Adapted from Problem 1 of Demonstrating the Fundamental Theorem of Calculus
in the TI-83 and TI-83 PLUS GRAPHING CALCULATOR GUIDEBOOK. Using Derivative,
demonstrate graphically that the numerical integral of 1/t from 1 to X equals
the function ln(X), where X > 0
                                                         Plot1 Plot2 Plot3
1.   Change the ZOOM to "ZDecimal". Press [Y=].         \Y1=1/X
     Store 1/X to Y1 and ln(X) to Y2. Set the graph     -Y2=ln(X)
     style for Y1 to \ (line) and Y2 to -O (path).      \Y3=

2.   Run PROGDERI, or run Aurora and click DERI. Select "lower..." and then
     "X>0". Select either "oY1 INTEGRAL" and enter 1 and press [ENTER] when
     asked "0 or lower[,UPPER] LIMIT?", or select "oY2 DERIVATIVE" and then
     "F'(X)=ln(X)" when asked to choose again.

3.   After 10 seconds you get the result. Then compare the graphs. Press
     [ENTER] when "Pause >" is displayed to continue.


4- Support
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If you like Derivative you should send me a postcard! Please e-mail me if you
find any problems, or have any suggestions, corrections, etc. Please feel
free to edit Derivative, just e-mail me your revised copy (so that I can
incorporate the updates into the next version).

Internet e-mail:
     fairpo@breathemail.net

Mail address:
     Mark Fairpo, 90 Lee Street, Hull, (ENGLAND) HU8 8NN

You can always find the latest version of Derivative at:
     <http://www.ticalc.org>


5- Frequently Asked Questions
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Q1.  Why is Derivative delaying at my home screen, and can I speed it up?

A.   Relax. The home screen appears after any menu selection. A moving busy
     indicator is still displayed in the top-right corner of the screen.
     To quicken the drawing of graphs press [WINDOW] and set Xres=2.
     NOTE: Derivative exploits available and demanding Maths operations.

Q2.  What do those error messages in Derivative mean?

A.   When an error is detected, ERR:message and an error menu is displayed,
     avoid selecting "Goto". This table contains each likely error type:

   Error Types       Possible Cause and Suggested Remedies
   ----------------  -------------------------------------
   ERR:UNDEFINED Yn  The chosen function Y1 or Y2 is empty, Quit and enter
   ERR:ARGUMENT      The close parentheses ")" were omitted, Quit and include
   ERR:DATA TYPE     Not caused under typical usage, Quit and press [Graph]
   ERR:NONREAL ANS   A point cannot be calculated, increase Xmin or the LIMIT
   ERR:TOL NOT MET   As above
   ERR:INVALID DIM   The regression model cannot be fitted, make a selection
   ERR:DOMAIN        As above

Q3.  What does "CALCULATE" do?

A.   Based upon Macrosoft's acclaimed Aurora Calc, it is a Mini Calculator or
     cut-down TI-OS shell. Type "XX" or "EXIT" to return to Derivative.
     Press [2nd][ANS] to recall the last function or answer.

Q4.  How can I be more confident about my maths?

A.   Beginning with either [ZOOM] ZStandard or ZTrig. Try to get the "whole
     elephant" into your viewing window, rather than Zoom In on its trunk.

Q5.  How can I prevent funny decimals in the Xlist L1, the independent data?

A.   This can be fixed by constructing a "Friendly" window, where each pixel
     works out to a nice even value. The [ZOOM] ZInteger and ZDecimal
     commands make windows with pixel values of 1 and 0.1, respectively.

Q6.  Is Derivative fully compatible with my TI-83 Plus or TI-82?

A.   Yes. The TI-83 Plus was designed to work side-by-side. NOTE: If Language
     Localization is installed some text may display bilingually.
     Due to testing, Derivative will not be modified for the TI-82.

Q7.  What resources or variables do Derivative use?

A.   Derivative accepts either Function Y1 or Y2, and uses Variables X,Y & Z,
     Lists L1-L2, Stat plot Plot1, and clears Strings Str7-Str9.
     NOTE: Periodically selecting "ClrList L1,L2" frees upto 680 bytes.

Q8.  What contents are included in the Derivative package?

A.   Make sure you have the following files: deri.83g (Derivative 1.0),
     deri.txt (this document), derimenu.gif (animated screenshot), readme.bat
     (batch file for MS-DOS users), and 80XTHING.PDF (see below).

Q9.  Where can I learn more?

A.   How Do You Graph Derivatives and Antiderivatives? by John F. Mahoney
     is included as 80XTHING.PDF with acknowledgement to Eightysomething!,
     Fall 1997, our TI Newsletter where John is an editor, and must be read
     with Adobe Acrobat reader software. For a commentary on Gauss-Kronrod
     integration see <http://www.ti.com/calc/docs/faq/83faq057.htm>

Q10. Are there any similar programs readily available?

A.   POLFRAC.83G is a group file containing several programs written by
     Philippe Fortin and is released to the public on the TI program archive
     and the TI-GRAPH LINK disk. Its menus cover all the basic needs for
     SYMBOLIC ALGEBRA AND CALCULUS.

Q11. Are there any bugs in the TI-83 (using ROM version 1.07)?

A.   When using TI-GRAPH LINK for Windows to communicate during a Menu or
     Pause within a program, the calculator imitates an [ENTER] keystroke.
     Tracing when a program is awaiting a user value terminates the program.
     Another can be replicated by ensuring that at least Y2 is empty. Put any
     function in Y1 then run PROGDERI and choose any Y1 option before
     Quitting. Repeat with Y2. However, when repeatedly choosing a Y2 option
     an ordinarily valid "Equ>String(Y2,Str9)" instruction wrongly causes
     errors, normally "ERR:DATA TYPE" corrupting the Y-Vars memory.
     NOTE: THIS IS A STRICT SEQUENCE RARELY OCCURRING UNDER TYPICAL USE!

Q12. My calculator just froze or locked up, how do I reset?

A.   Take out one AAA battery, hold down the [ON] key for at least 10 seconds
     before replacing the battery. Remember to adjust the contrast [2nd][Up].

Q13. How do I learn my ROM (Read Only Memory or built-in software) version?

A.   Press [Mode][Alpha][S] and then any key except [ENTER], which runs the
     self-test and will RESET your calculator's memory.


6- Legal Stuff
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Great care has been taken to ensure Derivative operates as it should.
Derivative is provided "as is", by using Derivative, you agree to use it at
your own risk. All trademarks are acknowledged.

Derivative is (c) Copyright Mark Fairpo, 1999.


"The best gift in the world was wrapped in a manger."
     May God be with you in the (apparent) turn of the Millennia.


PLEASE DO NOT SEPARATE THIS DOCUMENT FROM DERIVATIVE!
