					TABLES 
	
				     Version 1.02

				   By Wout Klingens

Disclaimer & copyright
This program is Copyright (C) 1993, 1994 by Wouter C. M. Klingens, All Rights 
Reserved.

It is provided as shareware with the following limitations:

Shareware means in short: try it before you buy it. That means that if you are
satisfied with the program, you must register it. See for more information
about this subject the chapter 'Registration information'. Shareware means
also, that you may distribute this unregistered version of TABLES freely,
in fact, you are encouraged to do so with the limitation, that you also 
supply this document 'README.TXT' with it.
There is no warranty or claim of fitness or reliability. The program is 
distributed AS IS, and as such the author shall not be held liable for any loss 
of data, down time, loss of revenue or any other direct or indirect damage or 
claims caused by this program.

  

TABLES, an easy to use program for finding function values, derivatives and
roots of all(!) standard functions: polynomials, trigonometric function, 
cyclometric and exponential functions, etc. Look for the standard function list
in this document.

Written by me:

W. C. M. Klingens
Rudyard Kiplingerf 205
3315 AJ Dordrecht
The Netherlands.

Internet e-mail address: wkling@knoware.nl


The intro.
=======
Especially in The Netherlands, there is a movement going, which says that 
function analysis is best learned (among other things of course) by studying 
tables.
Now, if you are a pupil and you have to type about a 1000 values per year into 
your calculator whilst knowing, that you have to learn 50 new words by heart in
a foreign language before tomorrow, then you know, you need my program.
If you are a teacher however, you need my program because of the exact same 
reason: time.
As a special bonus, you, and of course your pupil, get the derivative of your 
function with it, with the matching tables.
Now, I know, that there are numerous programs, that do something like that. But 
not at my price. And why do you need an application, which can do it all, while 
you need only a part of it? My guess is, that when you get what you need with a 
few keystrokes, why bother with all the other?
The concept was to prevent timeconsuming actions, remember? So, my selling 
slogan is: easier to use is better and faster for the pupil and easier to teach 
for the teacher.

The particulars.
==========

System requirements.
==============
Any Dos machine will do. I recomment however a 80286 machine or better because 
of the speed.

The input box (F3).
=============

The function field.
-------------------
For the input of functions I chose for the syntax similar to BASIC. Partly 
because I think highly of the knowledge of young computerusers, partly because 
computertechnology will play a very important role in math and the pupil will 
have to get accustomed to "a language" like BASIC. This is the only(!) 
concession I do as far as the easy-to-use concept is concerned. 
For the moment the syntax of for instance the arctangent function will be 
'arctan' and not  'atan'. I found this clearer for the pupil. Maybe in future 
versions I will change that if you think otherwise. Please drop a message!
The function parser will accept a parameter function like f(x) = p*x^2. 
If you would like to input a parameterfunction then TABLES will assume, that t
he parameter will be 1. Use only the letter "p" as a parameter.

The limits fields.
----------------
The concept of domain is not implemented in TABLES.  So after you finished 
inputting your function you will be asked to input the left and right limit.
This means here, that TABLES will try to find roots in between those limits and 
nothing more. Trying to find roots means, that I chose for a numerical approach. 
That means, that the roots TABLES will find, will only be a close match to the 
real roots. Maybe in a future version I will implement an exact root in all 
cases, but in modern math (at least in The Netherlands) we find an approach 
more useful than a number like sqrt(2). You and I know that sqrt(2) rounds to 
2.41 so we can make a fairly accurate(?) estimate, but the pupil cannot. 
The left and right limit will also determine the resolution of the 
searchpattern of the roots: abs(right_limit - left_limit) / 1000. So TABLES 
makes an initial guess about the root, and the precision of that guess will 
depend on the difference between the right and left limit.
For instance a very well known function is: f(x) = x*sin(1/x). This one 
oscillates infinitely often between x and -x. So TABLES will find more roots if 
you set your limits between -1 and 1 than between -10 and 10.
If you input a left limit greater than or equal to the right limit, TABLES will 
assume the left limit to be -10 and the right limit to be 10, the increment 
will then be set to 1. This provides faster input of the limits.

The increment field.
--------------------
The increment field only determines the increment of the table. The table will 
calculate to a maximum of 10000 values from the left limit up. Beyond that, any 
calculus will be useless for the pupil.

                        
The window.
=========

The function window.
--------------------
This window shows the values of x, f(x) and f'(x). These values are rounded to 
4 decimals. The value of f'(x) is the exact value rounded to 4 decimals.

The limits window.
------------------
This window shows the left and right limits you inputted in the limits fields.
In between these values TABLES will try to locate the root(s).

The roots window.
-------------------
In this window TABLES solves the equation f(x) = 0. Because of the numerical 
solving algorithm I cannot guarantee the accurateness of these roots. Nor can I
guarantee TABLES will find all roots. For instance the function f(x) = sin(pi) 
has 'many' roots. Try to input this function and see what happens.
Of course TABLES will not find all roots of the function f(x) = x*sin(1/x).

The Derivative Window.
----------------------
The algorithm that determines the derivative will not simplify the derivative 
in a very dramatic way. First of all, I think the pupil will get 
"the hang of it" faster, if he or she discovers the way a derivative is found 
if he sees my derivative and recognises the theory from the book you use. 
Secondly I wanted to finish my application. A simplifying option (and only 
an option!) will maybe (depending on the reactions, so your opinion, please 
drop a message!) be added in future versions.

Implemented operators.
----------------------
+ : adding.
- : substraction.
* : multiplication.
/ : division.
^ : power.

Implemented constants.
----------------------
e, pi.
Scientific notations like 3.0E-2 are allowed. Watch the uppercase of the E!!

Implemented functions, syntax and meaning.
------------------------------------------
ln 		: natural logarithm
tan		: tangent
cos		: cosine
sec		: secant
abs		: absolute value
sin 		: sine
sqrt		: square root
sech		: hyperbolic secant
tanh		: hyperbolic tangent
cosh		: hyperbolic cosine
sinh		: hyperbolic sine
cosec		: cosecant
cotan		: cotangent
cotanh     	: hyperbolic cotangent
cosech		: hyperbolic cosech
arcsec 		: inverse secant
arccos        	: inverse cosine
arcsin         	: inverse sine
arctan         	: inverse tangent
arcsech  	: inverse hyperbolic secant
arctanh     	: inverse hyperbolic tangent
arccosh       	: inverse hyperbolic cosine
arcsinh       	: inverse hyperbolic sine
arccotan	: inverse cotangent
arccosec    	: inverse cosecant
arccotanh    	: inverse hyperbolic cotangent
arccosech   	: inverse hyperbolic cosecant

Examples of functions:
f(x) = x
f(x) = sin(x)
f(x) = sin(arctanh(x))
f(x) = x^2+7*x+12
f(x) = 1/x
f(x) = sin(x)^2
f(x) = e^x
f(x) = e^(x+1.0E-3) Again: Watch the upper and lowercase of the e!!
f(x) = pi*arccosh(x)

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Registration information.

TABLES is distributed as shareware. This means that you may use TABLES for 
21 days to evaluate its usefulness. If at the end of that time you are 
satisfied with TABLES as a product, you must register it. The basic 
registration fee for a single user version of TABLES is US$15.  See a later 
section for details on multi-user site licenses.

Cheques or Postal Orders should be made out to

W. C. M. Klingens

and sent to

W. C. M. Klingens
Rudyard Kiplingerf 205
3315 AJ Dordrecht
The Netherlands

Please fill out the following order form and send it along with your cheque 
or Postal Order to the above address.

Please note that International mail can be rather slow, and it may take up to 
2 months to receive your registration.

For Dutch users it will be a little easier:
Maak op gironummer 2769871 t.n.v. mij het vereiste bedrag over onder vermelding 
van "TABLES" en het aantal exemplaren, en u krijgt binnen 14 dagen uw 
geregistreerde versie thuis. Wilt u in ieder geval wel het registratieformulier
opsturen?

By the way. If you have any suggestions or questions regarding TABLES, please 
feel free to contact me. I will answer your mail as soon as I can.



   Tables version 1.02                                Registration Form
   -----------------------------------------------------------------
     Make checks payable to:
       W.C.M. Klingens
       Rudyard Kiplingerf 205
       3315 AJ Dordrecht
       The Netherlands
   -----------------------------------------------------------------
   
   TABLES version 1.02
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     ---------------------------------------------

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