Documentation for some TI-92 programs, collected under math-ext.zip

For bug reports or any other questions concerning these files feel free to mail me:
	Rolf.D.Alber@Studbox.uni-stuttgart.de

Or visit my homepage:
	http://wwwcip.rus.uni-stuttgart.de/~lrt11237/
 

This Zipfile should contain following programs:

	Const.92P	- Sets up some common physical constants 
	VField.92P	- Draws a 2-Dimansional vector-field
	Stream.92P	- Draws a streamline in a vector-field
	EQ.92P		- Simulates the equation-solver of the HP48 (solves what's missing)

All listed files including this documentation may be freely distibuted, except for commercial use.

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UNITS.92P

Program that writes common constants (p.e. Boltzmann constant, Lightspeed..etc.) to cetain vaiables.
Values and dimensions refer to metric system.


Syntax: CONST(x)

Const(9)	Displays a little help screen, for those who use to forget things once in a while
Const(1)	Stores common physical constants (without their Dimensions) to special variables.
Const(2)	Stores common physical constants (with their Dimensions) to special variables.
Const(3)	Displays the 1st half of the variables and their value to the I/O screen
		(Use F5 to switch between Home-screen and constant-table)		
Const(4)	Displays the 2nd half of the variables and their value to the I/O screen
Const(0)	Deletes all constants again

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VField.92P

Program draws a plane vector-field on the Graph-Screen.

Syntax: Vfield()

In the upcoming dialog you have to define:

Vx:	X-component of the Vectorfield
Vy:	Y-component of the Vectorfield
step x:	x-Distance to draw next vector. (Remember: lower value = field has higher density)
step y:	y-Distance of the above
length:	Factor for length of vectors. (default is 1, so each vector will be drawn with the length of 1 screen unit)
arrow:	if set to 1 draws a little mark at the end of the vector to show you th orientation.
	(this takes a little more time than without)

Here's an example for values that draw a nice vectorfield:

Vx:	y^2-x^2	
Vy:	-2*x*y
Step x:	1
Step y:	1
length:	.5
arrow:	1

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Stream.92p:

Program draws a streamline in a vectorfield by iteration.

Syntax: Stream()

In the upcoming dialog you have to define:

Vx:	X-component of the Vectorfield
Vy:	Y-component of the Vectorfield
xStart: x-coordinate for the origin of the stramline
yStart: y-coordinate for the origin of the stramline
steps:	Number of steps you want to draw
length:	length of 1 Step 
Clr:	if set to 1 clears the screen before drawing

After drawing one streamline the calc waits for you to press a key.
So done,the dialog pops up again to let you draw another stramline in thesame graph
(maybe from another starting point)

Please Note:
- for high step-lengths and "long" streamlines the drawn streamline can extremely differ from "reality".
- Be sure to validate a streamline by drawing it a second time with less lenght (higher resolution) over the first.
- a streamline can get "stuck" if it reaches a point where the vectorfield is zero. 

example Values:


Vx:	y^2-x^2	
Vy:	-2*x*y
Xstart:	-2
Ystart:	.5
steps:	100
length:	0.5
Clr:	0

(the second time the dialog pops up set the lenth to 0.2 to see what happens !)
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Eq.92P

Program simulates a nice feature of the HP-48 series which I missed on a TI.
On the HP-equation solver you can automatcly solve for the value that hasn't been defined.
That's extremely useful when you deal with multi-variable equations and want to know what 
happens to the other variables when you change one.

Syntax: Eq(equation,list of used variables)



Usage example:

In Thermodynamics, one often uses the equation for ideal gases: P*V/T=R
(p=pressure, v=colume, T=temperature, R=Gas-constant)

enter: EQ(p*v/t=r,{p,v,t,r})

(be sure that there are no values stored to these variables yet)

an input dialog appears and asks you to define the values in the equation.
enter the following:

	P: 20
	V: 500
	T: 	(let this field free)	
	R: 287

Important is that you leave one variable undefined (T in this example)

After confirmation the Dialog appears again with the missing value fit in correctly: 

	P: 20
	V: 500
	T: 34.84	
	R: 287

You now can change a certain value and let another one be solved.
Let's do an Isotherm compression to double the pressure:
change values to:
 
	P: 40	 (<- double pressure)
	V: 	 (leave undefined - that's the value we want to know)
	T: 34.84 (same, cos it's isotherme)	
	R: 287

The correct answer should be:

	P: 40	
	V: 250
	T: 34.84 	
	R: 287

To return to the home screen just confirm the dialog with no undefined variable.


PLEASE NOTE:
- you have to let one (and only one!) variable undefined, to let the TI know for what to solve.
- you don't have to use exact values for the variables you can offcourse set them variable
  example:
	 	P: 40	
		V: vol
		T:  	
		R: 287
	
  solves to:
	 	P: 40	
		V: vol
		T: 0.139373*vol 	
		R: 287
- please no circular definitions like  T=T. Use T=T1 instead.

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