NEWTONSM v1.5
TI-89
"Newton's Method"
by Dmitriy Myedvyedyev (aka Dima Medvedev)
medvedbr@hotmail.com
Category: MATH/CALCULUS
Starting - Completion Date: 11-24-2001 - 11-29-2001, five-six days (for this version only)
Special thanks to my Calculus teacher, Fred B.



-------------Description:
This is a Calculus program that does the Newton's method approximation for you. It comes with all the possible options I could think of. See instructions for more information.



-------------Instructions:
When you run the program, a dialog box is displayed. First it asks you to enter "f(x)=" -- enter the function you want to use Newton's method for. Then it asks you for your intial guess (note that guess cannot equal zero) -- that would be your first guess. Then you need to choose a calculation type. The two available types are "Accuracy" and "Iterations." If you chose accuracy, the approximation stops when a value of f(x) is within your specified range. In iterations, the program will do a specified number of calculations, no matter how close you come to f(x)=0. Only if you actually hit the root of the function you entered (if f(x) will actually equal 0) then all calculations stop, because there is no need to keep doing them since you have already hit the zero of the function. Then you need to enter "Accuracy/Iterations." If you chose accuracy, then this field specifies how close to 0 the values of f(x) should come in order to stop calculations. If you chose iterations, this will indicate how many times you want to do calculations. Make sure that if you use iterations, you need to enter a WHOLE number. Otherwise, it will take the least non-negative integer possible. So if you enter 2.999, it will do 2 calculations. If you enter a negative number, there will be 0 iterations.
Then you need to choose open or closed interval for accuracy. This is applicable only if you chose accuracy as your calculation type. This field specifies how close you want to come to f(x). So if you enter 0.001, the calculations will stop when -0.001<f(x)<0.001
(Note that if you choose closed interval in the next field, calculations stop when f(x) is great than or equal to -.001 and less than or equal to 0.001)
Then you are asked to choose an interval. This is also used for accuracy only. If you choose open interval, calculations stop when f(x) is within the specified range excluding the endpoints. If you choose closed interval, the endpoints will be included. In my Calculus class, we stop when f(x) has three zeros after the decimal. So I use Accuracy=0.001 and Open interval. That way the points -0.001 and 0.001 are not included. 
Then you are asked to choose display format. The two possible formats are "x, f(x)" and "x, f(x), f'(x)"
If you choose the first format, the output will be values of x and then values of f(x) (from left to right). You can also choose to display the derivative of the function, by choosing the second format, but then there will be less digits displayed in order to have room for all three values on the calculator screen. 



-------------Update(s):
None. This is the first version of the program.



-------------Known Bugs and Important Notes:
	If you choose huge numbers (like 999999999999) as your initial guess, than the output will be messed up, since you won't be able to see some "Ex" (where x is some integer) which mean "*10^x"
But, obviously, your first guess needs to be a number somewhat close to the actual zero of the function. If you have something like f(x)=x^2-1, then, of course, 99999999999 is not very close to the actual zero :-). 
And there will be a whole bunch of calculations. The program still works, but I don't think anyone would be happy writing down 50 values of x and 50 values of f(x) (and maybe f'(x)) 
	Calculations always stop if you hit the bull's eye. If f(x) becomes exactly 0 (which means that you found the actual zero), then you are done and the program stops. 
	Make sure your initial guess is not 0, since you can't divide by 0. But if you do, you will see an error message.
	To make it easier for you to write down all values that you need, when you have many calculations done, there will be a pause at the end of each page. Then you need to press enter, the screen will be cleared and a new page of values will be displayed. 
	Several variables are created when you run the program. Make sure there are no conflicts between several programs. You might wanna create a separate folder. I chose not to deal with local variables, because your program setting are often the same, and actual variables, you don't have to change them every time you run the program. All previous settings are automatically stored into variables.
	When you run the program, it changed your "Display Digits" mode settings so that values can be displayed nicely on the output screen (depending on whether you chose x and f(x) or x, f(x), and f'(x), there will be a different mode setting). The program saves your mode setting before you ran the program, and at the end of the program, your original settings are restored, so you don't have to go and manually change them. Please make sure you don't exit a program by pressin enter or on, because that often causes a break, and then the program execution is not finished, therefore your settings may not have been restored. If you get a break error, always make sure your mode display digits setting is the one you want. If you started the program and the dialog box is displayed, you may press ESC to safely exit the program, and you won't get any break errors.
	If your initial guess turns out to be within your specified accuracy range, then you get an error, asking you to pick a different guess.
	I think I have a lot of important stuff covered in this program, making it relatively user-friendly. It also reports some common errors that you might encounter. 
	If you find any bugs, please send me an e-mail.



-------------Thanks!
Thank you for downloading this program by Dmitriy Myedvyedyev. Please send your comments and/or suggestions to medvedbr@hotmail.com



-------------People to Remember:
Isaac Newton, Blaise Pascal, Euclid, Dmitriy Mendeleyev, Thomas Edison, Archimedes, Stephen Hawking, Albert Einstein, SB, SH, BM, AM, JC, FB, CC...  
             to be continued...

The universe... What a great puzzle! Number one on the unsolved mysteries list. 

-------------Dimalitious D-Myster-------------
Keep our world green! Protect trees to get us some mo' oxygen. Please recycle
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