Mathcad: how to obtain discrete differentials?

[anthonyQueen]

I am still using Mathcad 11, and only sometimes Mathcad 15 (hate Framenet in XP).

I do not konw how to obtain discrete differentials. The following example may explain my problem:

1. Let's start with an equation like this: y(x)=x^2 with x as a range variable: x:=0,1,..3.
2. One obtains y(x)=0, 1, 4, 9 (as a range column)
3. the derivative of y(x) (i.e. 2x) gives: DER1:= d y(x)/x = 0, 2, 4, 6, (as column range)
4. but the change of x is discrete: so the complete differential is: 2x+Delta_x.
5. Given that my Delta_x from the x range is 1, one is tempted to write DER2:=DER1+1 giving: DER2a=1, 3, 5, 7
6. Yet this is not fully correct since Delta_x is a variation, and any variation is between two values (the previous and the next). Hence it should probably be DER2b= 0, 1, 3,5,7. But I do not know how to obtain simply DER2b, with a formula like (5).

In any case, how do I obtain, starting with the initial value y(x)=0, all the range values of y(x) shown in step (2) [i.e. 0,1,4,9] using DER2a or b?

Thank you for any suggestion,

AQ

[Werner_E · Accepted solution]

Not sure but do you need some kind of discrete derivation?

Look if the attached file would help. Its saved in MC11 format.

[anthonyQueen]

@Werner Exinger

Thank you very much for you effort. I downloaded the file and started to have a look. My expertise is limited, but I have learned so far that the range variables have some limitations. I shall come back after having studied your example.

Thanks meanwhile,

AQ

[Werner_E]

You are welcome!

Its important in Mathcad to distinguish between range variables and vectors.

Find attached some excellent reading stuff by Stuart Bruff!!

[ValeryOchkov]

Anthony, do you know the Euler method of ODE solution? I see it in your question.

See please one Mathcad websheet http://twtmas.mpei.ac.ru/mas/worksheets/Euler.mcd

[anthonyQueen]

@Werner Exinger @Valery Ochkov

what a wonderful feedbacks. Thank you very much! I wanted acknowledge your help even before downloading your - no doubt - instructive examples.

Form Werner first MC11 file I already learned the use of the "stack" command, which solves somewhat the addition of "0" in step 6. I'm still learning the rest. Definitely vector variables seem more flexible for manipulation than range variables. I shall come back with some more mathcad knowledge later, thanks to your files.