1
$\begingroup$

We can use forward, backward or central difference formula to calculate the partial derivatives of a 1D (x) or 2D (x,y) function. What will be the formula using any of the methods to calculate the derivative of a 3D (x,y,z) function?

Like for 2D (x,y) function, the forward difference formula is -

enter image description here

$\endgroup$
  • $\begingroup$ Where's the "centering" in the above definition? $\endgroup$ – Riccardo Ceccon Mar 21 '18 at 17:21
  • $\begingroup$ My bad. It is forward difference formula. I corrected it. @RiccardoCeccon $\endgroup$ – user3503711 Mar 21 '18 at 17:37
1
$\begingroup$

I suppose that by 2D central differentiation formula you mean:

$f_x(x,y)=$lim$_{h\to 0}\frac{f(x+h/2,y)-f(x-h/2,y)}{h}.$

Now, for 3D functions there are no differences:

$f_x(x,y,z)=$lim$_{h\to 0}\frac{f(x+h/2,y,z)-f(x-h/2,y,z)}{h},$ and likewise for $f_y$ and $f_z.$

If you have other questions ask me, I don't know if this was your doubt precisely, maybe you were asking a different thing.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.