0
$\begingroup$

While studying 'curl' I came accross these terms:

enter image description here

Here, I don't understand the meaning of $\frac{dFz}{dy}$. Fz is a function of 'z', so what is the meaning of rate of change of Fz with respect to 'y'?

I understand differentiation as the rate of change of value of a function with respect to a change in the value of its domain. But 'y' here, is not the domain of 'Fz'. If it is, then what is the meaning of all this?

$\endgroup$
1
$\begingroup$

$F_z$ is not (necessarily) a function of $z$. Notationally if $F$ was a function of z we would write $F(z)$, not $F_z$.

What is meant is that $F$ is a "vector field". That is, $\vec{F}(x,y,z)$ is a function which assigns a vector to every position in 3-space. So $F_x$, $F_y$ and $F_z$ refer to the x, y and z-coordinates of $\vec{F}$ at any location.

Any coordinate of $F$ could be a function of any position coordinate (or of all three).

$\endgroup$

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.