Question

proof that Δz=mΔx+nΔy...?

Answer 1

Not sure what you mean there.

In general it's not true is it? Close to a particular point it's approximately equal.

Your equation is in fact the equation of a plane.

\[z-z _{0}=m(x-x _{0})+n(y-y _{0})\]

where \[x _{0},y _{0},z _{0}\] m and n will be specific values in a given case.

Answer 2

are you asking for the proof of greens theorem?

Answer 3

sure, why not.

Answer 4

haha no way greens theorem on OCW but heres a good proof
http://www.math.psu.edu/roe/230H/slides_14nov.pdf

this is how i was taught it