Question

Is there any connection between Green's theorem and Exact Differential Equation?

Answer 1

\[
P dx + Q dy =
\]
is exact if and only if
\[
\frac {\partial Q}{dx} -\frac {\partial P}{dx}=0
\]

Answer 2

The line integral over a closed regular curve C that encloses a region R
\[
\int_C Pdx + Q dy = \int \int_R \left(\frac {\partial Q}{dx} -\frac {\partial P}{dx} \right)\, dx\, dy
\]
That is Green Theroem.

Answer 3

The connection is. If P dx + Q dy =0 is exact, then
\[
\int_C Pdx + Q dy =0
\]

Answer 4

Oh .. thank you!!

Answer 5

yw