- #1
bobby2k
- 127
- 2
Hello
I have heard that Greens, Stokes and the Divergence theorem is the equivalent of the fundamental theorem in multiple dimensions. But is there some way to show the result under:
if
F(x,y) = [itex]\int_{-\infty}^x\int_{-\infty}^yf(x^{*},y^{*})dx^{*}dy^{*}[/itex]
this implies that
f(x,y)=[itex]\frac{\partial^{2} F(x,y)}{\partial x\partial y}[/itex]
Can tis be showed with Greens or Stokes, or derived on its own?
I have heard that Greens, Stokes and the Divergence theorem is the equivalent of the fundamental theorem in multiple dimensions. But is there some way to show the result under:
if
F(x,y) = [itex]\int_{-\infty}^x\int_{-\infty}^yf(x^{*},y^{*})dx^{*}dy^{*}[/itex]
this implies that
f(x,y)=[itex]\frac{\partial^{2} F(x,y)}{\partial x\partial y}[/itex]
Can tis be showed with Greens or Stokes, or derived on its own?