I am reading about differencial exact form, and i dont understand

[alejandrito29]

i am reading about differencial exact form, and i don't understand why

$$d \theta$$ is not a exact...

i think that is because $$d \theta$$ is not a total derivative of some function, since

$$d \theta = \frac{1}{x^2+x^2} (-y dx+xdy)$$ is not definned globally in x,y = 0,0...

¿is correct?

 

[Bacle]

I think the region where it is not exact is R^2-{(0,0)},

and one reason is that any candidate for a form θ with

dθ= (xdy- ydx)/ (x²+y²) would agree

with the arctan function, i.e., the angle function in polar coordinates

( set r²=x²+y² , and work with polar coordinates)

and there is no global angle function defined on R²-{0,0}