Homework Statement
I am trying to calculate the flux for the octant of a sphere, and I am trying to figure out how the mathematics, dot products, and dA works in the integral. I already did the quadrant for \hat{θ} where θ= π/2 (the bottom quadrant) and I did the left quadrant where \hat{n}...
Oh yes. You were right. I tried the derivation backwards and it only took about half a page. However I probably would never have thought about it, but there is a trick. The trick is to place (sin2θ + cos2θ) multiplying the cosø and the sinø in the equation. Once that's done you distribute...
I have not, however, it seems like such a process would be much too long. If someone asked you to solve this for a test, how would one solve this without taking so long to do this? To be fair, if each unit vector derivation (d\hat{r}/dt and d\hat{θ}/dt) was incredibly short, why would this one...
Homework Statement
I just want to know how to get from this: ∂ø^/∂ø = -x^cosø - y^sinø
to this: = -(r^sinθ+θ^cosθ)
Homework Equations
All the equations found here in the Spherical Coordinates section: http://en.wikipedia.org/wiki/Unit_vector
The Attempt at a Solution
I've...
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