/sci/ - Science & Math

>>5806190

what do you want to do? i'm not a mathematician, but I always know what to use because it's fucking logical, but in an abstract way I can't really help you.

>>5806215

I just want to know when to use a certain formula or method of resolution.

For example: evaluate <span class="math">\int \int_{S}^{ } \vec{F} \cdot d{\vec{S}}[/spoiler]. Then he gives what F is in terms of i,j,k and what the surface S is.

When do I know which theorem to use, if any? I'm totally lost.

>>5806220
Well the first thing you have to do is parametrize the surface, then express the vector field in terms of your parameters. After that it's just straight-forward calculation.

If you know that the vector field is always normal to the surface, you can use the divergence theorem to turn it into a volume integral. This could greatly simplify the problem.

In case the integrand is a vector field:

- Parametrize the surface or curve.
- Express the vector field in terms of the parameters (F(r(t)))
- Use a theorem (?). If so, which?

In case the integrand is a scalar function:

- ?

>>5806190
It's all Stokes' thrm.

Just remember that the Integral of a differentiable form ω over a boundary (surface) is equal to the derivative (curl, divergence, gradient) of that vector field over the manifold (area, volume)

I thought I was going to fail calc III until my prof on the last day presented Stokes' Thrm and tied all that bullshit together

>>5807044

Calc III does become a clusterfuck towards the end.

excerpt from the text:
>the cumulative (integrated) effect of the DERIVATIVES of a function throughout a region is determined by the values of the function on the boundary of that region

hope that helps

>>5807044
did you have Dr. Daileda at Trinity?