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Stokes' theorem relates the line integral around a surface to the curl on the surface. This tutorial explores the intuition behind Stokes' theorem, how it is an extension of Green's theorem to surfaces (as opposed to just regions) and gives some examples using it. We prove Stokes' theorem in another tutorial. Good to come to this tutorial having experienced the tutorial on "flux in 3D".
Conceptual understanding of why the curl of a vector field along a surface would relate to the line integral around the surface's boundary
Seeing that Green's Theorem is just a special case of Stokes' Theorem
Determining the proper orientation of the boundary given the orientation of the surface
Determining the proper orientation of a boundary given the orientation of the normal vector
Understanding when you can use Stokes. Piecewise-smooth lines and surfaces
Starting to apply Stokes theorem to solve a line integral
Converting the surface integral to a double integral
Finding the curl of the vector field and then evaluating the double integral in the parameter domain
Showing that we didn't need to use Stokes' Theorem to evaluate this line integral
Finishing up the line integral with a little trigonometric integration