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Where Green's theorem is a two-dimensional theorem that relates a line integral to the region it surrounds, Stokes theorem is a three-dimensional version relating a line integral to the surface it surrounds. For that reason, Green's theorem is actually a special case of Stokes Theorem.
Again, Stokes theorem is a relationship between a line integral and a surface integral. Before you use Stokes theorem, you need to make sure that you're dealing with a surface S that's an oriented smooth surface, and you need to make sure that the curve C that bounds S is a simple, closed smooth boundary curve with positive orientation.
Since Stokes theorem can be evaluated both ways, we'll look at two examples. In one example, we'll be given information about the line integral and we'll need to evaluate the surface integral. In the other example, we'll be given information about the surface integral and we'll need to evaluate the line integral.
0:00 // About Stokes theorem
2:41 // Example 1
10:46 // Example 2
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: green' theorem, stokes theorem, stokes theorem,stokes theorem, stokes theorem,positive orientation,vector calculus,boundary curve,calculus,surface integral,Krista King, apply stokes theorem,educational,line integral
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