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2025-04-16 09:29:11 -04:00
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Hello again! We're on the penultimate section in the chapter and in the entire book. In this section, we're covering <i>Stokes' Theorem</i>. Stokes' theorem Hello again! We're on the penultimate section in the chapter and in the entire book. In this section, we're covering <i>Stokes' Theorem</i>. Stokes' theorem
is an application of Green's theorem in 3 dimensions. This is much harder to visualize, but essentially, with Stokes' theorem, we can find the circulation of is an application of Green's theorem in 3 dimensions. This is much harder to visualize, but essentially, with Stokes' theorem, we can find the circulation of
a vector field on a curved surface. The critical idea is that, for a smooth open surface `S` with a smooth boundary curve `C`, the circulation about a vector field on a curved surface. The critical idea is that, for a smooth open surface `S` with a smooth boundary curve `C`, the circulation about
`C` is the surface integral of the curl over `S`: `int_C F cdot dr = INT INT_k (grad times F) cdot k dA`. This has an interesting consequence: `C` is the surface integral of the curl over `S`: `int_C F cdot dr = int int_k (grad times F) cdot k dA`. This has an interesting consequence:
the circulation about any two open surfaces with the same boundary curve is the same. the circulation about any two open surfaces with the same boundary curve is the same.
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[!]
[=post-]
<p>
Hello, everybody! This is the very last section in the Thomas textbook, and boy is it a doozy. We're finally applying divergence!
</p>
[/]
[=title "Multivariable Exam 3 Review: Thomas 16.8"]
[=author "Tyler Clarke"]
[=date "2025-4-16"]
[=subject "Calculus"]
[=unpub]
[#post.html]