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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
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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
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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
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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
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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
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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
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`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:
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`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:
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the circulation about any two open surfaces with the same boundary curve is the same.
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the circulation about any two open surfaces with the same boundary curve is the same.
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</p>
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</p>
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<p>
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<p>
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12
site/posts/multivariable-thomas-16.8.html
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site/posts/multivariable-thomas-16.8.html
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[!]
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[=post-]
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<p>
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Hello, everybody! This is the very last section in the Thomas textbook, and boy is it a doozy. We're finally applying divergence!
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</p>
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[/]
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[=title "Multivariable Exam 3 Review: Thomas 16.8"]
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[=author "Tyler Clarke"]
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[=date "2025-4-16"]
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[=subject "Calculus"]
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[=unpub]
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[#post.html]
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