From ac3c984f18de256bc9344502459d77ac0b3d858b Mon Sep 17 00:00:00 2001 From: Tyler Clarke Date: Wed, 16 Apr 2025 09:29:11 -0400 Subject: [PATCH] start on 16.8 --- site/posts/multivariable-thomas-16.7.html | 2 +- site/posts/multivariable-thomas-16.8.html | 12 ++++++++++++ 2 files changed, 13 insertions(+), 1 deletion(-) create mode 100644 site/posts/multivariable-thomas-16.8.html diff --git a/site/posts/multivariable-thomas-16.7.html b/site/posts/multivariable-thomas-16.7.html index 4b6b101..62a08dc 100644 --- a/site/posts/multivariable-thomas-16.7.html +++ b/site/posts/multivariable-thomas-16.7.html @@ -4,7 +4,7 @@ Hello again! We're on the penultimate section in the chapter and in the entire book. In this section, we're covering Stokes' Theorem. 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 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.

diff --git a/site/posts/multivariable-thomas-16.8.html b/site/posts/multivariable-thomas-16.8.html new file mode 100644 index 0000000..6fa4526 --- /dev/null +++ b/site/posts/multivariable-thomas-16.8.html @@ -0,0 +1,12 @@ +[!] +[=post-] +

+ Hello, everybody! This is the very last section in the Thomas textbook, and boy is it a doozy. We're finally applying divergence! +

+[/] +[=title "Multivariable Exam 3 Review: Thomas 16.8"] +[=author "Tyler Clarke"] +[=date "2025-4-16"] +[=subject "Calculus"] +[=unpub] +[#post.html] \ No newline at end of file