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You've just wandered into the coolest part of the math streaming ecosystem.
I had filmed reading comments and ranting about philosophy, physics, and history before this but it didn't turn out very well lol.
Last week idk if you noticed/if you've been here before but I typically do 1 hr -1 hr 30 min long videos each uploaded all at once but last week I experimented and split what would've been one long video into multiple shorter ~30ish min videos uploaded throughout the week.
This week, I'm front-loading uploading the reading and doing the fun/casual "just chatting" upload later this week.
Watch my video, then watch these two other videos and skim the following wikipedia article and not understanding tensors will become a thing of the past:
• What's a Tensor?
• Tensors Explained Intu...
en.wikipedia.org/wiki/Tensor
Get the Kreyszig Differential Geometry book I've been reading in these videos: amzn.to/3U6OnbH
📩 Questions/Business inquiries: anthonymakesvideos.info@gmail.com
TIMESTAMPS
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0:26 Starting to read § 31. Basic rules of tensor calculus
0:34 Tensor addition
1:20 Tensor component-wise multiplication by a scalar
2:17 Tensor product/outer product
4:25 Contraction of a tensor
7:47 Tensor inner product
8:47 Problem 31.1 Prove is a^{\alpha\beta} is a symmetric tensor and b_{\gamma\kappa} is a skew-symmetric one, a^{\alpha\beta}b_{\alpha\beta} = 0.
9:03 Problem 31.1 Proof.
9:55 Problem 31.2 Successive coordinate transformations applied to components of tensor.
10:42 Problem 31.2 Solution.
12:27 Starting to read § 32. Vectors in a surface. The contravariant metric tensor.
18:38 Theorem 32.1
22:04 Theorem 32.2
28:19 g_{\alpha\gamma} looks like it says gay
29:09 Lowering superscripts/raising subscripts
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