Contravariant, Covariant, and Mixed Tensors Differential Geometry Reading Stream Episode 13

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The reading from Differential Geometry by Erwin Kreyszig continues this time from chapter III, § 30.
The tensor calculus is starting to pick up so the products of multiple partial derivatives, covariant subscripts, and contravariant superscripts are quite challenging to read out loud and there are some real tongue-twisters in here, but that's part of what makes this fun.
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TIMESTAMPS
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0:15 This is episode 13 not episode 12 lol
0:35 Starting to read § 30. Contravariant, covariant, and mixed tensors.
5:24 Definition 30.1 Contravariant tensor of second order
9:38 Definition 30.2 Covariant tensor of second order
13:02 Definition 30.3 Mixed tensor of second order
16:33 Definition 30.4 Mixed tensor of order r+s, covariant of order r and contravariant of order s
17:52 Definition 30.4 casually flexing its chad BDE dominance over (soy) definitions 29.1, 29.2, and 30.1-30.3. [Mixed tensors of order r+s are absolute fkn units.]
19:32 The fundamental tensor is an example of a symmetric tensor
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[@idiosinkrazijske.rutine]

Valuable work, thank you!

[@AnthonyMakesVideos]

Of course! I do what I can 🙏

[@DOTvCROSS]

I have meet many students that could only point to the Latin symbol and have no idea how to pronounce it. That was me in my early math education, too proud to ask: Where was AMV's a decade ago? I would have watched and commented sooner, but I was responding to a 'beam' by scotty. We watched episode 16 today, I set the record straight. Einstein while working in the patent office kept getting knocked over by a light clock, that is how he came up with the whole thing.

[@AnthonyMakesVideos]

Thanks for taking care of that "beam" by scotty and setting the record straight. (P.S. This comment was featured in Ep. 16)