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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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