Tensor Calculus: the Derivative of a Tensor @FacultyofKhan

Uploaded September 2024 | Updated September 2026, 2 weeks ago

...is not a tensor, but sometimes it is.

Continuing on with #TensorCalculus, this video's going to find the derivative of a tensor with respect to a coordinate and derive its transformation law. I show that under affine coordinate transformations, such derivatives transform like tensors, but otherwise, they do not define tensors.

Questions/requests? Let me know in the comments!

Pre-reqs: The previous videos in the playlist - youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: drive.google.com/file/d/1UWeZWtXDn4fBdpis6TVUNCvHt7HjSHLm/view?usp=drive_link

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Tensor Calculus: the Derivative of a Tensor

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$Introducing Weird Differential Equations: Delay, Fractional, Integro, Stochastic! A brief standalone video that introduces weird types of differential equations, where weird means differential equations that arent conventionally taught unless you get to super specialized areas. Here, they include delay differential equations, integro-differential equations, stochastic differential equations, and fractional differential equations. Questions/requests? Let me know in the comments! Pre-requisites: know what a differential equation is (so basically 1st year undergrad calculus should be more than enough). Lecture Notes: https://drive.google.com/file/d/1zufFLUeUVR6NZqb0MHCQWlnN_6SpOqIb/view?usp=sharing Patreon: https://www.patreon.com/user?u=4354534 Twitter: https://twitter.com/FacultyOfKhan Special thanks to my Patrons for supporting me at the $5 level or higher: Aaron Kaw Cesar Garza Daigo Saito Alvin Barnabas Patapom Damjan Yenyo Pal Lisa Bouchard Gabriel Sommer Eugene Bulkin Rene Gastelumendi Nicholas Chowdhury Borgeth Jose Antonio Sanchez-Migallon$

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