Uploaded March 2019 | Updated September 2026, 3 weeks ago

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In this video, I define contravariant and covariant vector components. Here, we define contravariant and covariant vector components according to their transformation definitions. I also define invariants, which are quantities with intrinsic significance.

I describe two examples of contravariant and covariant tensors. For contravariant tensors, I use the tangent vector of a parametric curve. For a covariant tensor, I use the example of a gradient vector of a scalar field.

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Pre-reqs: The previous videos in the playlist - youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: drive.google.com/open?id=1E2I-LpQcKV-ERMUXqYMOtIH2dZs5EM5E
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