MTH623 Color Notes Lectures 59-110 by Shabbir Hussain

Tensor Analysis and its Applications PDF 36.3 MBUpdated 23 Oct 2026

Quiz MTH623 Color Notes Lectures 59-110 by Shabbir Hussain PDF 36.3 MB

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One of the (many) reasons why tensor calculus is so useful is that it allows a proper description of physically meaningful derivatives of vectors.
We have not mentioned this before, but taking a derivative of a vector (or of any tensor) is a non- trivial thing.
As usual, in a rectangular orthonormal coordinate system this is usually not an issue. But when the coordinates are curved (like in polar coordinates, for example) then this becomes a big issue. • It is even more of an issue when the manifold is curved (like in general relativity), the techniques we will discuss here will be equally well applicable for curved manifolds. • We want to construct a derivative of a vector in such a way that it makes physical sense even in the case of curved coordinates.

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