Gradient in different cooridinates

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Homework Statement



Printed textbook page, Appendix A.3 Gradient, showing equations A.2 to A.4 for the gradient of a scalar function t in orthogonal coordinates, and Table A.1 giving u, v, w, f, g, h for Cartesian, spherical and cylindrical systems.


Homework Equations





The Attempt at a Solution


I saw from a book this is a quick way to get gradient in different cooridinates.

However what f, g and h are? And how do I know that in rectangular coor. f=g=h=1 and etc?
 
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  • Printed textbook page, section A.3 Gradient, showing equations A.2 to A.4 for the gradient of a scalar t in orthogonal coordinates, and Table A.1 giving f, g and h for Cartesian, spherical and cylindrical systems.
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I am always a bit suspicious about these formulae. My advice id to go from first principles, learn how to do it and then when you need then again, look it up in a book.