Question: (a) Show that the coordinate transformation (x, y) ( with = x and ( = 1. ((/(x = 0 and (( / (y

(a) Show that the coordinate transformation (x, y) ( ξ with ξ = x and ( = 1. ((/(x = 0 and (( / (y = 0. This violates Eq. (5.6).
(b) Are the following coordinate transformations good ones? Compute the Jacobian and list any points at which the transformations fail.
(i) ξ = (x2 + y2)1/2, η = arctan(y/x);
(ii) ξ = ln x, ( = y;
(iii) ξ = arctan(y/x), ( = (x2 + y2)-1/2.

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