7.1. (Sec. 7.2) A transfonnation from rectangular to polar coordinates is (a) Prove w 2 = r.y~....

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7.1. (Sec. 7.2) A transfonnation from rectangular to polar coordinates is

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(a) Prove w 2 = r.y~. [Hint: Compute in turn Y; + Y;_I'(Y;+Y;_I) +Y;-2' and so forth.]

(b) Show that the Jacobian is w" -I cos"-2 /II cos" -3 /12 .. , cos /I" -2' [Hint: Prove

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where x denotes elements whose explicit values are not needed.]

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