Polar coordinates can be defined by the following mapping, and it's inverse, F : { y1 = x1 cos x2 y2 = x1 sin x2 F1 : { x1 = (y1)2 + (y2)2 x2 = arctan (y2 y1 ) 2 (a) Calculate the Jacobian of F and infer the region of which the mapping is bijective (one to one and onto). (b) Calculate the Jacobian of F1 for the region, {(r, )|r > 0, /2 < < /2} . (c) Verify that the two Jacobians are indeed inverses of each other. 3