MATH 2E Study Guide - Midterm Guide: Cylindrical Coordinate System, Uv Mapping, Cartesian Coordinate System
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Problem 1: find the jacobian of the transformation x = ln(uv), y = u2v. J = det (cid:20)xu xv (cid:21) yu yv (cid:20) v (cid:21) But, note that if we were to use the jacobian in an integral, we would use |j| = | u|: show that if f = g, then f = g + c where c is a constant. We see (f g) = 0 then. But only gradients of constants yield zero so hence f g = c where c is a constant, and rearranging, f = g + c. Problem 2: convert from spherical to rectangular coordinates the point (2, /4, /3). It"s not speci ed, but i think = 2, = /4, = /3. 2 . x = 2 cos /4 sin /3 = 2 1 y = 2 sin /4 sin /3 = (same) = z = 2 cos /3 = 2 1.
