MATH V1207 Midterm: MATH V1205 Columbia Spring01Mid2Ans

• School: Columbia University
• Department: Mathematics
• Course: MATH V1207
• Professor: All

Document Summary

Note that div(f ) = 2y + bz and curl(f ) = (2y by)i + 0j + 0k. Since f is conservative when curl(f ) = 0 we need b = 2: for this second number b, nd f so that (f ) = f . One choice is f = x2y + y2z: a. rewrite the following integral as an iterated integral in the order dydxdz: 1 z z 1 z x2 f (x, y, z)dydxdz: rewrite the integral in spherical coordinates. 3 cos( ) sin( )d d d : evaluate z zr e9x2+4y2 da where r is the region bounded by 9x2 +4y2 = 1. Let x = u/3 and y = v/2. Let s be the region in the (u, v)-plane bounded by u2 + v2 = 1. Then the jacobian of this transformation is j = 1/6. Let f = h1 + tan(x), x2 + eyi be a force eld.