Expand the function f(z) = (z − 1) / z^ 2 (z + 1)(z − 3) as a
Laurent series about the origin z = 0 in all annular regions whose
boundaries are the circles containing the singularities of this
function.
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find
the flux of F across S, the part of the paraboloid x2 + y2 + z = 29
that lies above the plane z = 4 and is oriented upward.
Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z +
z^3 ) across the outward oriented faces of a cube without the front
face at x = 2 and with vertices at (0,0,0), (2,0,0), (0,2,0) and
(0,0,2).