MATH 301 Study Guide - Midterm Guide: Branch Point, Inverse Hyperbolic Function, Unit Circle
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Math 301 final examination - april 2009: [10] find all values of: (a) (b) (c) (i2)i (ii)2 arcsinh(i, [18] evaluate the integrals; justify all steps carefully (a) (b) J =z x1/3 x2 1 x1/2 log(x) [hint: rst show that the image of the circle is real. ] Use the above mapping to nd the image of this uniform ow in the w plane de ned by (1). Represent the images parametrically as u(t), v(t), then eliminate v to give the streamlines in the form u = h(v). Write the solution in the form u(x, t) =z . G(x, t, )d : [18] (a) find the inverse laplace transform, justify all steps carefully. S (c) use a laplace transform to nd the solution to the problem: ut = uxx, 0 < x < , 0 < t, , t > 0. u(x, 0) = 0, u(0, t) =
