MAT 185A Final: MATH 185A Final Exam Winter 2010
Document Summary
Sample final exam questions: (a) consider the change of variables from (x, y) to (z, z) given by z = x + iy, If z denotes the partial derivative with respect to z keeping z xed and z denotes the partial derivative with respect to z keeping z xed, show that. 2 ( x + i y) , where x denotes the partial derivative with respect to x keeping y xed and. Show that f is analytic if and only if zf = 0. 1: let the simple closed curve be the positively oriented unit square with corners at z = 0, z = 1, z = 1 + i, z = i. Evaluate the following contour integrals: ez z2 z + 1 dz. (a)z . 2: find the radius of convergence of the following power series. (a) 3: let be the circle of radius 3 center the origin. Z ez z3 + 4z2 + 4z dz.
