MATH 3057 Midterm: Exam-MATH3057-2005February
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Students must count the number of pages in this examination question paper before beginning to write, and report any discrepancy to a proctor. This question paper may be taken from the examination room. This examination may be released to the library. " r d z a l ( i i ) f 1. I z z a n d z (a) state cauchy"s integral formula for derivatives. (b) evaluate. 1,6 - 4o"" where 7 is the circle of radius 4 centred at the origin, oriented counterclockwise. / a (a) state and prove liouville"s theorem. (b) let / be entire,vith lf (t)l> m > 0 for all zec. Prove that / is constant: (a) let u(r,a) be harmonic and suppose that u(r cos d, r sin a) : th,(i)" Find a(0,0). (b) find the maximum value of u : re(23) on the square. Hint: for z on the unit circle, cos(d) : i) ro" evaruat"
