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Unformatted text preview: Math 185. Sample Answers to First Midterm 1. (15 points) Carefully define the following. (In each definition you may use without defining them any terms or symbols that were used in the text prior to that definition.) (a). Boundary point of a set Answer (4 points): A point that is neither an interior point nor an exterior point of the set. In other words, a point all of whoseneighborhoods contains points in the set and points not in the set. (b). Harmonic conjugate of a function Answer (4 points): If u ( x,y ) is a harmonic function, then a harmonic conjugate of u is a harmonic function v ( x,y ) for which u and v satisfy the CauchyRiemann equations. (c). Region Answer (3 points): The union of a domain and some, all, or none of the boundary points of that domain. (d). The number Arg z Answer (3 points): The unique number Θ such that z = re i Θ and π < Θ ≤ π . 2. (10 points) Write √ 2 1 i 10 in x + iy form....
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 Fall '07
 Lim
 Math, Derivative, Interior, Complex number, Boundary

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