课程名称︰工程数学 下 课程性质︰必修 课程教师︰林沛群 开课学院：工学院 开课系所︰机械系 考试日期（年月日）︰2009/6/15 考试时限（分钟）：120 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.(15%) Determine the differentiability of the function f(z) = x^2 - i(y^2) . 2.(15%) Solve cos(z) = i. 3.(15%) Write the Laurent expansion of the function f(z) = z/(1+z^2) about the point (-i). sin(z) 4.(20%) Evaluate ∮ ───── dz Γ z^2 ∞ xsin(x) 5.(20%) Evaluate ∫ ───── dx 0 (x^2)+9 6.(15%) Let Γ be a closed path. Let γ1,...,γn be closed paths enclosed by Γ. Assume that no two of Γ,γ1,...,γn intersect, and no point interier to any γj is interior to any other γk. Let f be differentiable on an open set containing Γ, each γj, and all points that are both interior to Γ and exterior to each γj. proof n ∮ f(z)dz = Σ∮f(z)dz. (Extended Deformation Theorem) Γ j=1 --

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