課程名稱︰工程數學 下
課程性質︰必修
課程教師︰林沛群
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2009/6/15
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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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