課程名稱︰工程數學-複變
課程性質︰電機系大二必修
課程教師︰林坤佑
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰2018/03/20
考試時限（分鐘）：50分鐘
試題 :
1. If z = -√3 + i, please express ln(z) in the form of a + ib.(25%)
2. Show that the f(z) = z-bar^2 is not analytic at any point.(25%)
3. Prove that |cosh z|^2 = cos^2(y) + sinh^2(x).(25%)
4.
(a) Verify the function u(x, y) = e^x(xcosy - ysiny) is harmonic.(10%)
(b) Find v(x, y) which is the conjugate harmonic of u(x, y).(15%)