[理工] 複變
∮ cot(z) dz , where c:|z|=4
c
想法是 cot = cos /sin
所以在C內有 z= ±π,0這三個一階極點
cos(z)
Res f(z) = lim ─── =1
z→π z→π cos(z)
cos(z)
Res f(z) = lim ─── =1
z→-π z→-π cos(z)
cos(z)
Res f(z) = lim ─── =1
z→0 z→0 cos(z)
所以∮ cot(z) dz = 2πi {Res f(z) + Res f(z) + Res f(z)}
c z→π z→-π z→0
= 2πi*3 = 6πi
這樣有算錯嗎@@
每次算複變找分母是三角函數的極點都會怕怕的QQ
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※ 編輯: handsboy 來自: 140.116.109.179 (02/14 19:51)
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