Re: [複變] 複變積分3題
※ 引述《vul3au3 (:))》之銘言：
: 標題: [複變] 複變積分3題
: 時間: Sat Apr 23 10:41:02 2011
:
: 希望有高手可以幫忙:非常感謝!
:
: Problem # 1
: If C is simple closed curve enclosing a region of area A, prove that
: _
: A = (1/2i)∮z dz
: C
:
: Use this to evaluate the integral when C is the circle │z-2│= 3.
應該自己會導 if f = u+iv , u,v€C1 , C is simple closed curve
pf
then ∮ fdz = 2i∫∫ ──── dz , where p is partial derivative
C A p(zbar)
take f=zbar , done
and when C is the circle │z-2│= 3
A = 9pi^2 , so ~ done
: Problem # 2
: (a) If C is the circle │z│= 50, show that
:
: z^2 + 2z - 5
: ∮ ──────────── dz = 0
: C (z^2 + 4)(z^2 + 2z + 2)
:
:
: (b) Is the results of (a) valid if C is the circle │z-1│= 1 ?
for (a)
this function has four simple at 2i , -2i , -1+i , -1-i
calculate 2*pi*i*[Res(f;2i)+Res(f;-2i)+Res(f;-1+i)+Res(f;-1-i)]
for (b) this function is analytic on │z-1│< 1+e , e>0
so the result is 0
: Problem # 3
: evaluate
:
: dz
: ∫ ─────
: C z^2 + 1
:
: along the line x + y = 1 in the direction of x increasing.
題目是要求通式??
沒給起點跟終點
而且在i那點會爆點
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