[複變] 複變積分3題
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.
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 ?
Problem # 3
evaluate
dz
∫ ─────
C z^2 + 1
along the line x + y = 1 in the direction of x increasing.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 128.194.132.227
討論串 (同標題文章)