Re: [理工] [工數]-台科98-自動化
※ 引述《t5d (t5d)》之銘言：
: http://www-o.ntust.edu.tw/~lib/pdf/Master/98/m980101.pdf
: 想問4.5.6題要怎麼做
: Thanks~
-y x
4.考慮 F(x,y) = [_________ + 3x]i + [__________-y]j
x^2+y^2 x^2+y^2
▽XF = 0 , 且 (x,y) =(0.0) 為奇點
令F = ▽ψ
ψ=c為解 , ψ = -arctan(x/y) + (3/2)x^2 - 1/2y^2
(1)
∮f(x,y)dl = 0
c
(2) ∮ f(x,y)dl = ∮ f(x,y)dl
c c'(繞奇點的積分)
令 x= rcosθ , y=rsinθ , r→0 , θ:0~2π
∮ f(x,y)dl = -arctan(x/y) + (3/2)x^2 - 1/2y^2︳
= θ + (3/2)(rsinθ)^2 - 1/2(rsinθ)^2
= 2π
5.︳z+1+i/2︳ = 4 考慮複平面 , c為圓心在 z=-1-i/2 , 半徑為4的圓
e^(iz)
f(z) = _________ , z=±3i 為單極 且都在路徑內
z^2+9
e^(-3) e^(3)
∮f(z)dz = 2πi*[Resf(z,3i)+Resf(z,-3i)] = 2πi*[______ - ______]
6i 6i
= -2π/3 * (sinh3)
6. y'-ay = H(t)e^(-at)
F{y(t)} = Y(w)
1 -1
(iw-a)Y(w) = ________ , Y(w) = ___________
a+iw a^2+w^2
-1
y(t) = F{ Y(w)} = -1/(2a) * exp^(-a︱t︳)
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◆ From: 118.171.77.144
※ 編輯: kagato 來自: 118.171.77.144 (03/04 13:29)
※ 編輯: kagato 來自: 118.171.77.144 (03/04 13:31)
推
03/04 14:29, , 1F
03/04 14:29, 1F
推
03/04 14:33, , 2F
03/04 14:33, 2F
→
03/04 14:41, , 3F
03/04 14:41, 3F
推
03/04 14:42, , 4F
03/04 14:42, 4F
→
03/04 14:43, , 5F
03/04 14:43, 5F
推
03/04 14:48, , 6F
03/04 14:48, 6F
→
03/04 14:50, , 7F
03/04 14:50, 7F
推
03/04 14:54, , 8F
03/04 14:54, 8F
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