[試題] 106-2 林坤佑 工程數學-複變 第四次小考
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）︰2018/6/19
考試時限（分鐘）：50
試題 :
1. Smith chart is a useful graphical tool for the normalized impedence (z) and
reflection coefficient (Gamma).
(a) Construct a linear fractional transformation Gamma = f(z) that maps -i,
0, i of a straight line on z-plane onto -i, -1, i of circle on Gamma-
plane.(15%)
(b) Find the image curve of C1 = {z | Re{z} = 1} under the mapping function
Gamma = f(z).(15%)
2. Use the Schwarz-Christoffel formula to find the transformation w = f(z) to
map the domain D in Fig.1(a) to the domain D' in Fig.1(b).(30%)
(Hint: (a) Use w1 = f(-1) = -1 and w2 = f(1) = 1, (b)∫A/(1-z^2)^(1/2)dz=
sin^(-1)z)
3. Find a complex mapping from the disk |z - 1| ≦ 1 to the disk |w| ≦ 2.(10%
)
4. Find an appropriate conformal mapping and solve the Dirichlet problem as
shown in Fig.2.(30%)
∂^2 ∂^2
D.E. (---- + ---- )p(x, y) = 0, R = {z | |z| < 1},
∂x^2 ∂y^2
B.C. p(x, y) = 2 for z = e^(iθ), -π/2 < θ < π/2
p(x, y) = 2 for z = e^(iθ), π/2 < θ < 3π/2
https://i.imgur.com/I1SuXSX.jpg
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※ 編輯: misomochi (36.225.150.86), 04/16/2019 21:06:57
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