课程名称︰工程数学-复变
课程性质︰电机系大二必修
课程教师︰林坤佑
开课学院：电机资讯学院
开课系所︰电机工程学系
考试日期（年月日）︰2018/6/19
考试时限（分钟）：50
试题 :
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. (