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 --

※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 36.225.150.86 ※ 文章網址: https://webptt.com/m.aspx?n=bbs/NTU-Exam/M.1555419767.A.E5C.html ※ 編輯: misomochi (36.225.150.86), 04/16/2019 21:06:57