課程名稱︰工程數學下
課程性質︰必修
課程教師︰蕭浩明
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2020/6/24
考試時限（分鐘）：60
是否需發放獎勵金：是
試題 :
1. Given the Fourier transform F[ 1 / (x^2+b^2) ] = π/b e^(-αb),
∞ y(u) du 1
solve for y(x) from the integral equation ∫ ——————— = —————
-∞ (x-u)^2 + a^2 x^2 + b^2
z+4 dz
2. ∮ ———— c:|z+1+i| = 2
z^2+2z+5
∞ 0.5πsinω 0≦ω≦π
3. Solve f(t) for the integral equation ∫f(t)sinωt dt = {
0 0 ω>π
π dθ
4. ∫ ———————
0 1 + (sin^2)θ
1.Given that cos2θ = 1 - 2(sin^2)θ
2.Try to change the upper limit from πto 2πby using Chang of Variables so
the Cauchy integral of a full unit circle can be applied.
3.Let z = e(iθ) and convert this integral from θ to z.