课程名称︰工程数学下
课程性质︰必修
课程教师︰萧浩明
开课学院：工学院
开课系所︰机械系
考试日期（年月日）︰2020/6/24
考试时限（分钟）：60
是否需发放奖励金：是
试题 :
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.