Chemical Engineering Answers

5)Solve ∫0^t y''(τ)y'(t-τ)dτ=y(t),y(0)=y'(0)=20

4)Define Laplace transform and find Laplace transform of the periodic function f(t) =t,0≤t≤2 and f(t+2)=f(t)

3) Find the Laplace transform of 1-e^{-2t}/t

2)Solve y" + 3y' +2y= t²δ(t-2),y(0)=0,y'(0) =-2

1)Find the inverse Laplace transform of ∫s^∞ ln (u+2/u²+9)du.

12)Use Cauchy integral formula for derivatives evaluate ∮c z²-2z/(z+1)^2 (z²+4)dz, where C is |z + 2) <2.

11)Evaluate∫C Im(Z)dz, where C is z = {(t-2i, 1≤t≤2. ; 2-i(4-t), 2<t≤3

11)Evaluate∫C Im(Z)dz, where C is z = {(t-2i, 1≤t≤2. ; 2-i(4-t), 2<t≤3'

10)Using Residue theorem evaluate ∮c Z cosh πz/Z^(4)+5Z^(2)+4, where C is |z| = 3.

9)Find Laurent series expansion of the function 1/ z²+z-6 in the regions

1<|z-1 <4 and |z-1|> 4.