Chemical Engineering Answers

2) Find the Laplace transform of the periodic function f(t)=t ,0≤t≤2 and f(t+2)=f(t)?

1)Find the Laplace transform of sinh t/t?

21) Find the maximum value of the function f (z)=e^3z on the curve C:|z|=2.

20b)Use Cauchy integral formula for derivatives evaluate ∮c Sin 2πz/(z+1)² (z²+4)dz, where C is |z + 2| <2.

19)Evaluate∫C (x²+y²-ixy)dZ,Where C is z = {(t-2i, 1≤t≤2. ; 2-i(4-t), 2<t≤3.

18) Evaluate ∮(z)=1 Z² Sin1/z dZ?

16)Find Laurent series expansion of the function 2z/ z²-3z+2 in the regions

2<|z+1 <3 and |z-1|> 3.

15)Find the constants a and b such that the function f (z)=ax-3y+i(bx-2y) is analytic?

14)Show that u(x, y) = 2y + 3x²y-y³ is harmonic and find its conjugate harmonic function v(x, y) and the corresponding analytic function f(z).

13)Show that the function f (z)=(z̅ )²/z,z≠0 ;0, z=0 satiesfies Cauchy-Rieman equations at z=0.Does f'(0) exist?