Chemical Engineering Answers

5) Evaluate ∮c z³ Cos 1/z Where C is |z|=2.

4)Find the Laurent series expansion of the function 2z/ z²+2z-3 in the region 2<|z+1| <4.

3)Evaluate∫C z(ReZ)dz,Where C:z(t)=t, 0≤t≤1. ; 1+i(t-1), 1≤t≤2.

2) Show that v(x,y)=x²-y²-y is harmonic function.Find it's conjugate harmonic function u(x,y) and corresponding analytic function f(z).

1) Is the function f(z)={[Rez-lmz]²/|z|² ,z≠0 ;0 ,z=0 Continuous at z=0?

6)Solve ∂²z/∂x²-∂²z/∂y²=e^{x-2y}+ cos(2x+3y).

5) Find the particular integral of ∂²z/∂x²-3 ∂²z/∂x∂y+∂²z/∂y²= 2x sin y.

4)Find the complete integral of xp+3yq=2(z-x²q²)

3) Find the complete integral of p^3+q^3=27Z.

6) Solve the initial value problem y''-4y=cos 3t ,y(0)=0,y'(0)=1