Engineering Answers

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.

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

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20 a) State Cauchy-integral Theorem ?

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

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18) Evaluate ∮(z)=1 Z² Sin1/z dZ?

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17)State Residue theorem and evaluate ∮c cos πz+2z/(z+1)(z-2)² dZ, where C is |z| = 3.

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

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

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