Chemical Engineering Answers

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).

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

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Solve y"+3y'+2y=1, y(0)=0,y'(0)=1.

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Find the complete integral of the PDE px+qy+z=xq²

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Find the complete integral of the PDE px+qy+z=xq²

Find the Laplace transform of the periodic function f(t)=t ,0≤t<1 ; 2-t,1≤t≤2 and f(t+2)=f(t)?

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

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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).

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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? Explain the problem with step by step process?

12) Find the complete integral of the PDE p²+q²=1

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