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che132a-rec-4 - Chemical Engineering 132A Analytical...

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Chemical Engineering 132A Analytical Methods of Chemical Engineering Professor Mike Gordon, Fall 2011 Mathematica Assignment #4 Commands for today LaplaceTransform[f[t],t,s] Laplace transform of f(t): gives F(s) InverseLaplaceTransform[F[s],s,t] Inverse Laplace transform of F(s): gives back f(t) HeavisideTheta[t] Heaviside step function: H[t] DiracDelta[t] Dirac delta function: ( ) t δ Apart[expr] Separate expr into partial fractions 1) Find the Laplace transforms of the following functions: 6 cos(2 ) t e t - (a) 2 ( 3)* t H t e - - (b) ( ) t δ and ( 5) t δ - (c) Now work (a) by hand using one of the shifting theorems we talked about in class. 2) Find the inverse of the following s-space functions: 2 4 36 s s (d) 2 2 ( 16) s e s s - + (e) 2 1 1 s (f) Work (e) by hand using one of the shifting theorems we talked about in class. 3) What is the Laplace transform of a square pulse, P(t)? 1 3 5 ( ) 0 everywhere else t P t = Think about how you might define P(t) using Heaviside functions. Plot P(t) on [0,10]. Now compute the Laplace transform of P(t).
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