041907-132A-hw2 - function C ( s ). Calculate the inverse...

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C HEMICAL E NGINEERING 132A Professor Todd Squires Spring Quarter, 2006 Homework 2 Due Monday, April 23 Problem 1. Homogeneous, second-order ODEs. Page 43, probs. 2,4,5,6,34,35 Problem 2. Inhomogeneous, 2nd order ODEs – p. 59, probs. 15,16,20. Problem 3. Variation of parameters: p. 71 prob. 6 Problem 4. Laplace Transforms: p. 160 probs. 2,3,9,14,16,18,22,27,30,40,42,45,48 Problem 5. A continuously-stirred 10-liter tank initially contains pure water. Brine containing c ( t ) grams per liter is added at the rate of 5 liters per minute and Fows out at the same rate. Write a di±erential equation for the amount of salt in the tank at any time, and use the Laplace Transform to solve this equation in terms of the Laplace-transformed
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Unformatted text preview: function C ( s ). Calculate the inverse transform explicitly when c ( t ) = H ( t-1), and when c ( t ) = ( t-1)). Problem 6. Look at Heaths 2006 paper on semiconducting nanowire biosensors, linked on the web. Read as much of it as you like. Go to page 7 (page 16329 of the Journal) and look at the dierential equation (1). This is an equation for the number of receptors on the surface of the nanowire that get bound by target molecules in solution (whose concentration is C .) The problem is to solve this ODE to derive equation (2)....
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