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 ) = δ ( t-1)). Problem 6. Look at Heath’s 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 di±erential 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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