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HW01 - Homework 1 Due 24 August 2010 Each question is worth...

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Homework 1 Due 24 August 2010 Each question is worth 10 points 1.) Given the differential equation: t f t ( ) d d A f t ( ) + B e C t = Solve for f(t) given the initial condition that f(0) = D . 2.) Consider the system of coupled differential equations: t f d d A f B g + = and t g d d C f D g = What are the characteristic roots (i.e.. the eigenvalues) for this system of equations? 3.) Consider the equation: π x log 4 ( ) e x e 1 2 = Solve for x.
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4.) Solve the following linear boundary value problem for Φ . Make sure that you find ALL possible solutions: Φ 1 ( ) 0 = 2 x Φ d d 2 Φ + 0 = Φ 1 ( ) 0 = Solve the following linear boundary value problem for Φ . Make sure that you find ALL possible solutions: Φ π ( ) 0 = 2 x Φ d d 2 Φ + 0 = Φ π ( ) 0 = Say something about the difference between these two cases
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