assign3 - MAT1332A - Calculus for the Life Sciences II -...

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MAT1332A - Calculus for the Life Sciences II - Fall 2009 Assignment 3 This assignment is worth a total of 50 points. Due on Thursday, November 19, at the beginning of the lecture. Sorry, no late assignments will be accepted. Please write your answers neatly in complete and clear sentences. Explain your reasoning. Providing only an answer is not acceptable. Do staple your pages. (1) (a) [5 points] Check that z ( t ) = 1+ 1 + 2 t is a solution of the autonomous differential equation dz dt = 1 z - 1 with initial condition z (0) = 2. (b) [7 points] Estimate z (4) if z obeys the differential equation dz dt = 1 z - 1 with initial condition z (0) = 2. Use Euler’s method with Δ t = 1 for four steps. Compare with the exact answer in (a). (2) Consider the equation dx dt = ax - x 3 for both positive and negative values of x . (a) [2 points] Find the equilibria as functions of a for values of a between - 1 and 1. (b) [3 points]
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assign3 - MAT1332A - Calculus for the Life Sciences II -...

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