f03t1 - Math. 224. Test 1 Fall 2003. Oct.2 David Gurarie...

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Ma th .224 .T e s t1 Fall 2003. Oct.2 David Gurarie Name 1. Modeling. Set up di f erential equation models of the following systems. Classify them (DE/DS, f r s to rh ighe ro rde r ,l inea r/non l inear, autonomous, separable, etc.). Indicate solution method(s) for each one (analytic, numeric), but do not solve . (a) The logistic growth model with the growth rate k , carrying capacity N =6,in itial population y 0 , and harvesting rate b ( t ). Which b allow analytic solutions? (b) Mixing problem with incoming rate r 1 =3 m 3 /s , concentration α 1 = . 1 mg/m 3 , outgoing rate
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α ,andpaymentrate p . Write solutions, andsketchso lut ioncurves . Extra : explain the minimal payment rate, f nd total payment and the overpay factor. (d) Oscillator (mass-spring) system of mass m ,fr ict ioncoe cient α , spring constant k , suspended vertically in the external gravity force mg
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This note was uploaded on 05/09/2008 for the course MATH 224 taught by Professor Hahn during the Spring '07 term at Case Western.

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f03t1 - Math. 224. Test 1 Fall 2003. Oct.2 David Gurarie...

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