f01-rev1

# F01-rev1 - Math 224 Review problems 1 David Gurarie Name Topics 1 Modeling growth-decay(population et al heating-cooling free fall mixing chemical

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Math. 224. Review problems 1 David Gurarie Name Topics 1. Modeling: growth-decay (population et al), heating-cooling, free fall, mixing, chemi- cal reactions, f nancing, mechanics, geometry; (a) Multi-D models : interacting species (competition-cooperation), predator-prey, oscillators 2. Concepts: initial value problem, general solution, uniqueness, equilibriua, phase line 3. Methods, techniques: (a) Analytic : separation, mulitpiers, change of variables, linear approximation (b) Qualitative :s lope f eld, phase line, equilibria (stability and bifurcations) (c) Numeric :Eu le r Sample problems 4. Modeling. Write di f erential equation models for the following systems. Classify them as DE/DS, autonomous/non-autonomous, f rst or higher order, linear/nonlinear, separable etc. Indicate solution methods for each one. (a) The logistic growth model with the growth rate α = .4, threshold capacity N = 20 , initial population of 30, and di f erent harvesting methods ( f xed, variable, proportional to p ...) (b) Oscillator (mass-spring) system of mass m , damping coe cient α ,sp r

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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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F01-rev1 - Math 224 Review problems 1 David Gurarie Name Topics 1 Modeling growth-decay(population et al heating-cooling free fall mixing chemical

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