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Unformatted text preview: Math. 224. Review problems 2 Spring 02 David Gurarie Name Topics ² Linear models : oscillators, sliding chain, competitioncooperation, migration, buyer seller markets; boundary value problems (equilibrium heat distribution) ² Fundamental pair, general solution, IVPsolution, BVPsolutions ² Phaseplane, equilibria ² Eigenvalue method: real, complex, repeated ² Applications (damped oscillators, migration et al.) ² Bifurcations (tracedet plane) ² Method of characteristic polynomial for 2nd (and higher) order DE’s ² Forced oscillations: characteristic potential and undetermined coe¢cients ² Laplace transform method Sample problems 1. Modeling (a) Competitioncooperation: show that competing/cooperating species f x;y g with the natural growth rates a;b , and interaction coe¢cients f b;c g obey a di¤er ential system with matrix A = · a § b § c d ¸ : (i) Explain the meaning of § sign in terms of competitioncooperation (ii) Show that competition/ cooperation matrix A has real eigenvalues. (iii) What happens to eigenvalues of A when b has positive sign and c negative ? (b) Write DE, DS models for sliding chain (c) Predatorprey: write linear di¤erential model for a predatorprey model, and discuss its eigenvalues and behavior of solutions....
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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.
 Spring '07
 Hahn
 Math

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