s02-rev2 - Math 224 Review problems 2 Spring 02 David...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math. 224. Review problems 2 Spring 02 David Gurarie Name Topics ² Linear models : oscillators, sliding chain, competition-cooperation, migration, buyer- seller markets; boundary value problems (equilibrium heat distribution) ² Fundamental pair, general solution, IVP-solution, BVP-solutions ² Phase-plane, equilibria ² Eigenvalue method: real, complex, repeated ² Applications (damped oscillators, migration et al.) ² Bifurcations (trace-det 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) Competition-cooperation: 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 competition-cooperation (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) Predator-prey: write linear di¤erential model for a predator-prey model, and discuss its eigenvalues and behavior of solutions....
View Full Document

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.

Page1 / 4

s02-rev2 - Math 224 Review problems 2 Spring 02 David...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online