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math 310 a10 - MATH 310 Differential Equations Homework...

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MATH 310 Fall 2011 Differential Equations Homework Exercises, Set 10 Quiz on Wednesday, 30 November 2011 Course Information is on WebCT . The quiz will be based on the problems from Section 7.1 (converting between higher-order equations and first-order systems; nullclines and phase portraits) and Section 7.5 (linear constant coefficient systems with real eigenvalues). Textbook references are to: Boyce and DiPrima Elementary Differential Equations and Boundary Value Problems ” (9th edition). Reading : Sections 7.1, (7.2, 7.3), 7.4, 7.5, 7.6 Problems to prepare for quiz (no need to hand in): Section 7.1, # 3, 6, 10, 12 First-order equations, method of elimination, phase portraits For #10 & 12 , also plot fixed point(s) and nullclines in the phase diagrams, and use them to determine the regions where x or y are increasing/decreasing; hence sketch the phase portrait — see the lecture notes pp.7.8–7.11 . (Fixed point: where x 0 = y 0 = 0 — intersection of x - and y -nullclines; x -nullcline: where x 0 = 0 ; trajectories cross this curve vertically; y -nullcline: where y 0 = 0 ; trajectories cross this curve horizontally.)
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