Lecture 2102014.pdf

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Department
Mathematics
Course
MATH 2574H
Professor
Jasmine Foo
Semester
Spring

Description
Lecture 2102014Monday February 10 20141009 AM1 Brief recap of equilibrium solutions2 Numerical methods for solving first order ODEsExam no eqn sheet no calculatorEquilibrium solutions and stabilityAutonomous first order ODEsdxdtfxDefinition Equilibrium solutions or critical points of autonomous equations occur where fx0 Any root c of fx0 yields the constant solution xcWe can learn a lot about hte behavior of the solutions of autonomous ODEs without actually solving them but instead studying equilibrium solutionsIn particular we ca nstudy the stability of each critical pointDefinitiona critical point xc is stable if for every 0there is a0 such that x0 c xt cIt is relatively simple to study the stability of the critical pointsset derivative equal to 0 and find the rootsto be stable both sides n
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