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The natural log II 5.2, Math 221 Winter 2021

From  Rakesh Rakesh 0 likes 3 plays 0  

Discussion HW 3.6, 4.1, Math 221 Winter 2021

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Relative max/min I - 4.2, Math 221 Winter 2021

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Competing species III (phase portrait)

We combine the information obtained in parts I and II to draw the phase portrait.

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Competing species II (Nullclines)

Nullclines and direction field chart for a competing species problem.

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Competing species I

Drawing the global phase portrait for a system of ODEs modeling two species competing for the same source of food in an ecosystem.

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Closed orbits II and the Poincare-Bendixson theorem

Duluc's criterion for the non-existence of closed orbits and the statement of the Poincare-Bendixson theorem followed by remarks.

From  Rakesh Rakesh 0 likes 28 plays 0  

Linearization near a fixed point II

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Closed orbits I

Also includes Duluc's criterion for ruling out closed orbits.

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Linearization near a fixed point I

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Elementary properties of non-linear systems

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First order linear systems of ODEs - II

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Introduction and the damped driven pendulum

An introduction to Nonlinear Dynamics. A model for the damped driven pendulum and the qualitative questions of interest for its motion.

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First order linear system of ODEs - I

What is a linear system of ODEs?

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Derivation of Euler-Lagrange equation : Integral constraints

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Variable end points - general theory

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