Math 503 Advanced Calculus and Nonlinear Dynamics_ Fall 2020
Math 503 Advanced Calculus and Nonlinear Dynamics_ Fall 2020
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We combine the information obtained in parts I and II to draw the phase portrait.
Competing species III (phase portrait)
From Rakesh Rakesh
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Nullclines and direction field chart for a competing species problem.
Competing species II (Nullclines)
From Rakesh Rakesh
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Drawing the global phase portrait for a system of ODEs modeling two species competing for the same source of food in an ecosystem.
Competing species I
From Rakesh Rakesh
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Duluc's criterion for the non-existence of closed orbits and the statement of the Poincare-Bendixson theorem followed by remarks.
Closed orbits II and the Poincare-Bendixson…
From Rakesh Rakesh
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Linearization near a fixed point II
From Rakesh Rakesh
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Also includes Duluc's criterion for ruling out closed orbits.
Closed orbits I
From Rakesh Rakesh
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Linearization near a fixed point I
From Rakesh Rakesh
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Elementary properties of non-linear systems
From Rakesh Rakesh
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First order linear systems of ODEs - II
From Rakesh Rakesh
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An introduction to Nonlinear Dynamics. A model for the damped driven pendulum and the qualitative questions of interest for its motion.
Introduction and the damped driven pendulum
From Rakesh Rakesh
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What is a linear system of ODEs?
First order linear system of ODEs - I
From Rakesh Rakesh
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Derivation of Euler-Lagrange equation : Integral…
From Rakesh Rakesh
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Brachistochrone with end point on a curve
Brachistochrone with end point on a curve
From Rakesh Rakesh
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Variable end points - general theory
From Rakesh Rakesh
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Integral constraints - the theorem, solution of…
From Rakesh Rakesh
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