Diff Eq & Lin Alg: Hamiltonian & Gradient Systems, Lyapunov Functions, Intro to Laplace Transforms

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⏱️TIMESTAMPS⏱️
(0:00) Class plan
(0:31) Review Hamiltonian and Gradient system examples
(8:10) NDSolve and ParametricPlot3D to plot solutions on the graph of the Hamiltonian function
(12:12) Gradient solutions travel uphill on the graph of the potential function
(14:38) Lyapunov functions (the negative of the potential function for a gradient system is a Lyapunov function for the gradient system).
(17:27) Symbolic verification along a solution curve using the Chain Rule from Multivariable calculus
(22:37) Introduction to Laplace transforms

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  1. Bill Kinney
  2. hamiltonian and gradient systems
  3. hamiltonian systems
  4. hamiltonian system of differential equations
  5. gradient system
  6. lyapunov
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