Virtually Passed
5.0 A better way to understand Differential Equations | Nonlinear Dynamics | Bendixson's Criterion
Bendixson's criterion is another method used to disprove the existence of closed orbits. A periodic solution is a type of closed orbit. This theorem only holds for simply connected regions in 2D. The statement is that if on a simply...
Virtually Passed
3.0 A better way to understand Differential Equations | Nonlinear Dynamics | Linearization
These second-order nonlinear differential equations can be written in the form: dx/dt = f(x,y) dy/dt = g(x,y) Got a nonlinear differential equation? No problem, just linearize it! This method approximates the vector field as a linear...
Virtually Passed
3.1 Linearization PROOF | Nonlinear Dynamics
Nonlinear Dynamics mini-series Part 1: • 1.0 A better way ... Part 2: • 2.0 A better way ... Part 3: • 3.0 A better way ... This video shows a formal proof behind linearization for 2D flows: dx/dt = f(x,y) dy/dt = g(x,y) Step 1: Find...
Virtually Passed
A better way to understand Differential Equations | Nonlinear Dynamics (Part 3)
These second-order nonlinear differential equations can be written in the form: dx/dt = f(x,y) dy/dt = g(x,y) Got a nonlinear differential equation? No problem, just linearize it! This method approximates the vector field as a linear...
Virtually Passed
Linearization PROOF | Nonlinear Dynamics (Part 3 extra)
This video shows a formal proof behind linearization for 2D flows: dx/dt = f(x,y) dy/dt = g(x,y) Step 1: Find fixed points. This involves solving for where dx/dt and dy/dt both are equal to 0. Step 2: Approximate f(x,y) and g(x,y) as...