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Exponential Growth & Decay;
Logistic Growth
Newton's Law of Cooling
Radioactive Decay
Exponential Population Growth
Logistic Population Growth
An RC Circuit
Draining Tanks
Cylinder
Clepsydra
Cone
Sine
Cusp
Spring-Mass Systems
Unforced
Undamped
Underdamped
Critically Damped
Overdamped
Forced
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1.
2. (high freq force)
3.
4. (beats)
5. (beats)
6.
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7. (square-wave force)
8. (sawtooth force)
9. (sawtooth force)
10. Resonance
11. (sawtooth force & resonance)
12. Damped
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Approximation
Convergence of Euler’s Method 1, 2
Convergence of Picard Iteration 1, 2
Graphs and Phase Plane Orbits
Damped Pendulum
The Brusselator
Bifurcations
A Simple Hopf Bifurcation
The Brusselator
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Biological Systems
Predator-Prey
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1. (Slow spiral to equilibrium)
2. (Fast approach to equilibrium)
3. (Predator extinction)
4. (Periodic orbit)
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Harvesting a Logistic Population
Spruce Budworm Outbreak Threshold
Spruce Budworm Periodic Orbit
Fitzhugh-Nagumo
Mechanical Systems
The Simple Pendulum
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1. (w/ graph of θ versus t)
2. (w/ graph of θ versus t)
3. (w/ phase plane orbit)
4. (w/ phase plane orbit)
5. (w/ phase plane orbit)
6. (w/ phase plane orbit)
7. Damped. (w/ phase plane orbit)
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Simple Pendulum in 3D
Rayleigh's Equation
Three Bodies
Double Pendulum
Pendulum on a Rail
Spring Pendulum
Problem 10.5.4
Problem 10.5.5
Three Dimensional Systems
The Lorenz System
Lorenz Laser Show
Lorenz with Shadows
Lorenz Gumball Machine
The Rössler System
Rössler Laser Show
Rössler with Shadows
Rössler Gumball Machine
The Oregonator
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