Lecture 1 Notes

Experiment model u 2u u uv d 2 t x v 2v uv v d 2 t x

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Unformatted text preview: 6371 km ≈ 6411 km so not bad. • k is not constant either (depends on air density) - this is significant! A bacterial cell division regulator • Two interacting bacterial proteins that undergo complicated dynamics. • Differential equation model help understand how they work. Experiment Model ∂u ∂2u = u − uv + D 2 ∂t ∂x ∂v ∂2v = uv − v + D 2 ∂t ∂x Classifying DEs (Section 1.3) Classifying DEs (Section 1.3) • Ordinary differential equation (ODE) - a DE that involves derivatives of a function with respect to only one independent variable. Classifying DEs (Section 1.3) • Ordinary differential equation (ODE) - a DE that involves derivatives of a function with respect to only one independent variable. Logistic equation: dP = rP dt ￿ P 1− K ￿ Classifying DEs (Section 1.3) • Ordinary differential equation (ODE) - a DE that involves derivatives of a function with respect to only one independent variable. Logistic equation: Beam equation: ￿ dP P = rP 1 − dt K d4 w EI 4 = q dx ￿ Classifying DEs (Section 1.3) • Ordinary differe...
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