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Differential Equation Modeling

Mechanisms, equilibria, and long-run behavior · BC Calculus · greeting

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Owl · Mock interview — Differential Equation Modeling. I ask; you answer.

Owl · We'll write DEs from stories, solve or read them qualitatively, and interpret equilibria. Two traps: assuming exponential forever, and ignoring carrying capacity when the story clearly has a ceiling.

Larry’s gold answer — Show text to read it out loud.

Larry · gold answer · Unlimited growth often looks like dP/dt = kP. But if the lake has a carrying capacity K, we should multiply by a factor (1 − P/K) so growth slows as P nears K.

Owl: We'll write DEs from stories, solve or read them qualitatively, and interpret equilibria. Two traps: assuming exponential forever, and ignoring carrying capacity when the story clearly has a ceiling.

You: —