Differential Equations A — Modeling Change & Decay
Part 1 of 2. What a differential equation is, the exponential-decay law y′ = −k·y (verified numerically), and Newton's law of cooling.
Nature rarely tells you what a quantity is — it tells you how it changes. Cooling is proportional to temperature difference; decay to the amount remaining; acceleration to force. An equation about a derivative is a differential equation, and solving it means finding the function that obeys it. This is part 1 of 2.
- 01 The king of them all: y′ = −k·y ELI5: "it shrinks in proportion to how much is left." That one sentence — y′ = −k·y — governs radioactive decay, a draining capacitor, a drug…
- 02 Newton's cooling — decay with an offset ELI5: coffee doesn't cool toward zero, it cools toward the room: T′ = −k·(T − T_room). Same exponential, just measured down from the ambient line: T(t) =…
next course: Differential Equations B — Oscillation & Damping →