AP Calculus BC / Unit 7: Differential Equations
7.1 Modeling Situations with Differential Equations
Notes
A differential equation relates a function to its derivatives. Phrases translate directly:
- "Rate of change of $y$ is proportional to $y$": $\displaystyle \frac{dy}{dt}=ky$.
- "Proportional to the difference between $T$ and 70": $\displaystyle \frac{dT}{dt}=k(T-70)$.
Practice
"The rate of change of $P$ is proportional to the square root of $P$" is:
Rate of change means derivative.
$\displaystyle \frac{dy}{dt}=0.3y$ describes:
Growth proportional to the amount.
Newton's law of cooling for a room at 70°F:
Rate depends on the temperature difference.
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