P(t): the total population at time t / 특정 시각에서의 개체수,population

$\displaystyle \frac{dP}{dt}\propto P$

population_growth =,population_growth =,population_growth . population_growth
{
population growth
Up: 개체수,population 성장,growth ?
}// population growth population growth

A(t): amount of substance remaining at time t

$\displaystyle \frac{dA}{dt}\propto A$

물질의 연대 측정법:
ex. 현재 Ra 100 mg 이 있다. t시간 이후 양은?
$\displaystyle t=0,y=100,y=100e^{kt}$

뉴턴_냉각법칙

T(t): the temperature of a body at time t
T_m: the temperature of surrounding medium

$\displaystyle \frac{dT}{dt}\propto T-T_m$
$\displaystyle {dT\over dt}=k(T-T_m)$

x(t): the number of people who have contacted the disease at time t
y(t): the number of people who have not yet been exposed to the disease at time t
assumption: the number of interactions is jointly proportional to x(t) and y(t)

$\displaystyle \frac{dx}{dt}\propto xy$
$\displaystyle \frac{dx}{dt}=kxy$

$\displaystyle \frac{dX}{dt}=k(\alpha-X)(\beta-X)$

(input rate of salt) - (output rate of salt) = R_in - R_out
혼합물,mixture

$\displaystyle \frac{dh}{dt}=-\frac{A_h}{A_w}\sqrt{2gh}$

$\displaystyle L\frac{d^2q}{dt^2}+R\frac{dq}{dt}+\frac1Cq=E(t)$

$\displaystyle \frac{d^2s}{dt^2}=-g$

$\displaystyle m\frac{dv}{dt}=mg-kv^2$

$\displaystyle m\frac{d^2s}{dt^2}+k\left(\frac{ds}{dt}\right)^2=mg$

$\displaystyle \frac{d^2x}{dt^2}-\frac{64}Lx=0$

$\displaystyle \frac{dy}{dx}=\frac{W}{T_1}$