Calculus Volume 2

# Key Equations

Calculus Volume 2Key Equations
 Euler’s Method $xn=x0+nhyn=yn−1+hf(xn−1,yn−1),wherehis the step sizexn=x0+nhyn=yn−1+hf(xn−1,yn−1),wherehis the step size$
 Separable differential equation $y′=f(x)g(y)y′=f(x)g(y)$ Solution concentration $dudt=INFLOW RATE−OUTFLOW RATEdudt=INFLOW RATE−OUTFLOW RATE$ Newton’s law of cooling $dTdt=k(T−Ts)dTdt=k(T−Ts)$
 Logistic differential equation and initial-value problem $dPdt=rP(1−PK),P(0)=P0dPdt=rP(1−PK),P(0)=P0$ Solution to the logistic differential equation/initial-value problem $P(t)=P0Kert(K−P0)+P0ertP(t)=P0Kert(K−P0)+P0ert$ Threshold population model $dPdt=−rP(1−PK)(1−PT)dPdt=−rP(1−PK)(1−PT)$
 standard form $y′+p(x)y=q(x)y′+p(x)y=q(x)$ integrating factor $μ(x)=e∫p(x)dxμ(x)=e∫p(x)dx$
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