Differential Equations

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12 Terms

1
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<p>Order</p>

Order

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<p>Degree</p>

Degree

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<p>Directional Derivatives</p>

Directional Derivatives

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<p>Gradient</p>

Gradient

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Exponential Change

MODE 3 - 5

<p>MODE 3 - 5</p>
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Natural Population Growth

C - initial value

<p>C - initial value </p>
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Newton’s Law of Cooling

T = Ts + (To - Ts)e-kt


Ts - Surrounding Temperature
To - Initial Temperature

<p>T = T<sub>s</sub> + (T<sub>o</sub> - T<sub>s</sub>)e<sup>-kt</sup></p><p><br>Ts - Surrounding Temperature<br>To - Initial Temperature</p>
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Newton’s Law of Heating

<p></p>
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Radioactive Growth/Decay

k (+) Growth
k (-) Decay

<p>k (+) Growth<br>k (-) Decay</p>
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<p>Logistic Model</p>

Logistic Model

xo - initial population
xmax - total population
x - current population after t years
t - years
k - constant of proportionality

<p>x<sub>o</sub> - initial population <br>x<sub>max</sub> - total population <br>x - current population after t years<br>t - years<br>k - constant of proportionality </p>
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Logistic Curve

y - current population
k - carrying capacity
x - time
c - constant of proportionality

<p>y - current population<br>k - carrying capacity<br>x - time<br>c - constant of proportionality </p>
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Change in Concentration

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