What is a Differential Equation?
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What is a Differential Equation?. Shows rate of changes of a variable with respect to time Examples: dN/dt = rN dN/dt= rN – bN 2 dN/dt = rN – cN 2 –dN 3 dN/dt = f(weather, habitat, harvest) A key idea is that N is a state variable,

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What is a Differential Equation?

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What is a differential equation

What is a Differential Equation?

Shows rate of changes of a variable with

respect to time

Examples:

dN/dt = rN

dN/dt= rN – bN2

dN/dt = rN – cN2 –dN3

dN/dt = f(weather, habitat, harvest)

A key idea is that N is a state variable,

And dN/dt defines a rate

Weather, habitat, other populations are

state variables that may also affect this rate


What is a differential equation

Dealing with Differential Equation

First step is to reduce higher order

Differential equations to first order

Example:

D2y/dt2 + q(t)dy/dt = r(t)

D2y/dt2 = r(t) - q(t)dy/dt

Define dy/dt = z

dz/dt = r(t) – q(t)z(t)


What is a differential equation

Dealing with Differential Equation

Second step is to convert differential

equation to a difference equation

Basic method emerges from Taylor

Series approximation


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