# What is a Differential Equation? - PowerPoint PPT Presentation

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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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#### Presentation Transcript

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

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)

Dealing with Differential Equation

Second step is to convert differential

equation to a difference equation

Basic method emerges from Taylor

Series approximation