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, 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: D 2 y/dt 2 + q(t)dy/dt = r(t) D 2 y/dt 2 = 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