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Computer Laboratory


Applications of Differential Equations

Population Dynamics

(continued from last page...)

We need to plug our value of k back into malthus. Since it's already in the form {{k -> 0.0198602}} we almost have what we need, i.e. a replacement rule. The only trouble we have is that it's buried a little too deep within braces, We can strip these away as we learned when we first came up with the [[1,1,2]] trick. Here we actually have an easier scenario. We wish to simply drill into the matrix one level down, so we pull out its first row using the [[1]] command. This leads us to the command:

malthus = malthus /. %[[1]]

Remember, the percent sign always refers to the previous output in Mathematica, in this case the solution we found for k. The [[1]] drills down a level into this solution, removing the unwanted outer braces.)

Let's go see what this produces...

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ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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