Setting the Stage for Logistic Growth

Posted: February 15, 2016 in Calculus: An Introduction, Differential Equations
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In order to achieve some degree of continuity, I continually strive to weave together concepts, not only within my own “area of influence”, but across other disciplines as well. Physics is naturally folded into the fabric of calculus for obvious reasons; others disciplines, not so much.

I wanted to raise awareness in students of how calculus appears in applications relating to Biology and Chemistry; logistic growth is the obvious choice for the former and is relatively straight forward once students have a feel for differential equations.

The notes directly below make clear (I hope) the distinction between two types of growth from the context of differential equations.  The exponential growth model below will be expanded upon to eventually derive the well-known formula for logistic growth.

Separable Diff Equations2

 

The application to Chemistry that was alluded to earlier will require First Order Differential Equations, another “diversion” that can be pursued when a change of pace is needed. We will hopefully be afforded the time to develop an adequate understanding of this before semester’s end.

Thanks for reading.

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