Abstract

Citation

Researchers should cite this work as follows:

• Kerckhove, M. (2023). 2012-Michael_Kerckhove-From Population Dynamics to Partial Differential Equations. SIMIODE, QUBES Educational Resources. doi:10.25334/0PCT-S625

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Kerckhove, Michael.  2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 1-18.

See https://content.wolfram.com/uploads/sites/19/2012/12/Kerckhove.pdf. Accessed 28 March 2023.

Abstract: Differential equation models for population dynamics are now standard fare in single-variable calculus. Building on these ordinary differential equation (ODE) models provides the opportunity for a meaningful and intuitive introduction to partial differential equations (PDEs). This article illustrates PDE models for location-dependent carrying capacities, migrations, and the dispersion of a population. The PDE models themselves are built from the logistic equation with location-dependent parameters, the traveling wave equation, and the diffusion equation. The approach presented here is suitable for a single lecture, reading assignment, and exercise set in multivariable calculus. Interactive examples accompany the text and the article is designed for use as a CDF document in which some of the input can remain hidden.

Keywords: partial differential equation, population, population dynamics,  model, Mathematica