First Order Differential Equations And The Atmosphere

First Order Differential Equations and the Atmosphere
Author: Gerhard Ströhmer

College Mathematics Journal, Vol. 35, No. 2 (Mar., 2004), pp. 93-96

Published by: Mathematical Association of America

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Summary: This article develops three models relating pressure, density, and temperature as functions of the altitude above sea level. The first equation is obtained using the assumption that the temperature is constant throughout the atmosphere. To obtain the second equation, the author assumes that the temperature drops as the altitude increases. The third equation is an average of the first two equations. The logic behind this model is that the temperature drops more rapidly in the lower levels of the atmosphere. The three models are compared with the actual data. The author suggests that that these models could serve as a basis for either a series of exercises or a class project in an introductory differential equations class.

Thomas W. Judson, Stephen F. Austin State University, March 28, 2013.

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