Abstract
The Fahrenheit-to-Celsius temperature-conversion equation is a basic component of many introductory earth science courses. Despite its simplicity, it presents a challenge to students and instructors alike because residents of the United States are unfamiliar with the Celsius scale. By solving for the point at which these two temperature scales are equal, it is possible to use the equations for temperature conversion as a springboard to more advanced topics. It is demonstrated that temperature-conversion equations and chaotic equations can be solved using identical numerical and graphical techniques. As a result, the fundamental concepts of chaos theory and numerical methods can be introduced to students in the context of the simplest equations in the earth sciences. These solution methods are applied to the quantitative theory of the extratropical cyclone as an example of the utility and broad scope of this educational approach.
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REFERENCES
Beltrami, E., 1987, Mathematics for dynamic modeling: Academic Press, New York, 277 p.
Bryant, V., 1985, Metric spaces, iteration and application: Cambridge University Press, New York, 104 p.
Charney, J. G., 1947, The dynamics of long waves in a baroclinic westerly current: Journal of Meteorology, v. 4, no. 5, p. 135–163.
Eady, E. T., 1949, Long waves and cyclone waves: Tellus, v. 1, no. 3, p. 33–52.
Gill, A. E., 1982, Atmosphere-ocean dynamics: Academic Press, New York, 662 p.
Holton, J. R., 1992, An introduction to dynamical meteorology: Academic Press, New York, 511 p.
Knox, J. A., 1996, Teaching advanced concepts with simple temperature-conversion formulas: The Physics Teacher, v. 34, no. 7, p. 450–453.
Lorenz, E. N., 1993, The essence of chaos: University of Washington Press, Seattle, 227 p.
May, R. M., 1976, Simple mathematical models with very complicated dynamics: Nature, v. 261, no. 5560, p. 459–467.
Modis, T., 1992, Predictions: Simon & Schuster, New York, 300 p.
Moran, J. M., and Morgan, M. D., 1995, Essentials of weather: Prentice-Hall, Englewood Cliffs, NJ, 351 p.
Pedlosky, J., 1979, Geophysical fluid dynamics: Springer-Verlag, New York, 624 p.
Press, F., and R. Siever, 1982, Earth, 3rd ed.: W. H. Freeman and Co., San Francisco, 613 p.
Rasband, S. N., 1990, Chaotic dynamics of nonlinear systems: John Wiley & Sons, New York, 230 p.
Spiegel, M. R., 1968, Mathematical handbook of formulas and tables (Schaum's Outline Series): McGraw-Hill Book Company, New York, 271 p.
Stakgold, I., 1979, Green's functions and boundary value problems: John Wiley & Sons, New York, 638 p.
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Knox, J.A. From Celsius to Chaos to Cyclones: Using Temperature-Conversion Equations to Introduce Advanced Mathematical Concepts in Earth Science Courses. Mathematical Geology 32, 203–215 (2000). https://doi.org/10.1023/A:1007527423131
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DOI: https://doi.org/10.1023/A:1007527423131