Using data to motivate the models used in introductory mathematics courses

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Jun 2001 by Kerley, Lyndell, Knisley, Jeff

ABSTRACT: Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom justified. In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.

KEYWORDS: Modeling, Regression, Logistic Equation, Periodic Process, PC-Matlab, Maple.

1 INTRODUCTION

6 CONCLUSION

Thus, a set of data can be used not only to estimate the parameters of a given model, but it can also be used to motivate the functional form of the model itself. Moreover, there are many other applications of the ideas in this paper, and not all of them are in mathematics. Physicists might use it to motivate the concept of conservation of energy. Chemists might use it to motivate the study of higher order chemical reactions.

That is, anyone who is exposed to data sets and mathematical modeling should also be exposed to the fact that models are not justified solely by good fits and common sense. Hopefully, those of us using data and technology in our teaching will be able to use the ideas and examples in this paper to illustrate these ideas in a meaningful way.

REFERENCES

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5. Lumen, D. 1999. Data as an Essential Part of a Course in Differential Equations. In Revolutions in Differential Equations, Exploring ODEs with Modern Technology, MAA Notes 50. Washington DC: Mathematical Association of America.

6. Lumen, D.and D. Lovelock. 1999. Differential Equations Graphics, Model, Data. New York NY: John Wiley and Sons, Inc.

7. Rudin, W. 1976. Principles of Mathematical Analysis, 3rd Edition New York NY: McGraw-Hill.

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Lyndell Kerley1 and Jeff Knisley2

ADDRESS: Box 70663, Deptartment of Mathematics, East Tennessee State University, Johnson City TN 37614-0663 USA. Email: (1) kerleylm@etsu.edu and (2) knisleyj@etsu.edu.

BIOGRAPHICAL SKETCHES

Dr. Kerley earned an MA from Appalachian State University and a PhD in mathematics from the University of Tennessee in 1977. He has been on the mathematics faculty at East Tennessee State University since 1967. He taught one year at Winston Salem State University in 1982. His research interests are Fourier analysis, numerical analysis, and real analysis.

Dr. Knisley graduated with honors from Carson Newman College in 1985 and received his PhD in mathematics from Vanderbilt University in 1990. He has been an assistant professor at East Tennessee State University since 1990. His interests are in differential equations, complex analysis, and operator theory.