Estimating the Sensitivity of Fitted Parameters to Perturbations of Data with Calculus

摘要

This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing the reliability of the fitted parameters, fits in existing mathematics courses at levels from basic to multivariable calculus. The material for multivariable calculus explains methods of computation of quantitative criteria of “significance” that are currently the subject of scientific controversy. This article thus provides resources to strengthen students' mastery of calculus before, or in, mathematical modeling, probability, and statistics.