Inquiry-Based Learning of Transcendental Functions in Calculus

Abstract

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for understanding infinite series and growth functions later in the course sequence. Students further explore interconnections between such functions, culminating in the synthesis of the Euler formula . These activities have been implemented over several years with encouraging results.

Keywords:

• Inquiry-based learning
• teaching calculus
• transcendental functions
• Euler’s formula
• Taylor series

Acknowledgments

We would like to thank the anonymous reviewers for their insightful comments and suggestions.

FUNDING

We also appreciate support given by the NSF Grant No. 1355437 for the dissemination of these IBL modules for calculus to innovate undergraduate mathematics education.

Additional information

Notes on contributors

Celil Ekici

Celil Ekici has been working for the University of Virgin Islands since 2012 as an assistant professor of mathematics with a Ph.D. from the University of Georgia. He enjoys integrating different flavors of inquiry into mathematics and education courses for undergraduates and graduates. His research interests involve trigonometric functions in secondary and higher mathematics; mathematical modeling in K-16 STEM education; phenomenology of mathematics; population dynamics.

Andrew Gard

Andrew Gard joined the University of the Virgin Islands faculty in the fall of 2014 as an assistant professor of mathematics after obtaining his doctorate from the Ohio State University and completing a visiting role at Ohio Wesleyan University. His research interests include geometric optimization and big data analysis. In the classroom, he focuses on piloting and extending the use of inquiry-based techniques at all levels of mathematics.