A three-pronged lesson in differential equations in a calculus course: analytical, numerical, experimental

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically, and occasionally numerically. In this paper, we detail a three-pronged lesson introducing differential equations using analytical, numerical and experimental approaches in a large first-year differential calculus course. Presenting the three approaches in succession allows students to evaluate advantages and disadvantages. The lesson incorporates software and programming, and provides opportunities for active, experiential, team-based learning.