Of the many disciplines that rely on calculus, physics is among those with the strongest connections to this branch of mathematics. For instance, the derivative--one of the key notions of calculus--is used to describe velocity and acceleration, which play a central role in mechanics. In post-secondary education, in particular at the college level,…

Improving student success rates in introductory calculus and physics courses is critically important for our students' path in STEM fields. Many of the students who have an intuitive understanding of physics fail calculus and are pushed to delay or drop their majors in technical fields. One way of addressing this issue is by adopting a program…

Rate of change concepts from calculus are presented and applied rather differently in college mathematics, physics, biology, and chemistry classes. This is not simply a matter of pedagogical style but reflects real cultural differences between these disciplines. We describe the efforts of our interdisciplinary collaboration to understand and…

We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear…

Theorising STEM Education in the 21st Century is a book that captures the essence of Science, Technology, Engineering and Mathematics and the intricacies of STEM education in the contemporary society. It explores STEM as an interdisciplinary field as well as the individual disciplines that make up STEM. This ensures the field of STEM as a whole is…

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

San José State University, in partnership with California State University-Los Angeles and Cal Poly Pomona, was awarded a prestigious 2015 First in the World grant, sponsored by the Department of Education. The multi-campus effort is focused on bringing the flipped classroom model to seven STEM gateway courses over three years that have high…

Calculus students' difficulties in understanding integration have been extensively studied. Research shows that the difficulty lies with students understanding of the definition of the definite integral as a limit of a Riemann sum and with the idea of accumulation inherent in integration. We have created a set of manipulatives and activities…

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a…

This article uses calculus to find the center of mass of a soft, vertically suspended, cylindrical helical spring, which necessarily is stretched non-uniformly by the action of gravity. A general expression for the vertical position of the center of mass is obtained and compared with other results in the literature.

The interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

This article presents an application of standard undergraduate ODE techniques to a modern engineering problem, that of using a tuned mass damper to control the vibration of a skyscraper. This material can be used in any ODE course in which the students have been familiarized with basic spring-mass models, resonance, and linear systems of ODEs.…

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

This article is a project that takes students through the process of forming a mathematical model of bicycle dynamics. Beginning with basic ideas from Newtonian mechanics (forces and torques), students use techniques from calculus and differential equations to develop the equations of rotational motion for a bicycle-rider system as it tips from…