Conceptual Understanding in Introductory Physics XXVIII: Div, Grad, and Curl

You may not agree that the topic(s) of this question belong in an introductory calculus-based physics course, but I’m going to pretend they do for the duration of this post. Gradient, divergence, and curl are broached in Matter & Interactions within the context of electromagnetic fields. Actually, gradient appears in the mechanics portion of the […]

Matter & Interactions II, Week 6

I’m writing this a whole week late due, in part, to having been away at an AAPT meeting and having to plan and execute a large regional meeting of amateur astronomers. This week was all about the concept of electric potential and how it relates to electric field. I love telling students that this topic […]

Did Feynman Invent Feynman Notation?

In section section 27-3 of The Feynman Lectures on Physics, Feynman describes a notation for manipulating vector expressions in a way that endows nabla with the property of following a rule similar to the product rule with which our introductory calculus students are familiar. It allows a vector expression with more than one variable to be […]

HELP! A Stubborn Vector Identity to Understand

Over the past three years or so, I have been researching the history and implementation of Gibbsian vector analysis with the intent of finding ways to incorporate it more thoroughly and more meaningfully into introductory calculus-based physics (possibly algebra/trig-based physics too). Understanding the usual list of vector identities has been part of this research. One […]