# Help Me! Question About Tensors and Projections

I need some help. I am working hard to find ways to bring more geometry into introductory calculus-based physics (and conceptual physics as well). By geometry, I mean specifically the geometry associated with vectors and tensors, and the information encoded therein. Yes, I said tensors. I have been heavily influenced by these notes by Kip […]

# Conceptual Understanding in Introductory Physics XXIV

This question was inspired by chapters 13, 14, and 15 of Matter & Interactions and would, I think, make a good final exam question even in courses where M&I isn’t used. The story line in those chapters makes a wonderful progression through different charge distributions and their fields and interactions with other similar charge distributions. […]

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# Thoughts on Framing Math in Introductory Physics

This is basically a brain dump. I don’t expect it to be perfectly coherent. Since the summer AAPT meeting in College Park, I’ve been thinking a lot about how mathematics is approached in introductory physics. James Gates pointed out something I’d not realized before. If we consider mathematics a language, then in physics, we don’t speak the […]

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# Conceptual Understanding in Introductory Physics XIX

This is a very quick post addressing a frequently asked conceptual question. Maybe it my heightened awareness, but I’ve also seen this question asked a lot on various physics Q&A sites lately. It’s a question that gets to the heart of how vectors are often defined, loosely and incorrectly, in introductory physics. Here’s the question. […]

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# Conceptual Understanding in Introductory Physics XVIII

The Maxwell equations contain everything mentioned in an introductory calculus-based electromagnetic theory course, and then some. They contain detailed mathematical structure and deep insight into electromagnetic fields. They are a magnificent playground for learning the various theorems of vector calculus, and applying these theorems to the fields of particles naturally leads to things like divergence, […]

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# Conceptual Understanding in Introductory Physics XIII

This question may very well be beyond the scope of a traditional introductory calculus-based physics course, but given the recent trend in early introduction to computational physics with curricula like Matter & Interactions it may be within the scope of a reformed course. In classical physics, finding a particle’s trajectory under the influence of a […]

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# Conceptual Understanding in Introductory Physics XII

This is post is long overdue, and I’m sorry for that. Life and work got busy late in the semester. I have far many more ideas for more posts in this thread that I doubt I’ll ever be able to write them all up but I will try. In this post, I focus on an […]

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# Conceptual Understanding in Introductory Physics XI

In this post, I present a conceptual question that is so important, I feel that no undergraduate student should complete an introductory calculus-based physics course without being able to correctly answer it. Given the way introductory calculus and introductory physics are traditionally taught, I just don’t think there is nearly enough carryover from the calculus […]

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# Conceptual Understanding in Introductory Physics IX

The question in this post continues the thread related to vectors. We really need to do a much better job of treating vectors effectively, and accurately, in introductory. I have been heavily influenced by mathematics colleagues, and in particular by Keith Devlin, in that I have come to see that we should focus more on […]

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# Conceptual Understanding in Introductory Physics VIII

This post’s question reinforces the previous question in this series, which asks the reader to articulate why division by a vector is undefined in Gibbsian vector analysis. Here’s the question: Solve the following vector equation for a: Don’t be deceived. It’s not as straightfoward as it looks. I would really love hearing from colleagues who give […]

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