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The last time I taught freshman calculus-based E&M was in 2007. The main reason I haven't taught it since then is that I wasn't satisfied with my own presentation and didn't have good ideas for how to improve it so as to fix my own objections. There are at least three main things that I don't like about what I perceive to be the standard textbook treatment:

  1. They start with charge, the electric field, and Gauss's law. This is boring because there are few applications, and lab exercises are in short supply because electric fields are not easy to generate and measure directly. It takes much too long to get to DC circuits via this route.

  2. They never mention relativity, and E&M without relativity makes about as much sense as a bicycle for a fish.

  3. They present Maxwell's equations purely in integral form, which obscures the fact that the laws of physics are local, makes them not manifestly consistent with relativity, and makes the treatment of electromagnetic waves obscure.

Problems 1 and 2 are also issues in algebra-based freshman E&M, and I have solutions to these issues that I'm pretty happy with (book). Problem 3 is the one that I struggled with up until 2007 and never ended up happy with. I tried introducing the div, grad, and curl (as is done, for example, in the classic book by Purcell), but this was too difficult intellectually for my student population.

I'm going to be teaching calc-based E&M again in fall 2019, and am planning to spend a lot of time over my winter and summer breaks working up a new presentation. I have a few ideas for how to make this work better, but before I lock myself into a plan, I would like to see if there are other calc-based freshman E&M books out there that could give me new ideas.

Question: Can anyone point me to freshman E&M texts with unusual presentations or orders of topics?

My course is for an audience that has had a year of calculus, but has never seen div, grad, and curl. However, I'm also interested in books at other mathematical levels if they have interesting and nonstandard presentations.

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    $\begingroup$ Ben, are you familiar with David J. Raymond's A Radically Modern Approach to Introductory Physics? $\endgroup$ – Alfred Centauri Oct 2 '18 at 16:03
  • $\begingroup$ Ben, If your students haven't taken AP Physics C in high school, it would be best to teach mechanics first, then E&M, if you have that option. I taught high school AP physics for more than a decade, and it took me a while to understand that physics is very much like a foreign language, due to its standard nomenclature, rules, and concepts. With this being the case, it's easier to "get the feel" of physics when learning mechanics than when learning E&M. $\endgroup$ – David White Oct 2 '18 at 17:09
  • $\begingroup$ Ben, one other comment ... if you must teach E&M, it would help if you would poll the class and find out who has taken AP Physics C in high school. For the people who haven't taken that class, you may want to warn them that your course will be very difficult. $\endgroup$ – David White Oct 2 '18 at 17:12
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    $\begingroup$ @DavidWhite In many (most, I think; certainly everywhere I learned or taught) places the course Ben is talking about has a semester course in intro mechanics as a prerequisite. And in most places the high-school AP C course is sufficient to meet that prerequisite, but I recommend that most students take the college course even so; simply because it lets them become familiar with the pace and intensity of college courses (I make the same recommendation for students who passed out of first semester calculus, too). $\endgroup$ – dmckee Oct 2 '18 at 21:11
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    $\begingroup$ @DavidWhite: What dmckee said is an accurate description of my situation. $\endgroup$ – Ben Crowell Oct 3 '18 at 0:17
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I've used "Field and Wave Electromagnetics" by David K. Cheng during my undergrad/masters in EM/photoncs. The first chapter is devoted to introducing the mathematical concepts needed to understand the mathematics of vector fields and any related math.

Contents:

1: The electromagnetic field

2: Vector analysis

3: static electric fields

4: Solutions to electrostatic problems

5: steady electric currents

6: static magnetic fields

7:T Time-varying fielkds and maxwells equations

8: Plane electromagnetic waves

9: Theory and pplications of transmission lines

10: Waveguides and cavity resonators

11: antenna and radiating systems.

The first good half of the book works with the maxwell equations in their vector form.

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  • $\begingroup$ Interesting, thanks. I imagine this is for an upper-division course that has vector calculus as a prereq? It seems to start off with a focus on fields rather than circuits, which is an idea that I had also been playing around with. $\endgroup$ – Ben Crowell Oct 3 '18 at 0:29
  • $\begingroup$ @BenCrowell Oh perhaps i didn't read your OP enough, i didn't understand you wanted the circuitry integrated and connected, this is purely a book covering static fields and radiation fields. I'd say that linear algebra isn't nessecarily a prerequisite since the first chapter will cover it (for a motivated student) but i would definetly recommend it. In fact, a lot of people fail this course their first time here since their multivariable calculus is not strong enough (less emphasis on linear algebra). $\endgroup$ – DakkVader Oct 3 '18 at 7:22
  • $\begingroup$ The first course we use this in is in a course with only electrostatics and magnetostatics, it is the second course in the second year here (5 year programme, bachelor and thesis packed into one with the ability to stop after 3 years with just a bachelor), and by that time the students have linear algebra, multivariable calculus etc, so perhaps this is too early for your students? Second course it is used in is in a masters course in radiative fields. $\endgroup$ – DakkVader Oct 3 '18 at 7:24
  • $\begingroup$ The book is much too advanced for my students, but that doesn't mean it's not of interest in terms of the presentation and order of topics. I'm not looking for a book to adopt, I'm looking for books to spark ideas so I can do my own presentation. $\endgroup$ – Ben Crowell Oct 3 '18 at 13:53

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