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