Curl nl

[nelong]

@mitchkeller I have the broad strokes of green's thm and stokes' thm in here as well as a file structure for all of the must-have sections. I wanted to send this out to you while I type up the divergence theorem. It has taken me a long time to format everything even though these are rough ideas. I'm slowly getting PreText into my fingers...

[nelong]

@mitchkeller I have coarse outlines for the divergence theorem and flux integrals in now

[nelong]

@mitchkeller I have updated most files to have consistent tabbing and ptx usage. Everything builds well on my end. Let me know if there is more to do for this merge.

[mitchkeller]

I ran the validator against this branch and found a bunch of things that should get repaired before merging. Validation report attached. (We can talk about some of the things in it when we talk in a bit. The validator can be a bit obtuse at times, and I have plenty of experience understanding what on earth it's saying. I have culled all validation issues involving interactive since it is not yet in the schema properly.)

The tool to use for validation is https://github.com/relaxng/jing-trang, so maybe seeing about getting that up and running to check that you've got things fixed as you work through?

Curl_NL_validation_20200421.txt

[nelong]

@mitchkeller I did the updates on the curl section. After incorporating your suggestions, I think the content here is stronger. I have gone back and forth about adding a subsection about vector potential functions but I think that will be so rarely used that we should skip the idea for now. I am moving back to finalize stuff in the divergence section then I need to work on CalcVR for a couple of days. My collaborator on CalcVR is learning PreTeXt now so we may have questions for you at a later date.

[nelong]

@mitchkeller The divergence section has been edited as well. I hope to pick up the flux integral section in the next few days but I need to write up some other stuff now.

[nelong]

@mitchkeller I have the bulk of the flux integral completed. For working on the divergence theorem section, I will use the div_thm branch. Let me know if you have any questions. See you in a few weeks.

[mitchkeller]

@mitchkeller I have the bulk of the flux integral completed. For working on the divergence theorem section, I will use the div_thm branch. Let me know if you have any questions. See you in a few weeks.

Had a chance to go over this not too carefully today, but I'm liking it. There appears to be a missing yellow vector in Figure 1.8.4.

Are you envisioning that this section will do more with calculating flux through surfaces z=f(x,y), more with parts of cylinders, and something with spheres, or is this going to wind up more as a "the idea of a flux integral" (analogous to what we have for line integrals) and then we have a section that gets more into having students do those specific types of surfaces?

[nelong]

@mitchkeller The flux integral section has a simple surface for the development (z=f(x,y)) and first activity but I plan to add more flux stuff for other kinds of surfaces (there is one cylinder surface in the last activity). I plan to have a variety of surfaces involved in the exercises. Do you think a greater focus is needed on either case?

[mitchkeller]

@mitchkeller The flux integral section has a simple surface for the development (z=f(x,y)) and first activity but I plan to add more flux stuff for other kinds of surfaces (there is one cylinder surface in the last activity). I plan to have a variety of surfaces involved in the exercises. Do you think a greater focus is needed on either case?

This may be my bias toward the Hughes-Hallett approach showing, but I tend to think of the big three of flux integrals being flux through z=f(x,y), part of a cylinder, and part of a sphere. I'm not a fan of the HH method of saying "Here's the magic formula for computing the flux when your surface is X", however. Rereading the last activity, I think it's a nice treatment of the cylinder. Maybe another activity that has two parts to it and looks at z=f(x,y) from a computational perspective (I think it's a nice choice for the motivation that you've done earlier, but I'm not seeing a computational task for the students yet.) and then does the flux through part of a sphere? I'm wary of shunting the full development of any of those three into an exercise.

[nelong]

I think I can make that work.