You haven’t seen much from me for a few weeks, but I’ve been doing a lot behind the scenes.
It’s been about three weeks since I’ve published my last article for two reasons:
- I want to finish writing most of the articles in the Mathematical Objects arc before I publish future articles.
- I’ve been tutoring students more frequently since they’ve been having tests and finals.
As you can imagine, the second reason is not going to be as much of a problem soon, so I want to focus on the first reason.
Plans for the Road to Quantum Mechanics
I want to start this update by talking about my plans for the series yet again. This time, I’ll have a much greater focus on the next few articles.
Finishing The Mathematical Objects Arc
Currently the plan for the next few articles in the series will be
- The Generalized Stokes’ Theorem
- An Intro to Tensors
- The Levi-Civita Symbol and Alternating Tensors
- Tensors in Physics (maybe)
- Maxwell’s Equations and Differential Forms
Of these articles, I’ve written the majority of the content for The Generalized Stokes’ Theorem, An Intro to Tensors, and Maxwell’s Equations and Differential Forms. I have started neither Tensors in Physics nor The Levi-Civita Symbol and Alternating Tensors, but I know neither will be difficult. For Tensors in Physics, I plan on talking about continuum mechanics and the multipole expansion using tensors. That article will likely be shorter than my normal articles because I don’t feel that I need to go into any significant depth. For a start, I haven’t built up a Quantum Mechanical model of a solid, so we won’t be able to go into too much depth into the underlying Physics. Plus, if you think of the multipole expansion like a Laurent series, it’s short enough to cover. Likewise, I shouldn’t have too much trouble with The Levi-Civita Symbol and Alternating Tensors because it’s a well-covered topic and the only goal is to rewrite differential forms in terms of tensors.