My way of taking a break from the … everything of everything has been to try my hand at an updated edition of Silvanus P. Thompson’s classic text, Calculus Made Easy (1914). The book deserves its reputation and holds up quite well overall; I have seen folks who aren’t at all “math people” be charmed by his writing style. However, it is outdated in places, with the occasional antiquated turn of phrase or poorly-aged example. Fortunately, Project Gutenberg has a transcribed version including a ZIP file of the LaTeX source code and auxiliary files. So, I went for a minimal update, fixing the archaisms that pose noticeable stumbling blocks. The result is now available as a PDF document and as source code.
The one thing in Thompson’s presentation that I didn’t particularly like is how he introduces derivatives of trig functions. It presumes that the reader has a lot of trig identities in their back pocket, and it makes a simplification that is hard to justify without going into limits, a topic that Thompson doesn’t explicitly teach. I’ve tried my hand at a replacement that appeals to the way he does teach.
Further modifications may come as people apprise me of all the things I missed. I do wish to keep it short and sweet, rather than adding multiple new chapters.