I wonder what is the best calculus textbook that can be found in Project Gutemberg today. The essence of the subject surely didn't change much in the last 100 years, and publishers today care mostly about sabotaging second hand market by constantly changing exercises and order of subject from one edition to another. Why just not break the museum piece and learn from old books?
There's already open calculus textbooks (see link below for example) that can mention stuff like calculators and computers while also taking advantage of modern typesetting and modern writing styles. Notation has also changed over time, for example using a double struck Z to represent the set of integers only dates to the 1930s but is widely used and understood now.
> publishers today care mostly about sabotaging second hand market by constantly changing exercises and order of subject from one edition to another
Yeah I know what you mean! Eight edition is the same as seventh, but with random permutation of problem sets, just enough so you can't use for class assignment. I once had a teacher who would give us the inverse permutation to make it easy for students to use the older edition, but he was the exception...
Why do you want to learn calculus? If it's for review/fun, I'd like to recomment the MECH+CALC book that I wrote. It's not free, but very cheap. See preview here https://minireference.com/static/excerpts/noBSmathphys_v5_pr... Currently v5.4. I've been treating the problem sets as an append-only list so numbers are "backward compatible" with older versions.
This looks terrific, thank you! I just browsed the PDF, every single page that I looked at is useful content. Just for example, the page with the graphs of position, speed, and acceleration. I'll be honest with you, though. I understand the need to market and be edgy, but the profanity is completely out of place and is a factor in me not buying the book for my teenage daughters. I teach them to present themselves with dignity, and I would be undermining that education by introducing a profane book.
Without a doubt, Calculus Made Easy[0]. Though, I find the PG layout to be atrocious, thankfully, someone has put the material onto a much nicer website [1].
Maybe Calculus Made Easy by S. Thompson (more recently revised by Martin Gardner, but that new edition is under copyright). Maybe Hardy's Course of Pure Mathematics. However...
Modern books use, in some areas and cases, more modern notation and approaches. That's helpful because math is not just knowledge but a language for communicating that knowledge.
If money is an issue[1], either of those Gutenberg texts (re-done with LaTeX), or the OpenStax calculus book are perfectly adequate. There's also no reason you couldn't use an AP Calculus review guide, or Schaum's Outlines, which aren't free but are in the <$25 range. Combined with resources like Youtube math channels, Wikipedia, Mathworld, and Sage and Mathematica (version 12 is freely available for the Raspberry Pi, though it'll be limited by hardware performance), anyone could learn calculus from the most dull and stilted and antiquated-notation calculus books ever written.
Math presented in a slightly obtuse way that doesn't lend itself to instant understanding might actually be better, as it forces the reader to think about the concept more, increasing retention.
Nobody needs Spivak's Calculus. I think it's a bit like the subtle meaning of Frost's Road Less Traveled. Everyone self-rationalizes about how their favorite math book is obviously the best, but in reality most of them probably learned the core of that subject from a different, less elegant book. It's not that it doesn't matter at all; better presentations might avoid an occasional unnecessary struggle over a concept, or lead to faster intuition of a visualization here and there, but it ultimately doesn't matter very much.
However, if you can buy a book (or pirate it) and want a modern digital alternative less like OpenStax or Stewart's, and more like Spivak (which sadly is only available in scans), Velleman's Calculus isn't bad, and you can supplement that with a modern analysis book like Tao, Pugh, or Abbott.
[1] Unless you are flat broke—in which case there's no reason even the most IP-respecting person should feel guilty about raiding libgen for learning material—the cost of a textbook approaches irrelevance when you'll spend 50, 100, or even more hours working through it. The opportunity cost of that time at minimum wage is many times the price of the textbook. What are you trying to accomplish by finding something free? Nobody needs to buy expensive textbooks anymore, but if you're opposed to paying money for textbooks on principle, you might ask yourself why.
