3Blue1Brown has an excellent video series that introduces calculus using very intuitive animations and explanations: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53...

If you dive into Analysis (the underlying theory behind calculus) this book - "How to Think About Analysis" by Lara Alcock is the book I wish I had when I studied it. Calculus by Spivak is the book I learnt from but it is probably not the easiest, it is very thorough though.

Yeah, judging by the terseness, this is clearly aimed at undergrads. Then again, this is covered in literally every calculus class, so I'm not sure who this is supposed to be for.

ChatGPT.

You can ask for a syllabus first, then go through it.

It's interactive, and it covers in detail everything you don't get. You can ask infinite many practice material, exercises, flashcards, or anything you want.

https://calculusmadeeasy.org/1.html

You could se if it helps with https://betterexplained.com/calculus/lesson-1/ or https://youtu.be/WUvTyaaNkzM

https://minireference.com/

"The No Bullshit Guide to Math and Physics"

https://en.wikipedia.org/wiki/Calculus_Made_Easy#:~:text=Cal...

1910 book, but actually does the job well

Fair, sorry about that

> if anyone knows of an introduction to the basic fundamentals of calculus that a motivated but under educated maths gronk can grok, I would gratefully appreciate a link or ten.

"The basic fundamentals of calculus" usually go under the name "real analysis".

You have many options for studying it.

MIT OpenCourseWare: https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/

Free calculus-through-nonstandard-analysis textbook: https://people.math.wisc.edu/~hkeisler/calc.html

Lean4 game implementing Alex Kontorovich's undergrad course: https://adam.math.hhu.de/#/g/alexkontorovich/realanalysisgam... (also includes videos of the course lectures)

I like the idea of the lean4 game, because if you do your work in lean you'll know whether you've made a mistake.

("Standard analysis" uses limiting behavior to ask what would happen if we were working with infinitely large or infinitesimally small values, even though of course we aren't really. "Nonstandard analysis" doesn't bother pretending and really uses infinitely large and infinitesimally small values. Other than the notational difference, they are the same, and a proof in one approach can be easily and mechanistically converted into the same proof in the other approach.)

Note that the ordinary course of study involves learning to do calculus problems first (in a "calculus" class), and studying the fundamentals second (in an "analysis" class). The textbook I linked is a "calculus" textbook, but there is a bit more focus on the theoretical backing because you can't rely on the student to learn about nonstandard analysis somewhere else.

Here's my understanding: 1: In the 'olden days' the area A(x) under the graph f(x) used to be approximated as a Riemann sum. 2: Using limits, as the delta x in the Riemann sum->0, we'd call that an integral and set it to be the exact area A(x). 3: If we then look at some small change in A(x), we might notice f(x) = A'(x)... mind blown. 4: since we can now say A is an anti-derivative of f, we have A(x)=F(x)+C (we have to add the C because the derivative of a constant is 0). 5: Using logic and geometry we have C=-F(a) which leads to... 6: The area under the graph f between [a,b] is A = F(b)-F(a). 7: We don't have to cry anymore about pages of Riemann sum calculations.

I recommend Math Academy + Mathematica + YouTube + ChatGPT, Gemini, or Claude Opus and a LOT of motivation.

Khan academy