alt Hacker News> This post introduces the Riemann integral
Sweet! I'm keen to learn about the basic fundamentals of calculus!
> For each subinterval ...(bunch of cool maths rendering I can't copy and paste because it's all comes out newline delimited on my clipboard) ... and let m<sub>k</sub> and M<sub>k</sub> denote the infimum and supremum of f on that subinterval...
Okay, guess it wasn't the kind of introduction I had assumed/hoped.
Very cool maths rendering though.
As someone who never passed high school or got a degree thanks to untreated ADHD, 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.
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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.
You could se if it helps with https://betterexplained.com/calculus/lesson-1/ or https://youtu.be/WUvTyaaNkzM
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.
Fair, sorry about that
https://en.wikipedia.org/wiki/Calculus_Made_Easy#:~:text=Cal...
1910 book, but actually does the job well
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
3Blue1Brown has an excellent video series that introduces calculus using very intuitive animations and explanations: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53...