Calculus

What Hacker News says

1. jacobolusSep 2025
   For a more conceptual introduction leaning on using computers, whose goal was getting STEM students up to speed to understand the context of work in their various fields, you might enjoy https://www.science.smith.edu/~callahan/intromine.html

   For something more traditional, take a look at textbooks by Piskunov, Courant, or Apostol. Spivak's Calculus has excellent problems if you are looking for something more abstract and rigorous (probably better after a first course). https://archive.org/details/n.-piskunov-differential-and-int... ; https://archive.org/details/ost-math-courant-differentialint... ; https://archive.org/details/calculus-tom-m.-apostol-calculus... ; https://archive.org/details/introductory-calculus-book-colle...

   Finally, if you want a strategy for those tricky integrals, per se, take a look at Schoenfeld's "Integration: Getting it All Together", https://files.eric.ed.gov/fulltext/ED214787.pdf ; some results of teaching the solution of integrals by this method were presented in https://www.jstor.org/stable/2320344

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2. anthkMar 2025
   - pdftotext from poppler-tools under Linux/BSD

   - wv/odt2txt and friends

   - cp/m can read TXT files generated from gnuplot

   - A Forth with Starting Forth it's hugely valuable, ditto with a Math Book like the Calculus from Spivak.

   Not a collapse, but a network attach on infra makes most modern OSes unusable, they need to be constantly updated. If you can salvage some older machine with DuskOS+networking, simple gopher and IRC clients/servers will work with really low bandwidth (2/3 KBPS and less).

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3. throwaway81523Jul 2024
   You might like Michael Spivak's "Calculus" as a rigorous approach to what might as well be called introductory real analysis.
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4. hedoraMay 2024
   If you want the opposite of that: University students that come into college with strong calculus fundamentals, then I suggest "Calculus" by Michael Spivak.

   I haven't used calculus in a decade, but I use things I learned from working through that book pretty much every day I write code.

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5. seanhunterMar 2024
   This is one of those things that is extremely insidious because it holds a kernel of truth but the author takes it to a place that in my opinion is really unhelpful.

   For example, his opening paragraph "One of the main problems..." seems fine to me for setting the context, but I would immediately want him to follow with "Let ..." and state the proper definition. All of the extra fluffiness means I have to do two translations - from the fluffy part to the actual maths and then back again - each time to understand what he is getting at.

   In my opinion, great maths writing is both rigourous and engaging. I would use "Calculus" by Michael Spivak as an example. It's really lovely to read but also concise and elegant and the beauty of (and love for) the maths comes through on every page. The author isn't trying to turn it into a short story and it's not padded out with additional rhetorical bullshit like "And now we come to a key player: the group of deck transformations." That sentence makes me want to puke just a little bit.

   But all of the above is a matter of opinion. This, for me is a hard nope:

      This may require “watering down” the results being described — stating corollaries or special cases instead of the full theorems in their maximal generality. Sometimes you may even need to leave out technical conditions required for the results to really be true.
   

   I really really hate it when people do shit like this. State things properly even if you need to say something like "don't worry about x y z condition I put there for now which will be explained later". He says you must warn the reader you're doing this but basically I think this is just a hard pass from then onwards.

   Like if you want to give a simpler version of something, you can by all means do:

   This is known as seanhunter's theorem, which is usually stated as, if blah blah blah...

   When x is a real number greater than zero this can be simplified as follows:

   If x is the number of minutes spent in a meeting and p is the number of participants, then the expected value of the meeting is given by

   v= r/sqrt(x^3p^2) r~N(mu, sigma^2)

   ... or whatever.

   So you give the real version and then the "special case" version that is actually useful most of the time. Like when people give you Fermat's little theorem[1] and they say a^p is congruent with a mod p but that is equivalent to saying if p does not divide a then a^(p-1) congruent with 1 (which is the one you're going to actually use most of the time).

   [1] https://en.wikipedia.org/wiki/Fermat's_little_theorem

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6. laichzeit0Jan 2024
   Yeah I laughed a bit when I saw Rudin’s book on that list. Understanding Analysis would be a better choice, even the end chapters of Spivak’s Calculus are a great into to Real Analysis.
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