6 ms·

Calculus Made Easy by Silvanus P. Thompson (1910)

265 points by avinassh 3y ago

2OEH8eoCRo0 3y ago
My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.
- fiforpg 3y ago
  What better hobby to pick for those cold winter evenings, than to do some integrals! Edit: I can recommend this book for a self-guided study https://archive.org/details/zeldovich-higher-mathematics-for-beginners-and-its-application-to-physics-mir-1973 https://archive.org/details/zeldovich-higher-mathematics-for... The author was a Soviet nuclear physicist (who participated in the creation of the H-bomb), so his main point isn't rigor. It can be a nice change of perspective from standard American texts.
  - srvmshr 3y ago
    Although Soviet-era books were notoriously terse & difficult to digest, they had some very aesthetic typesetting. I have owned a few (Problems in Physics by Irodov, & another by Krotov) and they all share similar design aesthetics.
- hotnfresh 3y ago
  Late 30s here. I keep feeling like I should learn math better, but damn, I just never need it. It’s much easier to learn stuff I need. As it is, I’ve lost everything back to about 8th grade math because I’ve never used any of it, so it’s just as gone as all the French I used to know but never found an excuse to use. [edit] and I’m dreading my kids getting past elementary school math because they’re gonna be like “why the hell am I spending months of my life on quadratic equations?” and I’m not gonna have an answer, because IDK why we did that either. At least I have answers for calculus, even if they’re not much good (“so you can do physics stuff”, “right, but will I ever need to do physics stuff?”, “uhhh… unless you really want to, no.”)
  - mlyle 3y ago
    Quadratics are useful-- finding dimensions of things in the plane; relating area and constrained side lengths, etc. They come up a lot if you want to solve problems. And good luck taking on calculus without being super solid in the mathematical tools you use against quadratics -- factoring, completing squares, manipulation of binomials, pairing up like terms, etc.
  - JadeNB 3y ago
    The quadratic equation is completing the square while inexplicably avoiding all the intuition of completing the square. For example, to solve x^2 + 6x + 5 = 0, you would re-write it as (x^2 + 6x + 9) - 4 = 0, which is (x + 3)^2 - 4 = 0 and hence equivalent to (x + 3)^2 = 4, so that x + 3 = ±2 and hence x = 3 ± 2 is 1 or 5. Euclid thought of things this way, though his language is, of course, very different to modern language; see, for example, Proposition 6 of Book II (http://aleph0.clarku.edu/~djoyce/elements/bookII/propII6.html http://aleph0.clarku.edu/~djoyce/elements/bookII/propII6.htm...). That's the same answer as the quadratic formula, but makes a lot more sense to me! Of course I've cooked the numbers so that you don't wind up with surds in the answer, but those are just complications in bookkeeping, not in concept.
  - drdec 3y ago
    Learning mathematics teaches you general concepts of critical thinking. For example, the way to solve a quadratic is to reduce it to a form one knows how to solve (via competing the square). The specifics of the mathematics are not the prize, the methods of thinking are.
    - hotnfresh 3y ago
      If this is true, there is surely a way to present material honing that specific skill as a game or series of games that would generate more intrinsic interest from more kids than math does. I don’t think the methods of thinking per se are why we teach math, though. Might be part of it, but if that’s all, I think we could do a lot better for a lot less effort for all concerned. I think it’s because the math itself is useful. If in fact the point were to teach methods of thinking, I doubt we’d teach it as we do math—why would we, when it generates such resistance and loathing from so many students?
Qem 3y ago
Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus. It can be freely downloaded at https://people.math.wisc.edu/~hkeisler/calc.html https://people.math.wisc.edu/~hkeisler/calc.html Relevant wikipedia entry: https://en.m.wikipedia.org/wiki/Nonstandard_analysis https://en.m.wikipedia.org/wiki/Nonstandard_analysis
- btilly 3y ago
  I have mixed feelings about this. I've been through nonstandard analysis. My response was, "We shouldn't need the axiom of choice to define the derivative." But I think that it is extremely important to understand that the infinitesimal notation really MEANS something. Here is some Python to demonstrate. # d is a functor. It takes a function and returns a second function. # The second function captures the change in f over a small distance. # The dx/2 business reduces artefacts of it being a finite distance. def d (f, dx=0.001): return lambda t: (f(t + dx/2) - f(t - dx/2)) # d²x / dx² def second_derivative (f): return lambda t: d(d(f))(t) / (d(x)(t) * d(x)(t)) def x (t): return t def cubed (t): return t*t*t print("The second derivative of cubed at 1 is near", second_derivative(cubed)(1))
  - btilly 3y ago
    Dang it! I hate re-reading after the time for editing is over and finding a stupid mistake. The Python is correct, but the comment is not. The formula for the second derivative should be, of course: # d²y / dx²
  - finite_depth 3y ago
    Most calculus students don't need the full formal power of rigorous analysis. Calculus, taken alone and with the elementary properties of the real numbers assumed and a few elementary properties of infinitesimals (0 <<< infinitesimal^2 <<< infinitesimal <<< any positive real), can get you a lot of power for very little formal work.
analognoise 3y ago
I think it would be fun to go through all of these books in a group, but to also do worksheets with something like XCas, Maxima, Fricas, etc.
deleted 3y ago
[deleted]
threatofrain 3y ago
Consider Analysis 1 by Terry Tao. It walks you from the very beginning and also uses a conversational style. It's one of the most pedagogically smooth or gentle books I've ever read.
wallflower 3y ago
My calculus teacher tried to talk me out of taking the AP Calculus AB exam because I wasn’t doing that well in his class. “Calculus the Easy Way” which teaches in the setting of a mythical fantasy world where applied problems are solved with calculus unlocked the secret of calculus for me. I ended up scoring a “4” which was a big triumph for me, as it placed me out of taking calculus with all the people who did not want to be taking calculus. https://www.thriftbooks.com/w/calculus-the-easy-way-easy-way-series_douglas-downing/305442/#edition=4365096&idiq=3925121 https://www.thriftbooks.com/w/calculus-the-easy-way-easy-way...
- marai2 3y ago
  Douglas Downing's Trigonometry Made Easy is also a really great book for non-maths people. Same approach of situating Trigonometry in a mythical fantasy land. I remember Trigonometry as a chore of trying to memorize double-angle formulas and such, but this book really helped connect trig in an intuitive way. I didn't know he had a calculus book, I'll have to check it out now.
  - varrock 3y ago
    > Douglas Downing's Trigonometry Made Easy is also a really great book for non-maths people. > but this book really helped connect trig in an intuitive way. To me, understanding math in an intuitive way is actually how "maths people" think about math. The numbers and formulas are just a means to an end to get there.
del_operator 3y ago
I picked this book up when I was learning Algebra to see what the hype was about as a kid. It was dull. I went back to the library stacks after some weeks and found Calculus and Pizza to be even easier to swallow. Calculus Made Easy is a good book. It made me appreciate even easier books when you need them and have enthusiasm for learning a topic.
gramie 3y ago
I graduated from engineering school more than 30 years ago, and learned how to apply calculus without understanding why it worked. This book helped me to finally understand.
jencuduwvd 3y ago
Does anyone know any other good resources for learning calculus at home? Preferably ones that show how and why. I did some in college but I've forgotten just about everything, and now I'm finding myself needing it again.
- mindcrime 3y ago
  > Does anyone know any other good resources for learning calculus at home? Professor Leonard: Calculus I - https://www.youtube.com/playlist?list=PLF797E961509B4EB5 https://www.youtube.com/playlist?list=PLF797E961509B4EB5 Calculus II - https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw- https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1H... Calculus III - https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7 https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ... I consider him one of the best lecturers in math education, at least for these subjects. And in particular because he is very detailed in his explanations. He points out that most students who struggle with Calculus struggle because they (never mastered | forgot | whatever) their basic Algebra. So he does a very thorough job of explaining all of the subtle algebraic manipulations that go on as he works through derivatives, integrals, etc. TBH, I think a person who wanted to learn the equivalent of high-school algebra could just about doing it by watching his Calc I series... and treat any Calculus they learn as "found money." But assuming you remember at least a little algebra and really want to learn Calculus, I think he's one of the best at teaching it. Note that most of his lectures are live lectures to an actual class, so IMO the best way to approach it is to pretend you're right there in class. Listen, take notes, and then when he puts an example on the board pause the video and work through the example. Just restart the video when you finish the problem or if you get stuck. If you want to work additional problems, go on Amazon or Alibris or whatever and buy a cheap used copy of one of the enormous Calculus books, and/or a Shaum's Outlines book on Calculus, or one of those "1001 solved problems in $SUBJECT" books... or some combination of all of the above. Also as a side-note, speaking for myself, I find that I can follow his material find at 1.25x speed, so I pretty much always watch on 1.25x. I could probably manage 1.5x if I really tried, but the time savings from just doing 1.25x is enough to make me happy. YMMV, of course.
- nerdponx 3y ago
  The 3blue1brown "Essence of Calculus" series is a great (re-)introduction to the material, focusing primarily on intuition and understanding. https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&si=ej2ujPfVgS75MVOM https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVR...
xcjs 3y ago
I love projects like this, but I really wish instead of converting text resources to web sites that these projects would produce epub outputs. It's great for distribution, offline reading, and scaling to different display sizes, aspect ratios, and resolutions.
- MrBlueIncognito 3y ago
  I wonder if there will be a time when textbooks will be created in digital-first format, instead of being mere replicas of what print books are. It doesn’t have to be static text and images on A4 pages.
- marcusverus 3y ago
  The page links to a pdf version[0], which can easily be converted to epub using Calibre[0], which is free and open-source. [0] https://www.gutenberg.org/ebooks/33283 https://www.gutenberg.org/ebooks/33283 [1] https://calibre-ebook.com/ https://calibre-ebook.com/
  - xcjs 3y ago
    I'm familiar with those tools, but they don't preserve the formatting of the source document (when PDF) and certain types of embedded resources don't transfer properly. Some PDF documents don't contain the source text as digitized text, either. It's just a bundle of scanned images.
- Almondsetat 3y ago
  Epubs are horrible for technical documents
  - xcjs 3y ago
    Only if they exist as poor conversions. Properly formatted epub documents are worth their weight in effort. Epub documents _are_ HTML files in a zip archive - I'd argue that if a web site is a proper presentation of the source material, an epub is even better. Additionally, PDF documents _are_ worse for any kind of document technical or otherwise. PDF documents are primarily Postscript instructions without any relation or hierarchy to the included elements. Epub documents/HTML provide semantic relationships and hints to the content.
tarkin2 3y ago
Has anyone been through the calculus courses on khan academy? What did you think?
- MrBlueIncognito 3y ago
  I went through them a long time ago. It’s not the most in-depth resource, but you will learn enough calculus for when you need to actually apply it or even just pass tests. Also learning math on KA is really fun, there’s something they just get right. I’d definitely recommend giving it a try. If you don’t feel satisfied after going through the courses, you can always pick up a book afterwards to dig deeper.
WillAdams 3y ago
A newer text is: _Make: Calculus: Build models to learn, visualize, and explore_ by Joan Horvath and Rich Cameron https://www.goodreads.com/book/show/61739368-make https://www.goodreads.com/book/show/61739368-make It's part of a series with matching books on Geometry and Trigonometry.
arbuge 3y ago
If you don't read anything else in this, read the "Epilogue and Apologue".
fakecontent000 3y ago
Want a simple to boost Calculus scores globally? Make the notion standardized. I passed Calculus one and this notion is unrecognizable to me.
lesona 3y ago
Would anyone have any recommendations for books/textbooks of this style and the comment's Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler on Algebra/PreCalc & Trig? I've always wanted to learn math but my teachers could never explain it to me in a way that clicked and any textbook I've read couldn't either. These two above really seem to be in my wheelhouse.
- jskherman 3y ago
  Perhaps Axler's "Precalculus: A Prelude to Calculus"?
andrewfromx 3y ago
When they came to require still smaller subdivisions of time, they divided each minute into 60 still smaller parts, which, in Queen Elizabeth's days, they called “second minùtes” (i.e.: small quantities of the second order of minuteness). Nowadays we call these small quantities of the second order of smallness “seconds.” But few people know why they are so called.
- schoen 3y ago
  A "third minute" (of 1/60 second) could be useful in talking about human reaction times. We could say that people commonly have a reaction time of 7 to 15 thirds, and that alcohol consumption may slow that reaction time by a further 8 thirds or more. Or, speedrunners and professional musicians can practice motions (relative to their own motions or to an ongoing rhythm) that are accurate to about 1 third. I assume the terminology would be too easy to confuse with ⅓, so maybe they would have to be called "terces" or "tertians" or "tertiaries" or something. (Specifically, we want to say (1/60)³ hour rather than (1/3) minute!) And maybe it's not a great thing to introduce a non-decimal unit when we're also trying to get rid of them in many other contexts.
  - schoen 3y ago
    I should follow up and say that I learned that this unit has already been referred to under the name "tierce", although it's not at all common. It could also be useful for measuring latency of Internet connections, although these have commonly gotten faster over time and many latencies can be under a tierce. On the other hand, the round-trip latency to a satellite in geostationary orbit is about 14 tierces.
hyperific 3y ago
> What one fool can do, another can. This quote helped me get over my fear of math. It's probably the fewest words that have made the largest impact in my life.
photon_lines 3y ago
I love this book!!! I also just finished writing a visual/geometric intro to Calculus and the derivative which you can find here: https://photonlines.substack.com/p/visualizing-the-derivative https://photonlines.substack.com/p/visualizing-the-derivativ...
Ninjinka 3y ago
My classical high school used this book
Dropbysometime 3y ago
Thank You. Already loving reading the text. Life long struggle with Calculus ʃ the beast
rottc0dd 3y ago
Another book on calculus for beginners I really liked [1]. [1] - https://www.amazon.com/Short-Calculus-Original-Undergraduate-Mathematics/dp/0387953272 https://www.amazon.com/Short-Calculus-Original-Undergraduate...
QuadrupleA 3y ago
This is the book I learned calculus from (a paperback copy) several years ago. Fairly enjoyable - but I've only found uses for calculus a handful of times as a developer sadly.

265 points by avinassh 3y ago

My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.

fiforpg 3y ago
What better hobby to pick for those cold winter evenings, than to do some integrals! Edit: I can recommend this book for a self-guided study https://archive.org/details/zeldovich-higher-mathematics-for-beginners-and-its-application-to-physics-mir-1973 https://archive.org/details/zeldovich-higher-mathematics-for... The author was a Soviet nuclear physicist (who participated in the creation of the H-bomb), so his main point isn't rigor. It can be a nice change of perspective from standard American texts.
- srvmshr 3y ago
  Although Soviet-era books were notoriously terse & difficult to digest, they had some very aesthetic typesetting. I have owned a few (Problems in Physics by Irodov, & another by Krotov) and they all share similar design aesthetics.
hotnfresh 3y ago
Late 30s here. I keep feeling like I should learn math better, but damn, I just never need it. It’s much easier to learn stuff I need. As it is, I’ve lost everything back to about 8th grade math because I’ve never used any of it, so it’s just as gone as all the French I used to know but never found an excuse to use. [edit] and I’m dreading my kids getting past elementary school math because they’re gonna be like “why the hell am I spending months of my life on quadratic equations?” and I’m not gonna have an answer, because IDK why we did that either. At least I have answers for calculus, even if they’re not much good (“so you can do physics stuff”, “right, but will I ever need to do physics stuff?”, “uhhh… unless you really want to, no.”)
- mlyle 3y ago
  Quadratics are useful-- finding dimensions of things in the plane; relating area and constrained side lengths, etc. They come up a lot if you want to solve problems. And good luck taking on calculus without being super solid in the mathematical tools you use against quadratics -- factoring, completing squares, manipulation of binomials, pairing up like terms, etc.
- JadeNB 3y ago
  The quadratic equation is completing the square while inexplicably avoiding all the intuition of completing the square. For example, to solve x^2 + 6x + 5 = 0, you would re-write it as (x^2 + 6x + 9) - 4 = 0, which is (x + 3)^2 - 4 = 0 and hence equivalent to (x + 3)^2 = 4, so that x + 3 = ±2 and hence x = 3 ± 2 is 1 or 5. Euclid thought of things this way, though his language is, of course, very different to modern language; see, for example, Proposition 6 of Book II (http://aleph0.clarku.edu/~djoyce/elements/bookII/propII6.html http://aleph0.clarku.edu/~djoyce/elements/bookII/propII6.htm...). That's the same answer as the quadratic formula, but makes a lot more sense to me! Of course I've cooked the numbers so that you don't wind up with surds in the answer, but those are just complications in bookkeeping, not in concept.
- drdec 3y ago
  Learning mathematics teaches you general concepts of critical thinking. For example, the way to solve a quadratic is to reduce it to a form one knows how to solve (via competing the square). The specifics of the mathematics are not the prize, the methods of thinking are.
  - hotnfresh 3y ago
    If this is true, there is surely a way to present material honing that specific skill as a game or series of games that would generate more intrinsic interest from more kids than math does. I don’t think the methods of thinking per se are why we teach math, though. Might be part of it, but if that’s all, I think we could do a lot better for a lot less effort for all concerned. I think it’s because the math itself is useful. If in fact the point were to teach methods of thinking, I doubt we’d teach it as we do math—why would we, when it generates such resistance and loathing from so many students?

Qem 3y ago

Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus. It can be freely downloaded at https://people.math.wisc.edu/~hkeisler/calc.html https://people.math.wisc.edu/~hkeisler/calc.html Relevant wikipedia entry: https://en.m.wikipedia.org/wiki/Nonstandard_analysis https://en.m.wikipedia.org/wiki/Nonstandard_analysis

btilly 3y ago
I have mixed feelings about this. I've been through nonstandard analysis. My response was, "We shouldn't need the axiom of choice to define the derivative." But I think that it is extremely important to understand that the infinitesimal notation really MEANS something. Here is some Python to demonstrate. # d is a functor. It takes a function and returns a second function. # The second function captures the change in f over a small distance. # The dx/2 business reduces artefacts of it being a finite distance. def d (f, dx=0.001): return lambda t: (f(t + dx/2) - f(t - dx/2)) # d²x / dx² def second_derivative (f): return lambda t: d(d(f))(t) / (d(x)(t) * d(x)(t)) def x (t): return t def cubed (t): return t*t*t print("The second derivative of cubed at 1 is near", second_derivative(cubed)(1))
- btilly 3y ago
  Dang it! I hate re-reading after the time for editing is over and finding a stupid mistake. The Python is correct, but the comment is not. The formula for the second derivative should be, of course: # d²y / dx²
- finite_depth 3y ago
  Most calculus students don't need the full formal power of rigorous analysis. Calculus, taken alone and with the elementary properties of the real numbers assumed and a few elementary properties of infinitesimals (0 <<< infinitesimal^2 <<< infinitesimal <<< any positive real), can get you a lot of power for very little formal work.

analognoise 3y ago

I think it would be fun to go through all of these books in a group, but to also do worksheets with something like XCas, Maxima, Fricas, etc.

deleted 3y ago

[deleted]

threatofrain 3y ago

Consider Analysis 1 by Terry Tao. It walks you from the very beginning and also uses a conversational style. It's one of the most pedagogically smooth or gentle books I've ever read.

wallflower 3y ago

My calculus teacher tried to talk me out of taking the AP Calculus AB exam because I wasn’t doing that well in his class. “Calculus the Easy Way” which teaches in the setting of a mythical fantasy world where applied problems are solved with calculus unlocked the secret of calculus for me. I ended up scoring a “4” which was a big triumph for me, as it placed me out of taking calculus with all the people who did not want to be taking calculus. https://www.thriftbooks.com/w/calculus-the-easy-way-easy-way-series_douglas-downing/305442/#edition=4365096&idiq=3925121 https://www.thriftbooks.com/w/calculus-the-easy-way-easy-way...

marai2 3y ago
Douglas Downing's Trigonometry Made Easy is also a really great book for non-maths people. Same approach of situating Trigonometry in a mythical fantasy land. I remember Trigonometry as a chore of trying to memorize double-angle formulas and such, but this book really helped connect trig in an intuitive way. I didn't know he had a calculus book, I'll have to check it out now.
- varrock 3y ago
  > Douglas Downing's Trigonometry Made Easy is also a really great book for non-maths people. > but this book really helped connect trig in an intuitive way. To me, understanding math in an intuitive way is actually how "maths people" think about math. The numbers and formulas are just a means to an end to get there.

del_operator 3y ago

I picked this book up when I was learning Algebra to see what the hype was about as a kid. It was dull. I went back to the library stacks after some weeks and found Calculus and Pizza to be even easier to swallow. Calculus Made Easy is a good book. It made me appreciate even easier books when you need them and have enthusiasm for learning a topic.

gramie 3y ago

I graduated from engineering school more than 30 years ago, and learned how to apply calculus without understanding why it worked. This book helped me to finally understand.

jencuduwvd 3y ago

Does anyone know any other good resources for learning calculus at home? Preferably ones that show how and why. I did some in college but I've forgotten just about everything, and now I'm finding myself needing it again.

mindcrime 3y ago
> Does anyone know any other good resources for learning calculus at home? Professor Leonard: Calculus I - https://www.youtube.com/playlist?list=PLF797E961509B4EB5 https://www.youtube.com/playlist?list=PLF797E961509B4EB5 Calculus II - https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw- https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1H... Calculus III - https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7 https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ... I consider him one of the best lecturers in math education, at least for these subjects. And in particular because he is very detailed in his explanations. He points out that most students who struggle with Calculus struggle because they (never mastered | forgot | whatever) their basic Algebra. So he does a very thorough job of explaining all of the subtle algebraic manipulations that go on as he works through derivatives, integrals, etc. TBH, I think a person who wanted to learn the equivalent of high-school algebra could just about doing it by watching his Calc I series... and treat any Calculus they learn as "found money." But assuming you remember at least a little algebra and really want to learn Calculus, I think he's one of the best at teaching it. Note that most of his lectures are live lectures to an actual class, so IMO the best way to approach it is to pretend you're right there in class. Listen, take notes, and then when he puts an example on the board pause the video and work through the example. Just restart the video when you finish the problem or if you get stuck. If you want to work additional problems, go on Amazon or Alibris or whatever and buy a cheap used copy of one of the enormous Calculus books, and/or a Shaum's Outlines book on Calculus, or one of those "1001 solved problems in $SUBJECT" books... or some combination of all of the above. Also as a side-note, speaking for myself, I find that I can follow his material find at 1.25x speed, so I pretty much always watch on 1.25x. I could probably manage 1.5x if I really tried, but the time savings from just doing 1.25x is enough to make me happy. YMMV, of course.
nerdponx 3y ago
The 3blue1brown "Essence of Calculus" series is a great (re-)introduction to the material, focusing primarily on intuition and understanding. https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&si=ej2ujPfVgS75MVOM https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVR...

xcjs 3y ago

I love projects like this, but I really wish instead of converting text resources to web sites that these projects would produce epub outputs. It's great for distribution, offline reading, and scaling to different display sizes, aspect ratios, and resolutions.

MrBlueIncognito 3y ago
I wonder if there will be a time when textbooks will be created in digital-first format, instead of being mere replicas of what print books are. It doesn’t have to be static text and images on A4 pages.
marcusverus 3y ago
The page links to a pdf version[0], which can easily be converted to epub using Calibre[0], which is free and open-source. [0] https://www.gutenberg.org/ebooks/33283 https://www.gutenberg.org/ebooks/33283 [1] https://calibre-ebook.com/ https://calibre-ebook.com/
- xcjs 3y ago
  I'm familiar with those tools, but they don't preserve the formatting of the source document (when PDF) and certain types of embedded resources don't transfer properly. Some PDF documents don't contain the source text as digitized text, either. It's just a bundle of scanned images.
Almondsetat 3y ago
Epubs are horrible for technical documents
- xcjs 3y ago
  Only if they exist as poor conversions. Properly formatted epub documents are worth their weight in effort. Epub documents _are_ HTML files in a zip archive - I'd argue that if a web site is a proper presentation of the source material, an epub is even better. Additionally, PDF documents _are_ worse for any kind of document technical or otherwise. PDF documents are primarily Postscript instructions without any relation or hierarchy to the included elements. Epub documents/HTML provide semantic relationships and hints to the content.

tarkin2 3y ago

Has anyone been through the calculus courses on khan academy? What did you think?

MrBlueIncognito 3y ago
I went through them a long time ago. It’s not the most in-depth resource, but you will learn enough calculus for when you need to actually apply it or even just pass tests. Also learning math on KA is really fun, there’s something they just get right. I’d definitely recommend giving it a try. If you don’t feel satisfied after going through the courses, you can always pick up a book afterwards to dig deeper.

WillAdams 3y ago

A newer text is: _Make: Calculus: Build models to learn, visualize, and explore_ by Joan Horvath and Rich Cameron https://www.goodreads.com/book/show/61739368-make https://www.goodreads.com/book/show/61739368-make It's part of a series with matching books on Geometry and Trigonometry.

arbuge 3y ago

If you don't read anything else in this, read the "Epilogue and Apologue".

fakecontent000 3y ago

Want a simple to boost Calculus scores globally? Make the notion standardized. I passed Calculus one and this notion is unrecognizable to me.

lesona 3y ago

Would anyone have any recommendations for books/textbooks of this style and the comment's Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler on Algebra/PreCalc & Trig? I've always wanted to learn math but my teachers could never explain it to me in a way that clicked and any textbook I've read couldn't either. These two above really seem to be in my wheelhouse.

jskherman 3y ago
Perhaps Axler's "Precalculus: A Prelude to Calculus"?

andrewfromx 3y ago

When they came to require still smaller subdivisions of time, they divided each minute into 60 still smaller parts, which, in Queen Elizabeth's days, they called “second minùtes” (i.e.: small quantities of the second order of minuteness). Nowadays we call these small quantities of the second order of smallness “seconds.” But few people know why they are so called.

schoen 3y ago
A "third minute" (of 1/60 second) could be useful in talking about human reaction times. We could say that people commonly have a reaction time of 7 to 15 thirds, and that alcohol consumption may slow that reaction time by a further 8 thirds or more. Or, speedrunners and professional musicians can practice motions (relative to their own motions or to an ongoing rhythm) that are accurate to about 1 third. I assume the terminology would be too easy to confuse with ⅓, so maybe they would have to be called "terces" or "tertians" or "tertiaries" or something. (Specifically, we want to say (1/60)³ hour rather than (1/3) minute!) And maybe it's not a great thing to introduce a non-decimal unit when we're also trying to get rid of them in many other contexts.
- schoen 3y ago
  I should follow up and say that I learned that this unit has already been referred to under the name "tierce", although it's not at all common. It could also be useful for measuring latency of Internet connections, although these have commonly gotten faster over time and many latencies can be under a tierce. On the other hand, the round-trip latency to a satellite in geostationary orbit is about 14 tierces.

hyperific 3y ago

> What one fool can do, another can. This quote helped me get over my fear of math. It's probably the fewest words that have made the largest impact in my life.

photon_lines 3y ago

I love this book!!! I also just finished writing a visual/geometric intro to Calculus and the derivative which you can find here: https://photonlines.substack.com/p/visualizing-the-derivative https://photonlines.substack.com/p/visualizing-the-derivativ...

Ninjinka 3y ago

My classical high school used this book

Dropbysometime 3y ago

Thank You. Already loving reading the text. Life long struggle with Calculus ʃ the beast

rottc0dd 3y ago

Another book on calculus for beginners I really liked [1]. [1] - https://www.amazon.com/Short-Calculus-Original-Undergraduate-Mathematics/dp/0387953272 https://www.amazon.com/Short-Calculus-Original-Undergraduate...

QuadrupleA 3y ago

This is the book I learned calculus from (a paperback copy) several years ago. Fairly enjoyable - but I've only found uses for calculus a handful of times as a developer sadly.