There is a 1998 update to the book with "modernized" english (I think it is clearer while preserving a dated style) and some additional chapters. ISBN-10: 0312185480
You say 1.9MB, the Gutenberg page says 1.8MB, and the download itself is only 1.18MB thanks to gzip. The main difference is that the Gutenberg PDF is a transcribed, cleaned-up version.
As much as this probably makes me sound like an audiophile, I actually prefer the raw scans over what may essentially be a reprint. They show all the blemishes, unofficial additions, and other marks that make the book look more "real" and give it character.
In this instance, the raw scan has a picture of the cover, as well as an interesting note handwritten near the beginning: "Property of Edward M Sumner" with an address. IMHO these sorts of historical artifacts are worth preserving too. I've come across scans with random notes, bookmark fragments, and newspaper clippings included, and it's always fun to ponder how they got there. (Who is this person and how did he get the book? Is he the one who scanned it? Etc.)
This is why I love used books. My copy of Schopenhauer's collected essays has gone through 4 owners since 1914, all 4 of whom have signed and dated the front cover, all of 4 of whom have marked and underlined at different spots (including, now, myself). My copy of Riverside Chaucer went through two students before me. And they all pick up their own unique scents along the way (my girlfriend jokes that I only buy books to smell them).
Just a side note, off topic: I was that king off person who had a shelf in my house with 300 printed books (and some more stored in boxes in the basement).. it was always a pain when I had to move to a new apartment!
After the e-books and pdfs came by we got a lot of flexibility .. now it's easy to have 3000 volumes in the hard disk. You can literally carry a library with you..
I ended up giving away most of them, apart if some classics (e.g. The art of computer programming from Knuth, Operating Systems, from Tanenbaum, and some other classics for image processing..)
The only thing I miss very much is that I loved the feeling of picking up one at random and expend a couple of hours ... I just can not have the same feeling with e-books.. :(
That was my guess too, but this one actually isn't. Amazon uses "?ref" for reference (innocuous), and "?tag" for affiliates.
For quick reference, a.co and amzn.com are official shorteners and considered safe. amzn.to links however are third-party and often used to conceal affiliate links.
LaTeX is not an aesthetic cure-all. The original, at least, has been subjected to the critical eye of a typesetter. There is no disputing taste, but I will anyway. If you're using an e-paper device, btw, you can vectorize the text in scanned pdfs like this by applying "Clearscan" in Acrobat, or the equivalent (after which, it becomes readable).
Must be something with the program you are using. I've just opened the file on my WP10 device with ancient Snapdragon 400 and I don't see any problem with reading, scrolling etc.
For what it's worth, this is available as a much leaner pdf [1] on Project Gutenberg now, including the TeX source that some kind person used to update it.
It's less than a decade from the cutoff date after which books stopped entering the public domain, so by Project Gutenberg standards, it is pretty modern.
Okay, fantastic, arguably a poor choice of word then. I think it's pretty obvious what I mean, and whether or not 1914 qualifies as 'modern' doesn't affect it in the slightest...
Not a poor choice of words at all, modern must be understood in context and you used it correctly. It would be impossible to ever use the word without a debate on definition otherwise. "How do I build a modern web app? .. Here, I found some relevant resources on vacuum tubes!"
A lot of the elements of what we'd call "modernity" were either introduced or became widespread in the course of the first World War so I'm not trying to just be a jerk here; I think it really is a useful dividing line.
I'm not sure I agree to it being anything stronger than a 'catalyst' period, but regardless; as elsewhere, by 'modern' I meant 'more recent than it is'.
exactly. this was driven home for me when I read babbit by sinclair lewis [1]. It's all about "keeping up with the jones's" consumerism in America. It's amazing that it was written 95 years ago.
I guess what I'm saying is, for me, '... made easy' sounds just as of our time as '... for dummies'. I'm in the UK, maybe it's a more recent phenomenon here? (I naïvely imagine cross-atlantic publication was rarer in the early C20?)
This is, actually, a really good book. Don't let the cheesy title throw you off. I learned more in the first few chapters than I did after a semester of calc classes. Highly recommended.
Summer of 1980, going into my senior year in high school, I mentioned I'd be taking Calculus next year to a co-worker a couple years older than I. He said he had the best book in the world on Calculus, and he loaned me his copy of Silvanus P Thompson's Calculus made easy. I thoroughly enjoyed that book, benefited from its intuitive explanations, and forever appreciated his recommendation.
If I may similarly influence anyone here, for themselves or someone they know, to read Calculus made easy to supplement their calculus coursework, I will be happy to have paid the favor forward in some small way.
By the way, Kalid Azad may be our modern day Silvanus P Thompson. And he has better tools[1], which he wields masterfully, than just pen and paper. Recommended too.
Betterexplained is right up there with the Khan Academy and Wikipedia. Between those three there aren't many subjects you can't improve your knowledge on from your livingroom.
Would you happen to know of any websites, video series, books, etc that would be in the same vein as these 2 sources but geared towards very young students (elementary/middle school math)? ...so that they can understand it conceptually from a young start.
EDIT: I'm working through Khan Academy with one of my kids...would like to find other resources as well.
Keep up with teaching your kids. I took calculus in 8th grade and having it as a base understanding has been invaluable in surviving college engineering.
Hmm, how about a technique rather than a resource...
Look for opportunities to expand what they're doing in school. For example, after my kids had covered place values in school, I taught them binary. Their knowledge of base 10 is so much more robust when they learn base 2 as well.
Point is, I bet you already know plenty to be that ideal resource you seek for them. Good for you for wanting to start early.
Thanks for that affirmation. I actually taught them binary counting too over a weekend a few months back...I was amazed how quickly they were able to pick up on it (3rd and 5th graders). With limited time/energy, I was hoping to find some great resources to add to what I can provide them individually.
I vividly remember cramming for a test my freshman year of college, not having things click, and the final Aha! when a semester of pain disappeared with a few visualizations. The contrast between how most classes presented the material and what actually worked for me was jarring, and I had to share what helped. I hope other people share what works for them, in any format they can.
Concur - Kalid approaches things through first principles and teaches the 'how' very well. The ideas and approaches can be translated into almost anything else. I hope he keeps on keeping on.
I assigned this in an Honors Calc II class I taught at a state university.
The main text was Stewart (decided at the department level), but I was teaching the Honors section which provided a good opportunity for me to ask for something extra. I had my students read this book alongside Stewart, and write weekly short essays comparing the two approaches. Many of the students turned in some quite good writing.
It's not rare that supports the people teaching the class. Nothing like pushing your own book to students that just have to buy it. In some cases the books don't even get used.
> ... a 1998 update by Martin Gardner is available from St. Martin's Press which provides an introduction; three preliminary chapters explaining functions, limits, and derivatives; an appendix of recreational calculus problems; and notes for modern readers. Gardner changes "fifth form boys" to the more American sounding (and gender neutral) "high school students," updates many now obsolescent mathematical notations or terms, and uses American decimal dollars and cents in currency examples.
This is an incredible book. I'm a visual thinker, and while this book lacks all the glossy pages of illustration found in a modern Calculus textbook, the writing style helps develop that visual intuition. In the same vein of concise Calculus books, Serge Lang's Short Calculus is also great (if you need a refresher, or if you're just starting out).
As someone who struggled through calculus, this book would have made a huge difference for me. Just reading through the first few pages brought a smile to my face that someone could so plainly explain these critical concepts in such a familiar way. Why didn't my professors do that?
Totally agree with you. I did advanced research in computer science without fully grasping integrals - only if I had this book!
But you're right, why can't things be like this? Then I think, there is a certain art to having the ability to explain something so easily.. props to reddit's elif subreddit (https://www.reddit.com/r/explainlikeimfive/)
Because to them it's obvious. Most maths teachers are so far ahead of the students they forgot they once were students themselves.
I've had 3 different ones in high school and the difference was incredible. All the way from 'only the best students learn anything' to 'everybody earns at least a passing grade'.
Maths and physics were the classes where the quality difference between the teachers stood out the most.
And to them it's wrong! Much is said in this book which is difficult (but not impossible) to rigourously justify. It took centuries for calculus to be placed on a rigourous mathematical foundation; this foundation (called "real analysis", largely developed in the 19th century) is quite different from the intuitive ideas presented in this book. The presentation here (in particular the idea that dx² is negligible) can be made rigourous through "non-standard analysis", but this 20th century development is less-known (in fact, unknown to many mathematicians) and perhaps even more difficult than real analysis.
Rigour is not necessary to understanding, and can even be fatal to understanding, but it's how mathematicians work, and generally mathematics is taught by mathematicians.
> and generally mathematics is taught by mathematicians
So that leaves the door wide-open to a whole army of mathematicians to who it is unknown that are teachers.
And those are the ones for who all of the above does not apply and who still treat their 'entry level problems' as obvious to all their students even when the evidence strongly suggests that to the students it is not at all obvious.
And I'm writing this as a high school kid who was pretty good in math but totally lost interest due to such teachers (that, and computers were far more interesting).
> this foundation (called "real analysis", largely developed in the 19th century) is quite different from the intuitive ideas presented in this book. ... (in particular the idea that dx² is negligible)
Thank you for posting this! Such things always bothered me in high school, seemed like approximations that ought to bite you in the behind at least in some corner cases. Another example from TLA:
> dy = 2cos(θ + 1/2 dθ) · sin 1/2 dθ
> But if we regard dθ as indefinitely small, then in the limit we may
neglect 1/2 dθ by comparison with θ, and may also take sin 1/2 dθ as being the same as 1/2 dθ. The equation then becomes:
> dy = 2cosθ × 1/2 dθ
This again seems like very sloppy and careless kind of approximation that ought to bite you in the back - but knowing there are just (supposed-to-be) intuitive non-rigorous methods, and that these have actual rigorous backing, somehow soothes me.
But this is true of every level of mathematics. See humorous proofs that 2=3 amounting to manipulations like 0a = 0b, cut the zeros, a=b. This is no fault of "nonrigorous elementary algebra", it's a matter of remembering all notations are abbreviations and you have to know how to manipulate them.
You can get away with dy and dx if you just think "I'm not writing integral signs because they're annoying" and remember the rules of working with integrals. This is how stochastic differential equations work -- they're not even differential equations because Brownian motion is not differentiable, they're just notation.
"dx^2 is negligible" can be alternatively (rigorously) obtained in standard analysis/calculus in the following sequence:
0) Intermediate value theorem (continuous function with image between b and c must be such that there is x such that f(x)=d for d between b and c. This can be first proved where d=0 -- it's the method of bisection by nested intervals, really -- and then generalized)
0.5) The actual definition of derivatives known to everyone.
1) Rolle's theorem, i.e. the Intermediate Value Theorem on first derivatives (if something goes up and down then it must have a critical pont).
2) Mean Value Theorem (Rolle's theorem but rotated)
3) Taylor's theorem.
The prologue had me hooked... I have never read anything like this in a text book. The self-deprecating humor immediately disarms you if you're the type that would go into something like this intimidated. I am definitely reading this.
IIRC this the book Richard Feynman said he checked out of the library and learned calculus from. Also, Feynman made comments similar to those in the Prologue.
IIRC, Feynman mentioned Woods in the context of differentiation under the integral sign, whereas J.E. Thompson was in the context of learning Calculus as a kid.
MIT recorded a set of Calculus video courses back in 1970s that they have since made publicly available. It is taught by a lecturer named Herbert Gross. His style of lecturing is clear, he states why things are defined the way they are and derives everything from first principles. There is an unusual mix of rigor and focus on building understanding - where everything comes from. It also taught me that math is about reasoning logically and rigorously and we shouldn't always rely on intuition (at least while doing math). Deriving almost all the basic calculus results that were drilled into me from the basic concept of a limit, deltas and epsilons was really refreshing.
Compared to more recent OCW calculus videos, I found this to be better in terms of respecting the learner's intellect, presenting the whole proof rigorously and teaching the student to think a certain way.
I watched those lectures in the early stages of my degree and, to confirm what you've stated, they helped me gain a more concrete understanding of the fundamentals of calculus. Highly recommended! Thanks for sharing.
So a while back, I said I am going to start writing "Colloquial books" about all of the courses I took as I relearn all of the stuff in my and other Engineering Branches (minus the grade-gun pointed at my head). One of the first courses are of course Calculus.
I skimmed through some of these video lectures, I wonder if I even should write books for this. Or simply href.
Thank you for the share. Will be of great help to me come summer.
I learned of this euphemism one night at our family dinner table, when I suggested to our teenage kids that we all take some time after dinner to "Netflix and chill." Needless to say, they were a bit surprised by the suggestion. :)
I just had a look at the first video in the first course on YouTube [0] and was delighted to see Herb Gross responding in the comments. Clearly this is a man who loves his subject and loves introducing it to others.
Yes, what a gem of a man.He also posted his email address in the comments for a young high school student for any further help. He is 88 years old now, I hope he is in good health.
That's so beautiful that I have to admit my eyes started to tear a little bit. It's lovely to live in a world in which wonderful people are empowered to touch people all over the world in such a powerful and profound way.
Reminds me of the MIT SICP lecture videos from the 80s. The concepts of black box abstraction and the simplicity of using LISP like lego building blocks blew my mind and made me switch from being a UX designer dabbling in Rails to a full blown programmer.
It was still entirely relevant to today even though it was a few decades old as the fundamentals of computer science are still fundamental.
Hearing that intro music still brings a smile to my face.
I just happen to be relearning math right now as I dive deeper into data science and this is perfect timing. Going to watch this series once I get through my math proofs book ("Book of Proof" by Richard Hammack which I recommend to people getting into math https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...).
Mathematics requires creativity. Conjectures do not arise from logic and rigor. If that were the case, they would never be wrong, and thus not require proof. If mathematicians don't come up with conjectures, then mathematics doesn't advance.
A formal system's territory is connected together by rigor; but whence comes the formal system itself? That has to be imagined.
198 comments
[ 2.3 ms ] story [ 232 ms ] threadThere is a much better PDF at Project Gutenberg [1].
The Gutenberg PDF is only 1.9 MB, compared to 12 MB for the scanned image PDF.
The Gutenberg page for this book [2] also has a link to the LaTeX source for the PDF.
[1] http://www.gutenberg.org/files/33283/33283-pdf.pdf
[2] http://www.gutenberg.org/ebooks/33283
https://github.com/nadvornix/calculus-made-easy/blob/master/...
Weirdly, I can telnet to port 80 & GET / on the ipv6 address just fine.
As much as this probably makes me sound like an audiophile, I actually prefer the raw scans over what may essentially be a reprint. They show all the blemishes, unofficial additions, and other marks that make the book look more "real" and give it character.
In this instance, the raw scan has a picture of the cover, as well as an interesting note handwritten near the beginning: "Property of Edward M Sumner" with an address. IMHO these sorts of historical artifacts are worth preserving too. I've come across scans with random notes, bookmark fragments, and newspaper clippings included, and it's always fun to ponder how they got there. (Who is this person and how did he get the book? Is he the one who scanned it? Etc.)
The problem with used books tho is that sometimes I find hair. Ugh.
The PDF is 1892715 bytes = 1.892715 MB. I rounded to two significant digits, giving 1.9 MB.
When Gutenberg says 1.8 MB they probably actually mean 1.8 MiB. 1892715 bytes = 1.80503368377685546875 MiB, or 1.8 MiB to two significant digits.
https://medievalbooks.nl/2016/02/26/dirty-old-books/
https://medievalbooks.nl/2015/04/24/rare-medieval-name-tags/
https://medievalbooks.nl/2015/04/17/texting-in-medieval-time...
https://www.amazon.com/s/ref=nb_sb_ss_i_3_20?url=search-alia...
Just click the book, then under "Share" click the email button, and you'll see..........
For quick reference, a.co and amzn.com are official shorteners and considered safe. amzn.to links however are third-party and often used to conceal affiliate links.
LaTeX is not an aesthetic cure-all. The original, at least, has been subjected to the critical eye of a typesetter. There is no disputing taste, but I will anyway. If you're using an e-paper device, btw, you can vectorize the text in scanned pdfs like this by applying "Clearscan" in Acrobat, or the equivalent (after which, it becomes readable).
[1] http://any2djvu.djvu.org/djvu/170421/82.132.237.218/57676.17...
(I included the link in case anyone was interested in the quality and to prove I didn't just make up the number!)
[1]: http://www.gutenberg.org/ebooks/33283
I don't know why exactly, it just sounds modern.
And anyway, I confess I don't know the industry at all, but I doubt anyone would talk about 1914 as representing 'modern publishing'.
[1] https://en.wikipedia.org/wiki/Babbitt_(novel)
If I may similarly influence anyone here, for themselves or someone they know, to read Calculus made easy to supplement their calculus coursework, I will be happy to have paid the favor forward in some small way.
By the way, Kalid Azad may be our modern day Silvanus P Thompson. And he has better tools[1], which he wields masterfully, than just pen and paper. Recommended too.
[1] https://betterexplained.com/
tx kjhughes
EDIT: I'm working through Khan Academy with one of my kids...would like to find other resources as well.
Look for opportunities to expand what they're doing in school. For example, after my kids had covered place values in school, I taught them binary. Their knowledge of base 10 is so much more robust when they learn base 2 as well.
Point is, I bet you already know plenty to be that ideal resource you seek for them. Good for you for wanting to start early.
I vividly remember cramming for a test my freshman year of college, not having things click, and the final Aha! when a semester of pain disappeared with a few visualizations. The contrast between how most classes presented the material and what actually worked for me was jarring, and I had to share what helped. I hope other people share what works for them, in any format they can.
The main text was Stewart (decided at the department level), but I was teaching the Honors section which provided a good opportunity for me to ask for something extra. I had my students read this book alongside Stewart, and write weekly short essays comparing the two approaches. Many of the students turned in some quite good writing.
This is an outstanding book.
This is a very small fraction of what goes on -
1) Many many professors have not written a/the book
2) You're not going to sell 1000000's of books through the 1 class you teach every semester. A few, yes. But lots, no.
https://en.wikipedia.org/wiki/Calculus_Made_Easy
Seems like a good update to a classic, but there are some in the reviews complaining about Gardner https://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/...
https://www.amazon.com/Short-Calculus-Original-Undergraduate...
But you're right, why can't things be like this? Then I think, there is a certain art to having the ability to explain something so easily.. props to reddit's elif subreddit (https://www.reddit.com/r/explainlikeimfive/)
Because to them it's obvious. Most maths teachers are so far ahead of the students they forgot they once were students themselves.
I've had 3 different ones in high school and the difference was incredible. All the way from 'only the best students learn anything' to 'everybody earns at least a passing grade'.
Maths and physics were the classes where the quality difference between the teachers stood out the most.
And to them it's wrong! Much is said in this book which is difficult (but not impossible) to rigourously justify. It took centuries for calculus to be placed on a rigourous mathematical foundation; this foundation (called "real analysis", largely developed in the 19th century) is quite different from the intuitive ideas presented in this book. The presentation here (in particular the idea that dx² is negligible) can be made rigourous through "non-standard analysis", but this 20th century development is less-known (in fact, unknown to many mathematicians) and perhaps even more difficult than real analysis.
Rigour is not necessary to understanding, and can even be fatal to understanding, but it's how mathematicians work, and generally mathematics is taught by mathematicians.
> and generally mathematics is taught by mathematicians
So that leaves the door wide-open to a whole army of mathematicians to who it is unknown that are teachers.
And those are the ones for who all of the above does not apply and who still treat their 'entry level problems' as obvious to all their students even when the evidence strongly suggests that to the students it is not at all obvious.
And I'm writing this as a high school kid who was pretty good in math but totally lost interest due to such teachers (that, and computers were far more interesting).
Thank you for posting this! Such things always bothered me in high school, seemed like approximations that ought to bite you in the behind at least in some corner cases. Another example from TLA:
> dy = 2cos(θ + 1/2 dθ) · sin 1/2 dθ
> But if we regard dθ as indefinitely small, then in the limit we may neglect 1/2 dθ by comparison with θ, and may also take sin 1/2 dθ as being the same as 1/2 dθ. The equation then becomes:
> dy = 2cosθ × 1/2 dθ
This again seems like very sloppy and careless kind of approximation that ought to bite you in the back - but knowing there are just (supposed-to-be) intuitive non-rigorous methods, and that these have actual rigorous backing, somehow soothes me.
You can get away with dy and dx if you just think "I'm not writing integral signs because they're annoying" and remember the rules of working with integrals. This is how stochastic differential equations work -- they're not even differential equations because Brownian motion is not differentiable, they're just notation.
0) Intermediate value theorem (continuous function with image between b and c must be such that there is x such that f(x)=d for d between b and c. This can be first proved where d=0 -- it's the method of bisection by nested intervals, really -- and then generalized) 0.5) The actual definition of derivatives known to everyone. 1) Rolle's theorem, i.e. the Intermediate Value Theorem on first derivatives (if something goes up and down then it must have a critical pont). 2) Mean Value Theorem (Rolle's theorem but rotated) 3) Taylor's theorem.
I love this book. What's the best way to learn a mathematical field? To discover it yourself, piece by piece!
I wish this were a series.
http://www.goodreads.com/book/show/7398477-calculus-for-the-...
"... I had a calculus book once that said, 'What one fool can do, another can'..."
I have this in Chapter 9: 'The Smartest Man in the World' in Feynman's book 'The Pleasure of Finding Things Out'.
Compared to more recent OCW calculus videos, I found this to be better in terms of respecting the learner's intellect, presenting the whole proof rigorously and teaching the student to think a certain way.
Calculus Revisited: Single Variable Calculus | MIT OpenCourseWare - https://ocw.mit.edu/resources/res-18-006-calculus-revisited-...
Complex Variables, Differential Equations, and Linear Algebra - https://ocw.mit.edu/resources/res-18-008-calculus-revisited-...
Calculus Revisited: Multivariable Calculus | MIT OpenCourseWare - https://ocw.mit.edu/resources/res-18-007-calculus-revisited-...
I skimmed through some of these video lectures, I wonder if I even should write books for this. Or simply href.
Thank you for the share. Will be of great help to me come summer.
Edit: add smiley face.
[0] https://www.youtube.com/watch?v=MFRWDuduuSw
It was still entirely relevant to today even though it was a few decades old as the fundamentals of computer science are still fundamental.
https://www.youtube.com/watch?v=2Op3QLzMgSY&list=PL8FE88AA54...
Hearing that intro music still brings a smile to my face.
I just happen to be relearning math right now as I dive deeper into data science and this is perfect timing. Going to watch this series once I get through my math proofs book ("Book of Proof" by Richard Hammack which I recommend to people getting into math https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...).
A formal system's territory is connected together by rigor; but whence comes the formal system itself? That has to be imagined.
What one fool can do, another can. -Ancient Simian Proverb
Monkey see, monkey do?