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Calculus Made Easy (1914) [pdf]
- cullinap 6y agogreat book!
- scruple 6y agoIt really is. I was shown this text in high school and it's the thing that got Calculus to click for me. I've recommended it dozens of times over the years and I've heard the same sentiment echoed nearly every time.
- zozbot234 6y ago(1914), rather.
- dang 6y agoSee also: 2018 https://news.ycombinator.com/item?id=18250034 https://news.ycombinator.com/item?id=18250034 2017 https://news.ycombinator.com/item?id=14161876 https://news.ycombinator.com/item?id=14161876
- nikivi 6y agohttp://calculusmadeeasy.org http://calculusmadeeasy.org is better rendering of the book
- champagnepapi 6y agoWow, if only I was shown this book earlier on in life ha.
- DaiPlusPlus 6y agoMe too: it took until 6 months after I started differential calculus (AS-level Pure 1 (UK)) before I grokked what the "d" in dy/dx meant (just like this person: https://physics.stackexchange.com/questions/65724/difference-between-delta-d-and-delta https://physics.stackexchange.com/questions/65724/difference... ) - before then I was treating the differentiation operator as a magic, irreducible, symbol and only getting so far in the course because I was remembering and applying the mechanics of differentiation (i.e. by-rote) instead of really understanding what I was doing.
- woah 6y agoThis is a good book, but the first time I read it, I was puzzled. There's all this stuff about "infinitely small pieces" like every other calculus resource. It wasn't until I had practice using the derivative rules and the chain rule that calculus clicked for me. I think calculus should be taught like "here's a set of tools to help you rewrite your equations to make them output the slope of their graph". Then, afterwards, you can get into what makes it all tick. Sort of like teaching a student to write "hello world" before diving into the low level mechanics of a compiler.
- ducttapecrown 6y agoThe low level "what makes it all tick" of calculus is known as analysis, set theory and the topology of the real line, and is the subject of upper division college math classes. The stuff about "infinitely small pieces" is a mnemonic made to help you remember and intuit the tools of calculus.
- hodgedual 6y agoYou know, I never understood this. Limits (how a function behaves as dx approaches zero) are much easier (for me) to understand than infinitesimals (an idea which obviously can't even exist on the real line), and it's much harder to end up in contradiction.
- todd8 6y agoI agree, I was a math major and remember how high school calculus using infinitesimals ended up confusing my friends in college.
- Koshkin 6y agoYet, the idea of infinitesimals is very popular in applications. For example, in undergrad physics courses, when deriving formulas (essentially, doing math!) they keep talking about a "small area" or a "small volume" (where a given function is assumed to stay constant).
- madhadron 6y ago
- blackrock 6y agoNice book. This looks like a good opportunity for someone to create a website for this, and animate it with some JavaScript code. And insert some ads: Please click here to buy some protractors for 25% off.
- yters 6y agofor another fundamentals approach https://www.amazon.com/Calculus-Ground-Jonathan-Laine-Bartlett/dp/1944918027 https://www.amazon.com/Calculus-Ground-Jonathan-Laine-Bartle...
- madballster 6y agoThat is a beautiful text. Shockingly much more intuitive, better graphs and examples than what we had in high school in the early 90s.
- jeffreyrogers 6y agoI've been relearning some math that I forgot so that I can learn general relativity (just for fun), and this was what I worked through to brush off my calculus. Really great book, and far superior to anything else I've seen. There seem to be two approaches to calculus: dumbed down and mechanical (pretty much any modern non-math major text) or abstract and proof based (something like Spivak). This first group of books takes pages and pages to get to the point and provides no understanding of why calculus works. The second book is just too hard for a normal person who doesn't already know the subject pretty well and who is trying to teach themselves. Calculus Made Easy fits right in the sweet spot. While it isn't entirely rigorous, it does justify everything clearly enough that you can see that the manipulations you're learning are valid. At the same time, it always remains focused on calculations, so you don't get lost in abstractions.
- gigatexal 6y agoi also love how this book takes a conversational and relatable tone. what a nice find, thanks to the op
- gyrfalc 6y agoThis series from 3blue1brown is also an excellent (re-)introduction. Maybe not deep enough to prepare you for relativity, though. https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53...
- jeffreyrogers 6y agoHis videos are good for giving intuition (I also liked the linear algebra ones), but it's really easy to fool yourself into thinking you understanding things better than you do, so you really need to work a lot of problems too.
- seemslegit 6y ago"But compare a farthing with£1000: relatively tothis greater sum, the farthing is of no more importance than11000of afarthing would be to a sovereign. Even a golden sovereign is relativelya negligible quantity in the wealth of a millionaire." I bet the SJWs of his time went out of their way to get him cancelled for using such a class-and-culture specific way of teaching math.
- yesenadam 6y agoI love the exercises in Godement's Algebra (1968), e.g. p111: 15. With the development of purely peaceful space research, the President-Director-General of the Societe Anonyme pour l'Exploitation Financiere de la Physique Purement Theorique, Commander of the Legion of Honneur, had been able to conclude some profitable contracts and has bought a country estate of 200 hectares in Basse-Normandie at 8,000 francs per hectare. Inspired by this example, a plumber employed by the company, earning 800 francs a month, decided to invest a tenth of his wages in savings bonds at 4% interest per annum. How many years will he have to work before he is in a position to buy an estate of 200 hectares in Basse-Normandie and live out the rest of his life in peace and comfort? (You should take account of compound interest, but ignore the effects of possible devaluations of the currency.) 16. According to Le Monde of 21st July 1954, the annual expenditure on the war in Indo-China is given by the following table (the unit is 1,000 million old francs): ... Use this example to verify the fundamental properties of addition (associativity and commutativity). 17. In November 1954, there were in Algeria 1,230,000 Europeans and 8,300,000 native-born Algerians. At the same date, the University of Algiers had 4,548 European and 557 Algerian students. Calculate the ratio between the chances of a European and those of an Algerian of receiving higher education.
- a9h74j 6y agoNice socially-conscious exercise. For possible comparison, I was interested to listen to an interview on KPFA progressive radio with the alleged "math is racist" woman, and unfortunately she did disappoint. One of her first examples was essentially: the one-drop rule involved counting, so counting can be racist. (Every culture counts to one.) On the plus side, in a YouTube video to math teachers she was more about pepping-up teachers, I thought.
- FranzFerdiNaN 6y agoIf only there was a book that explained linear algebra in this way.
- jlangemeier 6y agoLinear Algebra Done Right is, without a doubt, one of my favorites in this category. It tends to be taught as an intermediate or graduate level approach, but things clicked for me with Axler's explanations way better than about anything else I've used. http://linear.axler.net/ http://linear.axler.net/
- nextos 6y agoSadly the last edition turned their beautiful LaTeX typesetting into something really distracting. Aside from Axler, I wish someone picked up Halmos text and rendered it in a more modern way. It's a really good one, a bit more advanced, but the text is so cramped it's unpleasant to follow.
- rmrfstar 6y agoGilbert Strang's linear algebra OCW. It is clear, concise, and practical. As Euclid said, "there is no royal road to geometry."
- bmitc 6y agoThere is the No bullshit guide to linear algebra by Ivan Savov. https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0992001021 https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0...
- ars 6y agoMaybe try this: https://textbooks.math.gatech.edu/ila/index.html https://textbooks.math.gatech.edu/ila/index.html
- del_operator 6y agoI remember entering high school and picking up this book from the library in 9th grade. It was honestly not my favorite. It being called “Calculus Made Easy” had me feeling frustrated. I went to put it back and there was a book next to it called Calculus and Pizza. Within the introduction I got the intuitive feel for differentials and limits. I was able to play with the difference formula and take a much more enthusiastic high level trip through both differential and integral calculus. A big bonus was Calculus and Pizza allowed me to check my algebra in the back of the book and forward those questions to my algebra teacher. That was a few years before I was able to officially take calculus, so I kept re-reading chapters because they were fun. A book with an easy approach really needs to make the chapters super easy to restart and spiral through concepts. Stories and characters didn’t hurt to have too though.
- InnerGargoyle 6y agonow i have to find this one also.
- divbzero 6y agoBrowsing through Calculus Made Easy, I found it curious that the text begins with “On Different Degrees of Smallness” and the limit is mentioned qualitatively but not used formally. It reminds me of the preface to Elementary Calculus [1] [2] an excellent text that I discovered years after learning the subject using the limit: > The calculus was originally developed using the intuitive concept of an infinitesimal, or an infinitely small number. But for the past one hundred years infinitesimals have been banished from the calculus course for reasons of mathematical rigor. Students have had to learn the subject without the original intuition. This calculus book is based on the work of Abraham Robinson, who in 1960 found a way to make infinitesimals rigorous. While the traditional course begins with the difficult limit concept, this course begins with the more easily understood infinitesimals. [1]: https://www.math.wisc.edu/~keisler/calc.html https://www.math.wisc.edu/~keisler/calc.html [2]: https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Infinitesimal_Approach https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Infini...
- cuddlybacon 6y agoWhile I learned calculus, both in highschool and in university, both introductions belabored the concept of an infinitesimal. I remember a good portion of both classes finding the concept confusing. EDIT: It seems like the top-level comment by user woah also finds it confusing.
- apricot 6y agoWhen I took my first calculus class, in the 1980s, we spent the first few weeks of the course just computing limits. No reason was given, and no context, just techniques. I remember having to compute the limit of 2x+1 as x goes to 3 by writing it as the limit of 2x + the limit of 1, and then saying the first limit is 2 times the limit of x, and so on. Utterly boring, especially when the teacher couldn't even answer us when we asked "if we already know we'll get 7 by setting x to 3, why do we have to write all this?" The whole thing almost put me off math. There's a time and place to introduce properties of limits, but the first month of calculus 1 isn't it.
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- lloyddobbler 6y agoThis book is great. Although anytime I see it, my mind jumps to the meme about "If the people who wrote computer programming books wrote math textbooks." https://i.pinimg.com/originals/71/40/36/71403664364a825e76f091ce0a6b2892.jpg https://i.pinimg.com/originals/71/40/36/71403664364a825e76f0...
- julianeon 6y agoIf this book appeals to you then you should see 3 brown 1 blue's videos on YouTube. The way they show the squares with the 'little bits' added in Calculus Made Easy is essentially repeated in 3 brown 1 blue, with graphics.
- wenc 6y agoI was a voracious reader as a kid and came across this book when I was 12, and the prologue sounded particularly amusing to me: -- "Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics — and they are mostly clever fools — seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can." -- It made me believe I could really learn calculus by myself at age 12. After reading the first few chapters, nope. Turns out calculus is built on a foundation of algebra and geometry which I did not have until I was 16. Once I did have the foundation though, calculus became easy and mostly mechanical. But to a 12 year old, this book overpromised and underdelivered. I also found the exposition a little wordy and tedious, like it was written to explain calculus to an English major. It's the sort of book that one appreciates in retrospect after knowing the subject, but not while learning it. I discovered the most effective way for learning math is actually not by reading but to mechanically work through problems to cultivate intuitions and to develop a pattern matching schema. In doing so, one gains confidence that one can actually solve problems. Once this confidence is achieved, going back and delving into the underlying principles becomes so much more contextualized and rewarding. Learning math by reading books like this is like learning to ride a bike by reading about it. You try to understand all the principles, but when you need to deploy them, you find yourself unable to execute. Much better to do it the other way around. EDIT: but I want to soften that by saying that I appreciate not everyone learns this way. It's just I've seen too many struggle with math even though they've read the textbook countless times... when a simple change in stategy would yield much better results.
- kpgiskpg 6y agoCalculus Made Easy has a heap of exercises at the end of each chapter, it's not bad in that respect.
- deleted 6y ago[deleted]
- kpgiskpg 6y agoFunnily enough, I'm working through this book right now. The writing amuses me to no end, from the anachronism of calling it "the calculus" to the chain rule being referred to as a "dodge". It goes well with 3blue1brown's calculus series on YouTube, which gives more of a visual intuition for the concepts.
- bobobob420 6y agoThis is my favorite book on mathematics of all time. I am very happy you shared this so I can save it
- dunefox 6y agoHere: http://calculusmadeeasy.org/ http://calculusmadeeasy.org/
- snapetom 6y agoI love how people discover old, hidden gems like this. Despite what we know about how people learn and modern tools like video resources, every once in a while, someone unearths some decades-old resource that explains things far better than what's available now. It reminds me of when I was learning antenna theory and propagation. I was looking for something that started at step one. The best videos I found on YouTube were a series created in the 1950's by the Royal Canadian Air Force. https://www.youtube.com/watch?v=7bDyA5t1ldU https://www.youtube.com/watch?v=7bDyA5t1ldU
- sajforbes 6y agoA similar thing - the best explanation I've seen about how cars' differential steering works comes from 1937. https://www.youtube.com/watch?v=yYAw79386WI https://www.youtube.com/watch?v=yYAw79386WI
- mlaci 6y agoSimilar: Mechanical computers (for fire control) https://www.youtube.com/watch?v=gwf5mAlI7Ug https://www.youtube.com/watch?v=gwf5mAlI7Ug
- elf25 6y agoNOW YOU TELL ME! Where the Frack where you in 1985 when I was punching that crap into a broken TI-30 and busting lead pencils?
- transitorykris 6y agoBeautiful book, and incredibly lucid. Gave me a useful intuition on infinitesimals that never quite came out in the various standard calc texts. Second to this imo is Serge Lang’s A Short Introduction to Calculus.
- wandering-nomad 6y agoJust read initial few pages and it piqued my interest. Truly love the way it opens and kept me engaged.
- dunefox 6y agoHonest question: did calculus change enough in a hundred years to make this outdated? In other words, can I use this to refresh my calc knowledge in 2020?
- deleted 6y ago[deleted]
- kwhitefoot 6y agoNo calculus hasn't changed and yes if you work though all the exercises you will probably be better at calculus as far is it is explored in the book.
- flyingfences 6y agoI read the first few chapters when this book was last mentioned here and the only thing that stood out to me as "outdated" was the use of pre-decimalization British currency in examples - I think that most modern students will not naturally know how many pence are in a shilling and so forth.
- anthk 6y agoIs there a book like this but for metric?
- kwhitefoot 6y agoDo you mean using SI instead of Imperial units? What difference would it make? For instance Exercises IX (Chapter XI) says: (4) A piece of string 30 inches long has its two ends joined together and is stretched by 3 pegs so as to form a triangle. What is the largest triangular area that can be enclosed by the string? Just replace inches with your linear measure of choice, mm, rods, poles, chains, stadia, light years, or anything else; it makes no difference to the problem. Thompson could have said 'units of length' instead of 'inches'; but the whole purpose of the book is to build on easy notions that Thompson believed everyone could manage and perhaps even be familiar with already, so he used imperial units that were familiar to every handyman of the time instead of metric which would be familiar to far fewer and hence distracting. Also don't forget that there were several distinct 'metric' systems in the past before most of the world settled on SI (MKS, CGS, etc.)
- a3n 6y ago> What one fool can do, another can. (Ancient Simian Proverb.)
- haider_a 6y agoFor anyone interested in the history of calculus, there is an excellent paper: Grabiner, J. (1983). Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus. The American Mathematical Monthly, 90(3), 185-194. doi:10.2307/2975545
- InnerGargoyle 6y agoi think we need list of books like this on each subject which are more explanatory, intuitive rather than mechanical procedures.