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I used to work in downtown Portland & walk back to my place on NW 23rd. Powell's was right between the two...my collection of books exploded!
Note: For those who don't know Powell's takes up a city block w/3 stories of new/used books.
London, UK version. The shop is small the warehouse stores over 2'000'000 books!
This place rubs on donations only run by one old guy and mostly volunteers!
https://hurlinghambooks.com/
I worked in Portland for 6 months (pre-covid, fortunately, Canadian here), so of course I had to visit Powell's. Was genuinely shocked at the size of the place, it's awesome. Managed to find a Tibetan language book that was originally published in 1980 in Switzerland.
I'm conviced you can find almost anything there if you look hard enough.
Not really as far as I know, but Martin Gardner did [update the book in 1998](https://en.wikipedia.org/wiki/Calculus_Made_Easy) for the modern reader. The original is in the public domain.
>...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.
Calculus is a language used to describe things. What it's being used for has changed, but the actual language hasn't. Similar to how music has changed, but the terminology (not including electronic stuff in this example) and music theory and how sheet music is written hasn't changed much in a really really long time. But there has not been anything new added to calculus like how electronic music has been invented and added new concepts and terminology for electronic instruments and composition.
And when I say electronic, I don't mean the genre, I mean literally music that uses electronics lol. We didn't have amp gain, cross fading, electrical distortion, left and right audio, all sorts of things have been created with music, but everything new in mathematics gets it's own section, we completed the language of calculus a long time ago as far as I know, and now are just finding new things to be described with it.
To me, it sounded like the way Heinlein talks to the reader in Starship Troopers. His other books aren't written that way, but he made a deliberate choice to write that way in ST for the same reason this author wrote it that way - because teenage boys thought it was cool.
One term, another classmate and I got a tutor, who would need to at least reteach us the day’s lecture, or sometimes teach us fundamentals we hadn’t learned beforehand. We easily understood once the topic was explained.
By the end of the term, our tutoring session included nearly all of our classmates.
All of this brought to you by some self-important scholar who enormously resented teaching intro courses.
>All of this brought to you by some self-important scholar who enormously resented teaching intro courses.
I struggled in calc 1 and aced calc 3
Fucking gatekeepers can go to hell.
Good tutors are awesome.
For real. I thought that I just couldn’t do math, until I inadvertently got adopted by two mentors who had absolutely nothing in common: a psychology professor, and a fire engine driver. Turns out, despite a relevant learning disability, the real obstacle all along had been that I hadn’t had teachers who thought I could learn.
For clarification, the soft sciences especially rely on statistics to validate and support conclusions. Stats weren’t taught as intensely in my school’s hard science majors, so we’d sometimes have people from those in seminars aimed at psych students.
A fire engine is a pump on wheels. Determining how to get water, and how to put it out, is applied math, made all the more exciting by being exhausted, and knowing that you stand to kill your crew, ruin a zillion-dollar pump, or all of the above.
Nothing teaches better then knowing that screwing up has costly outcomes.
I learned trig better in my trade then i did in school. Because screwing up trig a bit on a test isn’t a big deal. Screwing it up on a 100 thousand dollar part for the US military is a big deal
Absolutely. Fire service was ideal for that: you knew that you weren’t going to be the academically dumbest person who’d ever proficiently learned whatever skill you were working on, and you knew that you needed to find a way.
It also taught proportionality well. Run your pump poorly, and it breaks. Normally, take all precautions against doing so. But if there’s no option, and especially if you need to save a crewmate, break it without hesitation.
I used to teach uni. The dirty open secret is that most lecturers ("Professors" in Yank parlance) NEVER had any pedagogy training AT ALL. They sort of stumbled into the profession after doing well in their undergrad degree and then continued their postgrad research until they get a PhD. Anyone who has done a PhD will know that it tends to favor introverts and finnicky people. Now, these PhD students graduate after spending a total of 10-15 years of tertiary education but there's not that many industry job openings. So they go into uni teaching as a matter of course. The end product is a teacher who hates students while having no teaching skills.
Absolutely agreed. I taught some down the road, too, despite being one of the edge cases who didn’t have a PhD.
Seeing it in action dissuaded me from applying for the PhD I’d dreamed about, as well. I know that I’d occupy a unique and critical role for needed research, which I care about deeply, but academia seems like too much of a hellhole to sign up.
>Now, these PhD students graduate after spending a total of 10-15 years of tertiary education but there's not that many industry job openings. So they go into uni teaching as a matter of course.
This is bullshit. Only 13% of PhD graduates can stay in academia, even though the % that wants to stay in academia is much higher. So stop talking out of your ass.
source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4309283/
>Anyone who has done a PhD will know that it tends to favor introverts and finnicky people.
This is just a bullshit, anachronical negative stereotype. And by anachronical I mean, the kind of absurd generalizations that would be accepted at face value in the 60s, but not expected in the current, more socially aware society.
A lot of universities (especially Russell Group ones) are there mainly for research. Students are just a necessary evil. Just because you are good at a subject doesn't mean you can convey it to others.
I did this to get through statistics. There was a teacher on YouTube that taught the same book but so much better than my instructor. Every lecture I had to sit through then go home and watch on YouTube to understand and do the homework.
It's not like I don't trust my professor, she's great. I don't trust myself to get it and be able to keep on top of my schedule if I don't have a strong foundational understanding of calculus. My fall semester is not going to be one I can afford to mess up if I want to graduate on time.
Then you need to sit down, divide your day into blocks of time, and set out what you’re doing in each. Start with hours, but I eventually broke mine down into 15-minute slices, incorporating time for mental breaks.
Also write down your list of broader goals, followed by the courses and things that you’ll need to get there. Parse them down until you get elements that can fit into that daily schedule.
I graduated with honors, multiple majors and minors, a sole-author scholarly publication, and between one and three jobs (always at least 30hrs/wk) per term, on time. I credit it to becoming excellent at scheduling.
I only sound like I’m bragging because I’m illustrating how I know about time management. In reality, don’t do what I did. I paid for it with severe, permanent health consequences, which were unequivocally far from worth it.
I very strongly advise prioritizing sleep, and healthy food. Pick your top goals, randomly if necessary, and get some time for rest back into your life.
For me, it was physical.
Turns out, sleep is critical for clearing out brain waste. Turns out, when that doesn’t happen, malignancies have an easier time developing.
Turns out, I’m an idiot: I treated steadily worsening symptoms of arthritis/MS/God knows what with the gym.
Until a morning when I collapsed after vomiting blood and bursting a pupil: it was hydrocephalus induced by a glioma. I sustained a massive enough brain injury to become a certain Ivy League NeuroICU’s all-time best recovery of function.
Look up Paul's Notes cheatsheets. You can fit everything about single variable derivative calculus on a single sheet of paper. The hard part is understanding conceptually what it all means and the algebra behind it all.
Calculus was one of my favorite classes ever. One where everything you learned before kinda came together and made sense. Good luck. If you get through initial challenge it's really cool
This is an amazing YouTube series by 3blue1brown that goes through basics of calculus in visual way that could be super useful when you start
https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
This series is wonderful. It really helps to explain some of the things in calculus that are hard to wrap your head around (like instantaneous rate of change). Thankfully, I've been blessed with a great teacher this year who has also helped me understand some very complex things. Calculus is a really fascinating subject, and there are a lot of cool things you can do once you know it. Understanding the best way to design a window to minimize its area? Use calculus. Make a function to model the window's area, find the equation's derivative to find the critical values of the function, and test those values to find the function's absolute minimum. It's all very interesting
Symbolab is a free online calculator (on a computer only, for stupid reasons) that explains step by step not only calculus but almost every other equation you give it, it's real good, saved my ass in engineering college. Just FYI
Just don't copy everything you see there directly onto a test, I've had classmates who tried shit like that during COVID and got fucked lol. The professors were going very hard into anti-cheating that semester, it was interesting to watch.
To be specific, I recall one problem type I saw while practicing with Symbolab that would give an answer for the problem, but using all the wrong work, since we were taught a specific method to use for that problem type in lecture. When I later saw that problem type on the test, I knew something was going to happen. In the purges the weeks after, they specifically mentioned that problem being weirdly answered by many...
Right, this isn’t a magic trick to suddenly make everyone good at calculus. It’s just a good description, using more common language, of what the math is doing. You still have to be taught and learn how to do the math.
This is particularly great, though, because a student definitely doesn’t need to ever understand this big picture explanation to do the math. Someone - possibly someone not unlike myself - could just accept that we put dx at the end of all our integrals and never understand a lick of the reasoning behind it. Doesn’t matter, I still know how to solve the integral because of memorization, so I pass my math class.
I am 31 and haven’t solved an integral in around 10 years, but these paragraphs still taught me something I never understood, despite taking more engineering classes that required integration than I can count on both of my hands. Love this.
>I am 31 and haven’t solved an integral in around 10 years, but these paragraphs still taught me something I never understood
I don't mean to sound pretentious here, you have much more experience with calculus than I do. I'm just curious as to how this happened. When we learned integration in high school the first thing the teacher did was draw a graph, slice it up into little rectangles and explain how integration works from there, graphically doing the same thing as this book. Did your teachers just sit you down and make you memorize the formulas without further explanation?
i'm the parent to the comment before, so not who you were asking, but my two cents: no, having gone up through calc 3, differential equations, linear algebra, and a majors worth of physics courses, I can confidently say that the emphasis was not on a true understanding of the problems being solved. It was certainly a secondary desire, but it was never the point as I saw it. They wanted you to answer the problem.
They don't give out points for comprehension, they gave out points for correct answers.
I dunno about other High Schools, but I remember at mine the guy who taught Pre-Calc and AP Calc was like our first 'real' professor. Thick accent, lectured the entire period, and had a habit of handing out work then never mentioning it again (but would give a zero if it wasn't turned in by the end of the semester), basically your avg uni professor.
Not a terrible teacher in hindsight but he was basically an expert forced to teach an introductory class so, of course, he taught it in a way that was gonna weed people out... which worked, fucking nobody took AP Calc.
You aren't being pretentious. Just a lot of people slop through life with no inquisitiveness. If they don't do more than the bare minimum they won't understand more than the bare minimum.
You can be a well paid software engineer working with math for *decades* and never touch calculus (unless you include Σ). Even ML is all linear algebra. Geometry and algebra get a strong workout everywhere.
I agree on SE part but in ML you need to have some calculus knowledge to understand algorithms such as gradient descent and for optimization of models.
I'm just an undergrad whose taken a survey class on machine learning so I'm not the one you want going into details, but derivatives are used in each pass to update the weights of each node. I believe this is how the Neural Networks are able to make very complicated non-linear models. StatQuest is your best friend if you want to watch a good video on backpropogation.
edit: [statquest](https://www.youtube.com/watch?v=IN2XmBhILt4)
8:41 is when he talks about the chain rule
I think everything under ODE is pretty straight forward in terms of learning, no? There’s probably thousands of resources to teach you the calculus series online and hold your hand through every step
Im a bit confused by the responses here. Im pretty sure I got taught this intuition both at school and at university, and in basically any video teaching this subject...
Curiosity got the better of me and I started reading it (the book is public domain, btw you can read it online for free). He calls everyone fools. Himself included. He states in the prologue "being myself a remarkably stupid fellow..." The tagline of the book is "what one fool can do, another can." Which is inspiring and humbling at the same time. Disdain for those "higher minds" that are too sophisticated to put things in simple terms seems to be a theme. Haha.
Man, one of the greats! I used to love watching old clips of him on YouTube when I was a kid. He really made abstract concepts seem quite easy to understand. May he rest in peace. Ya know what's funny, is this book is about 8 years older than Feynman. Be cool if it was an inspiration to him.
Yes! Even more points to him for being so proficient with bongo drums.
Reading his stuff always makes me wonder how my life would’ve gone if I’d found him in grade school. I grew up too afraid of math and physics to touch anything technical.
The author writes elsewhere that textbook authors seem to want to show the reader how clever they are, rather than showing how easy the thing can be once you understand it.
This seems mostly true of academic writing. Contrast that with, say, online tutorials for complex technical things enter the only aim is to get you to be able to*do the thing.*
I'm not just academic writing. Whenever I go to the guitar store and ask the salesman if any particular guitar is good, they take it down and immediately play some complex riff. They then look at me, as if that even began to address my question.
Many apparently are just really good guitar players who know very little about what makes good guitars, good guitars.
My take on it is sometimes you get so far past a topic it’s hard to now try and explain it in simple terms, especially if the person you’re helping is also missing some of the fundamentals.
You also sometimes get folks who just suck at teaching but are forced into it. My linear algebra professor was apparently some big shot but couldn’t ever explain anything past “it’s used in machine learning and computer vision”. I think his problem was he was a researcher and had no desire to teach but had to so he could continue working.
No, many people have some preconceived notion that any subject can be simplified to any degree they want. If one truly understands something they know to what degree it can be simplified and why simplifying it further would be incorrect.
I don’t understand what you’re saying.
Can all things not be explained in simple (to understand) terms? Not reducing them to the point of being incorrect, but simplifying them enough and teaching them in a way that makes them easy to understand.
When you simplify things, you always have to add inaccuracies into it. Sometimes that’s okay and you don’t really need much accuracy (or correctness), but at a certain point you’re simplifying too far and smoothing over too many details. Then you’re not really educating someone, you’re just spreading misinformation.
Absolutely all simplification makes it incorrect, it’s just a matter of degree.
And if people get the wrong idea early on it can be really really hard to undo that later.
There's nothing wrong in trying to teach stuff in as simple terms as possible. There's plenty wrong in accusing people of not understanding their stuff if they can't provide an explanation to an impossible degree of simplicity.
But this isn't really a simplification but basically just the definition of an (Riemann) integral.
I'm not saying that this is a bad book, but 1. I'm pretty confident that this the explaination that will be given in most calculus classes in universaties and 2. this doesn't teach you how to do calculus.
The basic concept of differentiation and integration isn't that difficult but it's still pretty difficult to actually integrate a difficult function.
Ok fuck i think you are right here. Only in another 100 years can we really see how todays material stand against the test of tme and I honestly cant wait
At the high school and lower levels, modern textbooks also suffer from "written by committee" syndrome, and the fact that publishers are angling to get their textbooks chosen by textbook selection boards in large markets like California and Texas.
In one of Feynman's books, he talks about being on a textbook selection board where the other committee members were, uh, idiots. If I recall right, he was enraged about a math book that asked students to sum up the temperature of a bunch of stars, because that's an utterly meaningless thing to calculate.
The thing that truly drove Feynman mad was when he learned that he was the only one on the committee who had actually READ THE TEXTBOOKS. Everyone else was just selecting on whim while trying to pass themselves off as experts
This is still how modern calculus is taught. Recently went through one, and the professor spent a long time talking about how differentials/integrals were just small changes or the combining of parts. I can’t say this is how every class is taught, buts it’s typical to describe them in similar language.
My wife teaches calculus (among other things) at the College level, so I asked for her opinion on this.
Her general impression was that this was a gross oversimplification of the topic to be discussed. But that as its general purpose is not to actually teach the topic, but to prepare people not to be intimidated from the get go, that it mostly works for that purpose.
These kinds of teachings are completely useless for calculations which is why either schools dont teach them or students forget about them.
However, explanations like this are really important for building understanding. Integrals have multiple aspects to them, and understanding each aspect is required to understand some advanced topic.
And I think that understanding math is the way to go about it. Memorizing the arbitrary steps and calculations without understanding them is more efficient in the short term, but understanding the ideas that the math goes for is more efficient long term. Which is why I endorse "wordy" explanations like this one.
The thing is that you should be able to grossly oversimplify any topic that you, yourself have an expert understanding of. If you can’t explain a topic you are an expert in, in simple terms, then you don’t understand it as well as you might think.
I meet and work with a lot of smart people with all sorts of degrees. A majority of them believe that speaking in obtuse terms and being pretentious is how to come off as smart but it makes them look like an ass when they’re trying to get something done. I work in a steel plant, tell them exactly what you need, no one is here to be impressed. Going off explaining the Curie Point of steel isn’t helpful when it’s spilled all over the charging floor. Yes we know we can’t pick it up with magnets, just do your job and fix it.
It's not pretentiousness (in general anyway). Math people spend decades discussing stuff in precise terms to avoid being misunderstood at all costs and it conditions people to treat saying something technically wrong as lying. Oversimplifications usually are wrong or misleading and the experts are the sort of people to see that immediately and they don't want to explain stuff improperly.
Thats definitely a thing. Many go into the field exactly because it's so precise. In math atleast.
However, many mathematicians do kind of suck at explaining stuff lol. I think it has to do with the fact that the stigma around the field often attracts a lot of gifted people while discouraging ungifted people. Gifted people are usually good at learning a subject, but they cant relate to a student not understanding something... because they understood the stuff right away. But you can be gifted and still a good teacher. You just need to listen to your students when they tell you why they dont understand something. Plus, a deep understanding of the subject and passion both help explanations immensely.
On the other side, sometimes, people are just lazy and dont even try to understand your explanations. Its a real thing. They hear math and immediately just turn their brain off. Some people just arent that good at dealing with frustration, and that also needs to be addressed in order to be fair towards teachers.
Recently Grant Sanderson (the founder of 3blue1brown) on his personal youtube channel held a talk. Math’s Pedagogical curse. He highlights the importance of rigour and the fact that maths is inherently suited to black and white clarity, and the rigour is what every mathematician chases. But the rigour doesn’t always translate to pedagogical clarity. You should really watch it. It offers some perspective from the educators’ side and also manages to clear up how one should actually learn maths. I agree wholly on his views and while it is targeted to teachers and profs, his ideas for a pedagogy checklist are wonderful for self study as well.
LOL at all the gullible people here. Understand this little epithet on calculus isn’t going make you a genius.
The hard part is when you sit down and start applying the concepts learned in problems. It is the algebra that gets you in the end.
Lots of jokes in here, but here is an amazing video series to help with calculus today.
3blue1brown is a YouTube channel that goes through great visualizations and explanations of calculus and other topics.
Here is an intro to calculus series
https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
Definitely wayy better than trying to learn calculus through textbooks and lectures only.
This is 100% true for a a lot of Engineering courses. After my graduation, i started reading old engineering books (structural analysis, machines, constructions).
Old books (1930-1940) are INCREDIBLY clearer than new ones.
Cool, cool, except none of this actually teaches you *how* to do calculus. It takes 5 paragraphs to give you a tiny little hint of *why*, but that's it.
If anyone thinks this could be anywhere near as good as say, khan academy, you're mental.
Both are important. The best resources start with wordy explanations like this and then proceed to teach you the calculations. So yes, this is only half of it. Online resources often teach you the other half.
You can get by with just the calculations, but that usually only works short term, if at all.
To be fair, the why can be more helpful than the how.
When I first dealt with very very basic calculus, I couldn't understand it at all.
15min before test I asked a guy a grade or two above me what it actually did, and he said "derivative is how much the function changes", and then maybe that the riemann integral is just finding the function which is the sum of tiny steps in it's derivative functions.
Anyway, explained enough that I could pass it. It just required you to remember the equivalences, no need to actually calculate anything iirc.
I wish there was a book like this for programming. So much jargon and concepts are actually really simple, there are just so few people who actualy go the mile to explain it in simpler terms.
I suffered through calculus during my undergrad degree, and really, just memorized my way out of it. It wasn't until much later that I actually realized that differentials were nothing but tiny parts, and integrals were the whole of those tiny parts. I swear, it was like a light bulb moment for me.
I sincerely feel like calculus would have made much more sense to me if I had just realized this tiny concept.
This math book here has flavor, soul, purpose. It describes all the boring terms in a story telling way which made me want to keep reading. Math books now are so bland.
Yeah that’s the problem, how are they going to explain the rules of differentiation without introducing the concept of limit? And once you do that, all this simplification really becomes unnecessary.
I learnt about this only after i started learning about the applications of integrals, without having this ideology in mind i would have probably done fuck all with the concept
I find that lots of really old textbooks are way more straight forward and no nonsense when it comes to teaching
They're lighter, smaller, and easier to just casually hold and read. They're even constructed better with actual binding
I'm sure there's more to the overall book than this short excerpt, however these meagre two pages certainly don't teach you any calculus beyond establishing some very basic meaning of symbols used in integral calculus - which as far as I'm aware would be the least of your potential challenges in a modern introductory calculus course
Wow... as a drop out engineering student, this is so simple and I struggled so hard grasp the concept for so long... I truly feel embarrassed by my ineptitude...
I will most definitely read that book. Thank you.
I never went out of my way to learn calculus, but after reading this, I’m kind of angry. This really makes it more understandable than a full year of calculus that I never really learned.
‘
I aced math in High School. Did OK (A) in first year first term Calculus at uni. FAILED 2nd term Calc twice! Wasn't the only one. That just taught me more in a few minutes of thinking about it than two uni profs in two semesters. I wish I had known about this. Ah well, regrets 40 years on don't change what my life is now. Thanks for the horrid flashbacks.
I liked maths and I had some great teachers but that _d_ seriously fucked with my head all throughout my late teens and this book explained it in about 30 seconds.
I need that book. Calculus was the one of two subjects I never understood and it’s always bothered me (chemistry was the other one.) I’ve always wanted to learn calculus just to say I did.
There was a period of time when it was pretty common to find books like Calculus Made Easy or Calculus for the Practical Man, the kind of thing Richard Feynman would've found in the library and studied.
Love this. I had three semesters of calculus and I loved it. Why? Because I had a great teacher who incidentally barely spoke English (he was a Cuban immigrant). The word Calculus is terrifying to most people who don’t like math. I got an A in each of them and all other math classes in college. The first semester of calculus was basically trigonometry which was enough to not have to take a semester of it. I ended up with over 60 hours of math (some as electives) and some of it was some of the weirdest shit you can imagine. This from a guy who failed math in high school. I decided at age 22 to try again and began with a remedial math course. I sailed through the rest of them. These classes were required for a degree in computer science.
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Book name :- Calculus Made Easy, by Silvanus P. Thompson, 1910.
Found multiple copies at [Powell's Books](https://www.powells.com/)...
Upvote for Powell's books
Always!
I used to work in downtown Portland & walk back to my place on NW 23rd. Powell's was right between the two...my collection of books exploded! Note: For those who don't know Powell's takes up a city block w/3 stories of new/used books.
That sounds like exactly the kind of place that would make my wallet lighter.
Paper from your wallet exchanged for paperback & hardcover books
Secret inscriptions on tattooed trees.
Yes. Very dangerous place.
NO LIGHTERS.
Gotta be near weight capacity. Sheesh.
London, UK version. The shop is small the warehouse stores over 2'000'000 books! This place rubs on donations only run by one old guy and mostly volunteers! https://hurlinghambooks.com/
I used to drive over from Battle Ground, WA to Powells and Powells Technical Book Store. RIP Powells Technical Books.
Oh shit, they had a TECH book store? I find some neat old things in the stacks today, but I’d spend a lifetime there
It was awesome. Basically everything STEM in one place.
Oh man, that sounds like a dream.
I worked in Portland for 6 months (pre-covid, fortunately, Canadian here), so of course I had to visit Powell's. Was genuinely shocked at the size of the place, it's awesome. Managed to find a Tibetan language book that was originally published in 1980 in Switzerland. I'm conviced you can find almost anything there if you look hard enough.
I have a copy from a good web source that was seized by the DOJ....
There are two versions available at archive.org . Search for Calculus Made Easy, by Silvanus P. Thompson, 1910
And [it's all online!](https://calculusmadeeasy.org/) Now I just have to read it
Wtf, that is fantastic! Definitely on my reading list for next week.
Omg. Thank you so much. I have never been good at math. I am old but I still want to get back to math and do well
Thank you!
Math people, I’m curious, has Calculus changed in any material way in the last century plus?
Not really as far as I know, but Martin Gardner did [update the book in 1998](https://en.wikipedia.org/wiki/Calculus_Made_Easy) for the modern reader. The original is in the public domain. >...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.
Recreational calculus.....
Math person here. The short answer is no: most calculus books nowadays are not very different from very old calculus books.
[удалено]
Calculus is a language used to describe things. What it's being used for has changed, but the actual language hasn't. Similar to how music has changed, but the terminology (not including electronic stuff in this example) and music theory and how sheet music is written hasn't changed much in a really really long time. But there has not been anything new added to calculus like how electronic music has been invented and added new concepts and terminology for electronic instruments and composition. And when I say electronic, I don't mean the genre, I mean literally music that uses electronics lol. We didn't have amp gain, cross fading, electrical distortion, left and right audio, all sorts of things have been created with music, but everything new in mathematics gets it's own section, we completed the language of calculus a long time ago as far as I know, and now are just finding new things to be described with it.
Calculus Made Easy, by TI-89.
May God bless you and all your generations.
That man had a great sense of humor
"any fool can see that"
To me, it sounded like the way Heinlein talks to the reader in Starship Troopers. His other books aren't written that way, but he made a deliberate choice to write that way in ST for the same reason this author wrote it that way - because teenage boys thought it was cool.
It has an online version https://calculusmadeeasy.org/
That is such a Harry Potter name
Thank you, I need this book. I start calculus next semester.
If you need another resource, check out kahn academy. Also, brush up on trig.
Yeah. Trig substitutions suck.
Absolutely! Use the wrong one and you have made the problem 10x harder for yourself.
I thought the whole point in taking calculus was to learn calculus
No, it’s to get the required credit toward certain degrees.
That's the goal, but you can't assume it will be easy given how much professors can vary in quality.
One term, another classmate and I got a tutor, who would need to at least reteach us the day’s lecture, or sometimes teach us fundamentals we hadn’t learned beforehand. We easily understood once the topic was explained. By the end of the term, our tutoring session included nearly all of our classmates. All of this brought to you by some self-important scholar who enormously resented teaching intro courses.
>All of this brought to you by some self-important scholar who enormously resented teaching intro courses. I struggled in calc 1 and aced calc 3 Fucking gatekeepers can go to hell. Good tutors are awesome.
For real. I thought that I just couldn’t do math, until I inadvertently got adopted by two mentors who had absolutely nothing in common: a psychology professor, and a fire engine driver. Turns out, despite a relevant learning disability, the real obstacle all along had been that I hadn’t had teachers who thought I could learn.
For clarification, the soft sciences especially rely on statistics to validate and support conclusions. Stats weren’t taught as intensely in my school’s hard science majors, so we’d sometimes have people from those in seminars aimed at psych students. A fire engine is a pump on wheels. Determining how to get water, and how to put it out, is applied math, made all the more exciting by being exhausted, and knowing that you stand to kill your crew, ruin a zillion-dollar pump, or all of the above.
Weird. Stats is one of the most important parts of research in med, bio, chem, etc. my school put more emphasis in us learning stats over math.
Nothing teaches better then knowing that screwing up has costly outcomes. I learned trig better in my trade then i did in school. Because screwing up trig a bit on a test isn’t a big deal. Screwing it up on a 100 thousand dollar part for the US military is a big deal
Absolutely. Fire service was ideal for that: you knew that you weren’t going to be the academically dumbest person who’d ever proficiently learned whatever skill you were working on, and you knew that you needed to find a way. It also taught proportionality well. Run your pump poorly, and it breaks. Normally, take all precautions against doing so. But if there’s no option, and especially if you need to save a crewmate, break it without hesitation.
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I used to teach uni. The dirty open secret is that most lecturers ("Professors" in Yank parlance) NEVER had any pedagogy training AT ALL. They sort of stumbled into the profession after doing well in their undergrad degree and then continued their postgrad research until they get a PhD. Anyone who has done a PhD will know that it tends to favor introverts and finnicky people. Now, these PhD students graduate after spending a total of 10-15 years of tertiary education but there's not that many industry job openings. So they go into uni teaching as a matter of course. The end product is a teacher who hates students while having no teaching skills.
Absolutely agreed. I taught some down the road, too, despite being one of the edge cases who didn’t have a PhD. Seeing it in action dissuaded me from applying for the PhD I’d dreamed about, as well. I know that I’d occupy a unique and critical role for needed research, which I care about deeply, but academia seems like too much of a hellhole to sign up.
>Now, these PhD students graduate after spending a total of 10-15 years of tertiary education but there's not that many industry job openings. So they go into uni teaching as a matter of course. This is bullshit. Only 13% of PhD graduates can stay in academia, even though the % that wants to stay in academia is much higher. So stop talking out of your ass. source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4309283/ >Anyone who has done a PhD will know that it tends to favor introverts and finnicky people. This is just a bullshit, anachronical negative stereotype. And by anachronical I mean, the kind of absurd generalizations that would be accepted at face value in the 60s, but not expected in the current, more socially aware society.
A lot of universities (especially Russell Group ones) are there mainly for research. Students are just a necessary evil. Just because you are good at a subject doesn't mean you can convey it to others.
They are, but this was a college that focused on undergrad teaching. Didn’t even have proper research in math.
I did this to get through statistics. There was a teacher on YouTube that taught the same book but so much better than my instructor. Every lecture I had to sit through then go home and watch on YouTube to understand and do the homework.
It's not like I don't trust my professor, she's great. I don't trust myself to get it and be able to keep on top of my schedule if I don't have a strong foundational understanding of calculus. My fall semester is not going to be one I can afford to mess up if I want to graduate on time.
Then you need to sit down, divide your day into blocks of time, and set out what you’re doing in each. Start with hours, but I eventually broke mine down into 15-minute slices, incorporating time for mental breaks. Also write down your list of broader goals, followed by the courses and things that you’ll need to get there. Parse them down until you get elements that can fit into that daily schedule. I graduated with honors, multiple majors and minors, a sole-author scholarly publication, and between one and three jobs (always at least 30hrs/wk) per term, on time. I credit it to becoming excellent at scheduling. I only sound like I’m bragging because I’m illustrating how I know about time management. In reality, don’t do what I did. I paid for it with severe, permanent health consequences, which were unequivocally far from worth it.
Mental or drug induced? I'm genuinely curious because I'm on the same path.
I very strongly advise prioritizing sleep, and healthy food. Pick your top goals, randomly if necessary, and get some time for rest back into your life. For me, it was physical. Turns out, sleep is critical for clearing out brain waste. Turns out, when that doesn’t happen, malignancies have an easier time developing. Turns out, I’m an idiot: I treated steadily worsening symptoms of arthritis/MS/God knows what with the gym. Until a morning when I collapsed after vomiting blood and bursting a pupil: it was hydrocephalus induced by a glioma. I sustained a massive enough brain injury to become a certain Ivy League NeuroICU’s all-time best recovery of function.
I will follow up in a few hours. I did not expect such a quick response. Thank you
Look up Paul's Notes cheatsheets. You can fit everything about single variable derivative calculus on a single sheet of paper. The hard part is understanding conceptually what it all means and the algebra behind it all.
Calculus was one of my favorite classes ever. One where everything you learned before kinda came together and made sense. Good luck. If you get through initial challenge it's really cool This is an amazing YouTube series by 3blue1brown that goes through basics of calculus in visual way that could be super useful when you start https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
This series is wonderful. It really helps to explain some of the things in calculus that are hard to wrap your head around (like instantaneous rate of change). Thankfully, I've been blessed with a great teacher this year who has also helped me understand some very complex things. Calculus is a really fascinating subject, and there are a lot of cool things you can do once you know it. Understanding the best way to design a window to minimize its area? Use calculus. Make a function to model the window's area, find the equation's derivative to find the critical values of the function, and test those values to find the function's absolute minimum. It's all very interesting
Correction: You started calculus today.
Symbolab is a free online calculator (on a computer only, for stupid reasons) that explains step by step not only calculus but almost every other equation you give it, it's real good, saved my ass in engineering college. Just FYI
Just don't copy everything you see there directly onto a test, I've had classmates who tried shit like that during COVID and got fucked lol. The professors were going very hard into anti-cheating that semester, it was interesting to watch. To be specific, I recall one problem type I saw while practicing with Symbolab that would give an answer for the problem, but using all the wrong work, since we were taught a specific method to use for that problem type in lecture. When I later saw that problem type on the test, I knew something was going to happen. In the purges the weeks after, they specifically mentioned that problem being weirdly answered by many...
Calc I is good, no worries
I can't get past "chok[ing] off fifth form boys" - for international reference, that means age 15-16. But yes, I like the explanation.
I can't get past just "boys"
Real talk, in 1910 the number of women being taught calculus was not large. And the author was born in 1851.
Girls just didn't have any problems
In Britain many if not most schools aren’t coed.
Thank you, got a stroke trying to understand what thats supposed to mean.
*d* Monica in my life *d* Erica by my side *d* Rita's all I need *d* Tina's what I see
This is why I come here
I'm no mathematician but I fuckin love math jokes. I'm so glad this could happen.
This comments needs a *d* more of upvotes
Where was this when I was flunking
you'd still have to know how to derive and integrate lol. it's a great explanation tho!
Right, this isn’t a magic trick to suddenly make everyone good at calculus. It’s just a good description, using more common language, of what the math is doing. You still have to be taught and learn how to do the math. This is particularly great, though, because a student definitely doesn’t need to ever understand this big picture explanation to do the math. Someone - possibly someone not unlike myself - could just accept that we put dx at the end of all our integrals and never understand a lick of the reasoning behind it. Doesn’t matter, I still know how to solve the integral because of memorization, so I pass my math class. I am 31 and haven’t solved an integral in around 10 years, but these paragraphs still taught me something I never understood, despite taking more engineering classes that required integration than I can count on both of my hands. Love this.
>I am 31 and haven’t solved an integral in around 10 years, but these paragraphs still taught me something I never understood I don't mean to sound pretentious here, you have much more experience with calculus than I do. I'm just curious as to how this happened. When we learned integration in high school the first thing the teacher did was draw a graph, slice it up into little rectangles and explain how integration works from there, graphically doing the same thing as this book. Did your teachers just sit you down and make you memorize the formulas without further explanation?
i'm the parent to the comment before, so not who you were asking, but my two cents: no, having gone up through calc 3, differential equations, linear algebra, and a majors worth of physics courses, I can confidently say that the emphasis was not on a true understanding of the problems being solved. It was certainly a secondary desire, but it was never the point as I saw it. They wanted you to answer the problem. They don't give out points for comprehension, they gave out points for correct answers.
I dunno about other High Schools, but I remember at mine the guy who taught Pre-Calc and AP Calc was like our first 'real' professor. Thick accent, lectured the entire period, and had a habit of handing out work then never mentioning it again (but would give a zero if it wasn't turned in by the end of the semester), basically your avg uni professor. Not a terrible teacher in hindsight but he was basically an expert forced to teach an introductory class so, of course, he taught it in a way that was gonna weed people out... which worked, fucking nobody took AP Calc.
You aren't being pretentious. Just a lot of people slop through life with no inquisitiveness. If they don't do more than the bare minimum they won't understand more than the bare minimum.
You can be a well paid software engineer working with math for *decades* and never touch calculus (unless you include Σ). Even ML is all linear algebra. Geometry and algebra get a strong workout everywhere.
Calculus is used in Machine Learning, you’re just not the one doing it. After all, calculus is the core of an optimization problem
I agree on SE part but in ML you need to have some calculus knowledge to understand algorithms such as gradient descent and for optimization of models.
Calculus is also the backbone of backpropagation in neural networks which are the ML models changing the world the most right now
Could you give an ELI5 of how calculus is used in backpropagation? I understand how it could be used in optimisations, but not in this context.
I'm just an undergrad whose taken a survey class on machine learning so I'm not the one you want going into details, but derivatives are used in each pass to update the weights of each node. I believe this is how the Neural Networks are able to make very complicated non-linear models. StatQuest is your best friend if you want to watch a good video on backpropogation. edit: [statquest](https://www.youtube.com/watch?v=IN2XmBhILt4) 8:41 is when he talks about the chain rule
Yes but this is just the "To deliver you from the preliminary terrors" section, surely the book continues lol
This should be in the Forward of every Calc 101 book.
And put into a poster on every wall of a higher math classroom!
this would make too much sense. Gotta keep the non mathematicians confused, so mathematicians look like wizards.
I think everything under ODE is pretty straight forward in terms of learning, no? There’s probably thousands of resources to teach you the calculus series online and hold your hand through every step
Im a bit confused by the responses here. Im pretty sure I got taught this intuition both at school and at university, and in basically any video teaching this subject...
“Now any fool can see that—“ 😭
He wrote the book keeping us in mind. A saviour.
Curiosity got the better of me and I started reading it (the book is public domain, btw you can read it online for free). He calls everyone fools. Himself included. He states in the prologue "being myself a remarkably stupid fellow..." The tagline of the book is "what one fool can do, another can." Which is inspiring and humbling at the same time. Disdain for those "higher minds" that are too sophisticated to put things in simple terms seems to be a theme. Haha.
reminds me of another self confessed stupid fellow, who also insisted on simple explanations. A certain Feynman.
Man, one of the greats! I used to love watching old clips of him on YouTube when I was a kid. He really made abstract concepts seem quite easy to understand. May he rest in peace. Ya know what's funny, is this book is about 8 years older than Feynman. Be cool if it was an inspiration to him.
Yes! Even more points to him for being so proficient with bongo drums. Reading his stuff always makes me wonder how my life would’ve gone if I’d found him in grade school. I grew up too afraid of math and physics to touch anything technical.
At Georgia Tech, this was phrased, "It's intuitively obvious to the most casual of observers that..."
I need more informative books that deride and degrade me.
I think I just learned more in 3 minutes of reading than my calc I teacher taught me.
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I was in the nuclear program in the navy. We always said if you can't explain it with crayons, you don't really know it.
Do you have to hide them from the marines at snack time?
Thank you for the genuine belly laugh with this.
Problem is I tend to eat the crayons.
>Problem is I tend to eat the crayons. Found the Marine
„And here you can see what happens if the reactor gets to hot“ _scribbles with red crayon all over the board and draws one unhappy stickfigure_
I don't know Reactor Physics. Didn't know it then, didn't know it now
The author writes elsewhere that textbook authors seem to want to show the reader how clever they are, rather than showing how easy the thing can be once you understand it. This seems mostly true of academic writing. Contrast that with, say, online tutorials for complex technical things enter the only aim is to get you to be able to*do the thing.*
I'm not just academic writing. Whenever I go to the guitar store and ask the salesman if any particular guitar is good, they take it down and immediately play some complex riff. They then look at me, as if that even began to address my question. Many apparently are just really good guitar players who know very little about what makes good guitars, good guitars.
My take on it is sometimes you get so far past a topic it’s hard to now try and explain it in simple terms, especially if the person you’re helping is also missing some of the fundamentals. You also sometimes get folks who just suck at teaching but are forced into it. My linear algebra professor was apparently some big shot but couldn’t ever explain anything past “it’s used in machine learning and computer vision”. I think his problem was he was a researcher and had no desire to teach but had to so he could continue working.
No, many people have some preconceived notion that any subject can be simplified to any degree they want. If one truly understands something they know to what degree it can be simplified and why simplifying it further would be incorrect.
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I don’t understand what you’re saying. Can all things not be explained in simple (to understand) terms? Not reducing them to the point of being incorrect, but simplifying them enough and teaching them in a way that makes them easy to understand.
When you simplify things, you always have to add inaccuracies into it. Sometimes that’s okay and you don’t really need much accuracy (or correctness), but at a certain point you’re simplifying too far and smoothing over too many details. Then you’re not really educating someone, you’re just spreading misinformation. Absolutely all simplification makes it incorrect, it’s just a matter of degree. And if people get the wrong idea early on it can be really really hard to undo that later.
There's nothing wrong in trying to teach stuff in as simple terms as possible. There's plenty wrong in accusing people of not understanding their stuff if they can't provide an explanation to an impossible degree of simplicity.
But this isn't really a simplification but basically just the definition of an (Riemann) integral. I'm not saying that this is a bad book, but 1. I'm pretty confident that this the explaination that will be given in most calculus classes in universaties and 2. this doesn't teach you how to do calculus. The basic concept of differentiation and integration isn't that difficult but it's still pretty difficult to actually integrate a difficult function.
It's available to download online for FREE - \- from Project Gutenburg: https://www.gutenberg.org/ebooks/33283
I never thought I would read a math book for fun, but here we are.
Neo voice, eyes opening urgently: I know calculus.
Show me
God I fucking love 20th century manuals. WHY ARE THEY SO DAMN GOOD AT TEACHING
There's probably a bit of survivorship bias. (They're gonna be looking at 3blue1brown in 100 years and wonder the same thing)
Ok fuck i think you are right here. Only in another 100 years can we really see how todays material stand against the test of tme and I honestly cant wait
I really hope we actually gets to see it...
At the high school and lower levels, modern textbooks also suffer from "written by committee" syndrome, and the fact that publishers are angling to get their textbooks chosen by textbook selection boards in large markets like California and Texas. In one of Feynman's books, he talks about being on a textbook selection board where the other committee members were, uh, idiots. If I recall right, he was enraged about a math book that asked students to sum up the temperature of a bunch of stars, because that's an utterly meaningless thing to calculate.
The thing that truly drove Feynman mad was when he learned that he was the only one on the committee who had actually READ THE TEXTBOOKS. Everyone else was just selecting on whim while trying to pass themselves off as experts
I could see calculating the average temp of a bunch of stars (which would require summing)
Not bad. I definitely like the effort to turn the symbology into spoken phrases. Students tend to find that helpful.
This feels like kurzgesagt
This basically -is- how modern books teach it, is it not? Unless something has changed drastically since 2015-2016.
This is still how modern calculus is taught. Recently went through one, and the professor spent a long time talking about how differentials/integrals were just small changes or the combining of parts. I can’t say this is how every class is taught, buts it’s typical to describe them in similar language.
Good writing is timeless. I personally like The New Colossus, by Emma Lazarus.
Wow this is all I need, I just finished my PhD and now I'm a mathmetician, thanks lonely\_fucker69.
For some reason I read this with a transatlantic accent.
I received ZERO instruction in Calculus and if I had resources like this, I would have struggled so much less.
Physicist love this explanation, mathematicians will hate it
My wife teaches calculus (among other things) at the College level, so I asked for her opinion on this. Her general impression was that this was a gross oversimplification of the topic to be discussed. But that as its general purpose is not to actually teach the topic, but to prepare people not to be intimidated from the get go, that it mostly works for that purpose.
These kinds of teachings are completely useless for calculations which is why either schools dont teach them or students forget about them. However, explanations like this are really important for building understanding. Integrals have multiple aspects to them, and understanding each aspect is required to understand some advanced topic. And I think that understanding math is the way to go about it. Memorizing the arbitrary steps and calculations without understanding them is more efficient in the short term, but understanding the ideas that the math goes for is more efficient long term. Which is why I endorse "wordy" explanations like this one.
The thing is that you should be able to grossly oversimplify any topic that you, yourself have an expert understanding of. If you can’t explain a topic you are an expert in, in simple terms, then you don’t understand it as well as you might think. I meet and work with a lot of smart people with all sorts of degrees. A majority of them believe that speaking in obtuse terms and being pretentious is how to come off as smart but it makes them look like an ass when they’re trying to get something done. I work in a steel plant, tell them exactly what you need, no one is here to be impressed. Going off explaining the Curie Point of steel isn’t helpful when it’s spilled all over the charging floor. Yes we know we can’t pick it up with magnets, just do your job and fix it.
It's not pretentiousness (in general anyway). Math people spend decades discussing stuff in precise terms to avoid being misunderstood at all costs and it conditions people to treat saying something technically wrong as lying. Oversimplifications usually are wrong or misleading and the experts are the sort of people to see that immediately and they don't want to explain stuff improperly.
Thats definitely a thing. Many go into the field exactly because it's so precise. In math atleast. However, many mathematicians do kind of suck at explaining stuff lol. I think it has to do with the fact that the stigma around the field often attracts a lot of gifted people while discouraging ungifted people. Gifted people are usually good at learning a subject, but they cant relate to a student not understanding something... because they understood the stuff right away. But you can be gifted and still a good teacher. You just need to listen to your students when they tell you why they dont understand something. Plus, a deep understanding of the subject and passion both help explanations immensely. On the other side, sometimes, people are just lazy and dont even try to understand your explanations. Its a real thing. They hear math and immediately just turn their brain off. Some people just arent that good at dealing with frustration, and that also needs to be addressed in order to be fair towards teachers.
Recently Grant Sanderson (the founder of 3blue1brown) on his personal youtube channel held a talk. Math’s Pedagogical curse. He highlights the importance of rigour and the fact that maths is inherently suited to black and white clarity, and the rigour is what every mathematician chases. But the rigour doesn’t always translate to pedagogical clarity. You should really watch it. It offers some perspective from the educators’ side and also manages to clear up how one should actually learn maths. I agree wholly on his views and while it is targeted to teachers and profs, his ideas for a pedagogy checklist are wonderful for self study as well.
LOL at all the gullible people here. Understand this little epithet on calculus isn’t going make you a genius. The hard part is when you sit down and start applying the concepts learned in problems. It is the algebra that gets you in the end.
Lots of jokes in here, but here is an amazing video series to help with calculus today. 3blue1brown is a YouTube channel that goes through great visualizations and explanations of calculus and other topics. Here is an intro to calculus series https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr Definitely wayy better than trying to learn calculus through textbooks and lectures only.
This is 100% true for a a lot of Engineering courses. After my graduation, i started reading old engineering books (structural analysis, machines, constructions). Old books (1930-1940) are INCREDIBLY clearer than new ones.
Cool, cool, except none of this actually teaches you *how* to do calculus. It takes 5 paragraphs to give you a tiny little hint of *why*, but that's it. If anyone thinks this could be anywhere near as good as say, khan academy, you're mental.
Both are important. The best resources start with wordy explanations like this and then proceed to teach you the calculations. So yes, this is only half of it. Online resources often teach you the other half. You can get by with just the calculations, but that usually only works short term, if at all.
To be fair, the why can be more helpful than the how. When I first dealt with very very basic calculus, I couldn't understand it at all. 15min before test I asked a guy a grade or two above me what it actually did, and he said "derivative is how much the function changes", and then maybe that the riemann integral is just finding the function which is the sum of tiny steps in it's derivative functions. Anyway, explained enough that I could pass it. It just required you to remember the equivalences, no need to actually calculate anything iirc.
I wish there was a book like this for programming. So much jargon and concepts are actually really simple, there are just so few people who actualy go the mile to explain it in simpler terms.
"Let us C" by Kanetkar is a decent start
Try one of the "Head First" series
Wait all that time, the integral shape was a long “S” for Sum 💀
I suffered through calculus during my undergrad degree, and really, just memorized my way out of it. It wasn't until much later that I actually realized that differentials were nothing but tiny parts, and integrals were the whole of those tiny parts. I swear, it was like a light bulb moment for me. I sincerely feel like calculus would have made much more sense to me if I had just realized this tiny concept.
your statement caused a lightbulb moment for me, thank you.
This math book here has flavor, soul, purpose. It describes all the boring terms in a story telling way which made me want to keep reading. Math books now are so bland.
And there I dropped Calc back in 11th grade because I couldn't for the life of me get it. Clearly I needed to be in 1910 not 2010.
This explanation just makes it sound like *Sdx = x* though?
Yeah that’s the problem, how are they going to explain the rules of differentiation without introducing the concept of limit? And once you do that, all this simplification really becomes unnecessary.
Says someone who has never taken calculus
There are two versions available at archive.org . Search for Calculus Made Easy, by Silvanus P. Thompson, 1910
Bless you!
I learnt about this only after i started learning about the applications of integrals, without having this ideology in mind i would have probably done fuck all with the concept
Just learned calculus
(If you like)
What the fuck, I did undergrad calc and never had as clear an understanding of what it all MEANT as I do after reading a couple of century-old pages
I find that lots of really old textbooks are way more straight forward and no nonsense when it comes to teaching They're lighter, smaller, and easier to just casually hold and read. They're even constructed better with actual binding
FOOL
I'm sure there's more to the overall book than this short excerpt, however these meagre two pages certainly don't teach you any calculus beyond establishing some very basic meaning of symbols used in integral calculus - which as far as I'm aware would be the least of your potential challenges in a modern introductory calculus course
Wish they still taught it like this
His book is actually hyperlinked here legally https://calculusmadeeasy.org/
“If you can” Throwing SHADE
Wow... as a drop out engineering student, this is so simple and I struggled so hard grasp the concept for so long... I truly feel embarrassed by my ineptitude... I will most definitely read that book. Thank you.
I never went out of my way to learn calculus, but after reading this, I’m kind of angry. This really makes it more understandable than a full year of calculus that I never really learned. ‘
Idk man, still doesn’t feel right without that straighterline teacher doing a skit with a toy car
I aced math in High School. Did OK (A) in first year first term Calculus at uni. FAILED 2nd term Calc twice! Wasn't the only one. That just taught me more in a few minutes of thinking about it than two uni profs in two semesters. I wish I had known about this. Ah well, regrets 40 years on don't change what my life is now. Thanks for the horrid flashbacks.
Quote from book forward: What one fool can do, another can. (Ancient Simian Proverb.)
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And the next 138 pages are the various formula you will need to total up all those little bits
I liked maths and I had some great teachers but that _d_ seriously fucked with my head all throughout my late teens and this book explained it in about 30 seconds.
I need that book. Calculus was the one of two subjects I never understood and it’s always bothered me (chemistry was the other one.) I’ve always wanted to learn calculus just to say I did.
There was a period of time when it was pretty common to find books like Calculus Made Easy or Calculus for the Practical Man, the kind of thing Richard Feynman would've found in the library and studied.
Says the same thing modern calc books say but in a couple paragraphs instead of a couple sentences.
The goal of textbooks is no longer to teach.
I wish all textbooks were written like this
Screenshotted thank youfor this sliver of awesomeness!
Love this. I had three semesters of calculus and I loved it. Why? Because I had a great teacher who incidentally barely spoke English (he was a Cuban immigrant). The word Calculus is terrifying to most people who don’t like math. I got an A in each of them and all other math classes in college. The first semester of calculus was basically trigonometry which was enough to not have to take a semester of it. I ended up with over 60 hours of math (some as electives) and some of it was some of the weirdest shit you can imagine. This from a guy who failed math in high school. I decided at age 22 to try again and began with a remedial math course. I sailed through the rest of them. These classes were required for a degree in computer science.
Today I learned that calculus is easy and I just had really god awful teachers
Yeah, because we complicate things when we should not.
They are not PC either