History of Calculus: Part 1 - Calculus in a Nutshell
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- Опубликовано: 5 фев 2025
- This is the first part of a series about the history of calculus. I wanted with this video to build a general overview of calculus by answering three main questions:
1. (0:26) What is calculus?
2. (2:50) Why do we need it?
3. (4:03) How does it work?
I tried to stay in this video on a very high level without digging much into mathematics as we are just starting :) I hope you find it helpful and you get something out of it.
Support this channel
Your support of the channel is very much appreciated. You can do so at the links below. Thanks for keeping me going :)
Buy me a coffee: www.buymeacoff...
Support me on PayPal: bit.ly/3Bxo5qG
Patreon: / tareksaid
List of videos in the series:
1. Calculus in a Nutshell
2. Integration in Ancient Times
3. The Fall and Rise of Geometry
4. Integration in the 17th Century
5. Differentiation in India and in the 17th Century Europe
6. Isaac Newton
7. Leibniz and his Notation
8. History of Applications of Calculus
9. Euler and the Bernoulli Brothers
10. The 19th Century - Tackling the Problem of Infinitesimals
11. The 20th Century - Non Standard Analysis
I know it's been a while since I published my first video but this time it won't take me long to publish other videos in the series. In the last 6 months I was researching the history of calculus and developing the story for the series. But now that this has been out of the way I promise that I will be publishing the videos much quicker.
Thanks a lot for your support
Main References:
The Historical Development of the Calculus ~ C.H.Edwards, Jr
The Origins of the Infinitesimals Calculus ~ Margaret E. Baron
The History of Calculus and its Conceptual Development ~ Carl B. Boyer
Infinite Powers ~ Steven Strogatz
Calculus Reordered ~ David M. Bressoud
Wow, a real teacher
A true masterpiece.. Please bring part 2 of this video as soon as possible...
Thanks for your kind words Aditya. Yes already started working on part 2! Will release asap
Oh! How I wish that this video had been my introduction to calculus when at school 70 years ago. I quickly learned the how of differentiation and integration, but the why of it eluded me for ages as we were told 'don't worry about that, it will come later'.
I’m glad you found the video helpful and that it gave you the “why” you wanted to know all those years ago Don :)
you just, reiterated , same thoughts, of ours !
Thank you Sir !
Excellent! The math in the typical textbooks is like packaged food items in the grocery stores, completely devoid of the history of how they had turned into their current forms. Thanks for giving math the life it deserves!
Thanks reza and I really like the analogy. I think picking up fruit directly from the tree is the most enjoyable way of having it and my goal with these videos is to help do the same but with ideas - seeing them directly from the source.
Such excellent graphical aids. These videos are obviously labors of much love.
Thanks, they were indeed :)
The cutting/stitching analogy was genius. Great video!
Thanks. I’m glad your liked it
I've been searching for an easy to understand video on calculus with great visuals. THIS IS IT! THANKS!!!
I am so glad that you found it and like it. Thanks :)
This series is amazing! I watched all 4 episodes after each other and I am literally sitting on the edge of my Ikea chair!
An amazing smooth introduction and explanation of a very complicated topic. Can’t wait to watch part 2.
Thanks for your support Tamer. It really means a lot. And yes I have already started working on part 2
The history of math is fascinating. Looking forward to more videos.
Thanks. I will post the next one soon. And I totally agree regarding the history of mathematics. There is a quote I found by James Whitebread Lee Glaisher which I really liked: "No subject loses more than mathematics by any attempt to dissociate it from its history."
Really looking forward to this series
Thanks Yohan. I am working on it. I hope you will like it.
Thanks
Tamer that's very generous! Really much appreciated
This is a video I've always wanted!
Thanks. I am glad you found it :)
You are very well organized in the way you work. The Lesson is PERFECT! For me, your videos are some of the best math content. Thank you very much for sharing your work.
Thanks for your kind words and support Moula. It really means a lot. Comments like yours motivate me to keep going
Simple, straight forward, intuitive, content packed. I know quality takes time. You are a hero.
Thanks for your kind words and support tobias. I really appreciate it. And thanks for pointing out the time thing. At first I was feeling time pressure and wanted to publish something within a month of my first video. But it took away from the joy and passion for this project. So I decided to focus on that instead and take my time. Having said that, now that the story for whole series has been developed, I think the next videos in the series would be published a lot quicker
@@tareksaid81 If this series has half of the explanatory power of your logarithm video, then the whole world could be able to have very deep seated intuition of what calculus let's us do as a tool. Do this right, your team and you will be legend.
@@tobiasgertz7800 Thanks and I'm aiming for it to be similar to the logarithms video :)
I would really appreciate your feedback on future videos. Thanks for your support, it really means a lot
I'm looking forward to part 2. I just saw your video on logarithms and was blown away.
Thanks for your kind words. I am currently working on part 2 and I will release it asap. I hope you will like it :)
Top notch storytelling! Very excited to watch part 2 😊
You love to what you teach, and you do it with a lot of care… The result is joy for those who learn! Thanks
Dear Tarek, thank you so much for this video! Having Covid and after only lying on my couch for the past 4 days and binge-watching RUclips.... it is the first time I actually felt like there is a human being on RUclips who does not want the humanity to deteriorate.... appreciate your work! Please let me know if I can support your work in any way.
Thanks for your kind words and your support. I really appreciate it. Sharing it would be great as the RUclips algorithm would think it is worthy. Some people suggested that I start a patreon account but I thought it was too soon as I only have two videos. I am planning on starting one at one stage.
Hope you feel better soon and here's a toast for uplifting humanity :)
Superb explanation! Easy to understand 💯
Glad RUclips recommends your videos to me
Thanks. I am glad you like it and found it easy to understand :)
This is a long comment. First, I would like to tell you that I arrived at your video by searching for "why do we study calculus", so it was by my need, not by a suggestion. I was so surprised to see you in another video! Second, I would like to tell you that I arrived at your video with logarithms also by searching (about a year ago), and I saw it at least 10 times (the same is true for this series). It's hard to find the proper words, but I think that you have something really special, and that is the desire to make the world a better place, the desire to make some order in the chaos (just to quote Aron Nimzovitch). Not just the simple desire, but a great satisfaction in doing it. I think that you have a great vocation to be an educator, and I strongly suggest that you should consider it seriously.
My heart goes with you and all your friends and family who had to leave their home country because of the war.
This is an incredibly amazing comment and I really really appreciate it. I am lost for words as it deeply touched me as I felt heard and seen. From the bottom of my heart thank you and apologies about the late response. I have been off my channel for a while but now I am back on track :)
I was thinking of pursuing an education role and now you have encouraged and inspired me to take action.
Thanks for your thoughts about my country, I have taken a snapshot of your comment and shared it with family and friends from Syria and they send their regards.
Thanks again for the deeply touching comment
@@tareksaid81 I am very glad that my thoughts resonated with you! Now I have also been heard. :)
As a Math history buff...all I can say is keep the expositions coming...😄😄
'Brilliant' cou;d use your talents Tarek!!
Thanks again... Yes I am working on part 3. Planning to publish in April
Fu*king hell, in less than 10 mins you've cleared up so much mental fog in my head bothering me since the early 2000s in uni class (and failing, but that's my ignorance)! Even looking at other math channels was such a challenging task, and I've asked for certain explanations (even to newly graduated students, kids of ex-colleagues) but received always the same repetitive answer. It's maddening because it seemed like they've memorized stuff without really understanding it; or because I'm too thick to understand, or they didn't know how to explain it.
One thing tho I believe should have been said from the start in this video about curves in calculus (probably is in part two, but I've to still see it, will do after commenting) is that it's a visual aid for a function.
Reminds me of a student in the same uni class who was puzzled in why there was a ball at the end of a semicircle (picture it starting from coordinates 0,0 curves upwards then finishes at π BUT with a circle, meaning it doesn't END there). The axis X and Y don't actually have to be perpendicular to each other, they could also be parallel, because the answer of the function will always be on Y axis, so there's actually a "hole" in the value π in axis Y, but to make things more visually better the axis are ⊥ to each other. However, TO ME this hasn't been fully explained in school (at least for what I recall, and again, the student in the uni class had the same erroneous idea) has made the initial idea of Y being the answer of any y= f(x)!
Anyway, can't change the past, just glad to have found your channel.
And now to part two.
P.S.: THANK YOU for your channel!
I’m really glad the video was able to clear up that mental fog for you! I completely understand where you're coming from-it's so frustrating when you're trying to dig deeper into a concept like calculus and all you get are those same repetitive, memorised answers. I've been there too.
I’ve found that looking into the history of these concepts really helps to have an intuitive understanding that often gets lost in modern teaching.
Regarding your point about curves and functions, you’re absolutely right that curves could be considered as visual representations of functions today. Historically however, curves were studied long before the concept of functions was formalised. Functions actually evolved from the study of curves, which is why in the video I mention that 'calculus originated as a tool to study and analyse curves.'
I’m really glad the video could help and thanks for sharing your thoughts
Finally! I just saw this on the main page and I was just .... *[GASP]* . I'll look at it as soon as I can and I'm sure that it's good. Please continue doing videos like this, I really like your style.
Thanks for your support Abdullah. It really means a lot. Yes, I already started working on part 2. Will try to publish asap
I am hugely impressed by this presentation. It is invaluable for students or non-math geeks, and you have a real gift for communicating these concepts. The analogies and illustrations here are commendable for their clarity and incisiveness. You are definitely on the right track taking an historical perspective, and explaining so well right from the outset what Calculus "does".
I love how you emphasise the critical role of curves in modelling all aspects of reality, and steer away from the abstractions of functions and limits in favor of visual geometry and intuitive ideas like infinitesimals. Understanding these was a breakthrough for me years ago in my own calculus journey. Your series promises to be a true service to math education. Bravo, sir!
I just saw the second of your series has been uploaded, and realised I had not yet commented on the first. I wish you every success and I am only sorry I cannot support you more, being poor currently in both time and money - but I will spread the word and recommend you wherever I can.
Such a beautiful and supportive comment is worth more than any financial support. I really appreciate it. Thanks :)
I struggled with the concepts of limits and functions when I was at school. I could solve problems, but I didn't know why we needed calculus at the time. Similar to you, it was a breakthrough moment for me when I got to understand calculus through infinitesimals. In fact, it made me appreciate limits more as only then I understood their true meaning.
I believe that limits and functions can only be understood, or at least appreciated, after developing an understanding of calculus through infinitesimals and curves.
Thanks again for your support. It means a lot
@@tareksaid81 I don't know what books you have been consulting for historical sources, but my favorite is one by Eli Maor, "e - The Story of a Number". It starts with compound interest and ends with Euler, by way of Logarithms and Calculus. It is only 200 pages but ranges from musical scales and harmonics to the philosophical implications of transcendental numbers whilst providing a clear explanation of what the Calculus of Liebniz and Newton "is" and "does". It is aimed at the educated reader and isn't beach-side holiday reading, but is still very accessible. Anyway, recommended - though I suspect it is out of print
@@horseloverfat6938 I did read it when I was working on the natural logarithm video but at the time I didn't pay much attention to the calculus chapters. Thanks for the reminder, I will check them out again.
The main resource I am using for the calculus series is:
-The Historical Development of the Calculus by C.H. Edwards
This is great!!! Loved the detail about Archimedes' gravestone!
It's very interesting indeed. Another interesting story linked to this is that Cicero, the Roman statesman and poet, visited the tomb of Archimedes more than a 100 years later and did find the cylinder and the sphere
Cutting and stitching is wonderful! This video eill make a perfect openers for my students later this year. Thank you. (Can't wait for fluxions!)
Thanks.. I will be talking about fluxions in the part in the series about Newton, which will be either part 5 or 6 of the series. I hope you will like it
Amazing work yours. Thank you.
Since "always" I had interest in the Mathematics behind the scenes History. Your job helps me to complete gaps I left for ages unanswered. Congratulations!
Thanks Osvaldo, I’m really glad that you liked the video and that it answered some of your questions. Hopefully you’ll like future ones too
Great work. Someone said that every new book is a linear combination of all previous books on the same topic. This video is much more than that. Iḿ gonna watch part 2 right now.
wow.. thanks for this thought and this compliment. It really means a lot to me. I hope you liked the rest of the series.
Superb simplification! Please continue your explanations to include the mathematics (equations and their solutions) that support Calculus.
Thanks... Yes this is definitely the plan - first is to build some intuition about calculus before introducing equations later
I've learned more from watching videos like this than I ever have from classes. Thanks for the amazing video.
Thanks, I am glad you learned from this video and hope you will learn a lot more when the series is finished :)
At the end if my 5th decades on earth…first time I understand calculus. Great work!
Thanks for your support and kind words Amar. It really mean a lot. I’m glad you found it helpful and that you got to understand calculus :) I hope you’ll like the future videos in he series
You deserve a Billion followers.
👏👏
Thanks for your timely comment suja V. I really appreciate it. Comments like yours motivate me to keep going :)
This should be required for all courses in Calculus.
Seus vídeos são muito bem elaborados e agradáveis ao conhecimento. Espero que você conquiste, o mais rápido, milhões de inscritos ! ❤
Thanks for your wishes, I really appreciate it. I have to work on making more videos to get to a million :)
Let me add my idea found recently to explain the cut and stitch method.
Always cut shape into what you already know at least or approximately like square,rectangle ,yriangle,trapezium , parallelogram not iregular shapeand stitch back.
Beautiful! You're aware, I'm sure, that the direct use of infinitesimals was put on a solid footing in the 20th century with nonstandard analysis. Or perhaps that's where we're headed? Anyway, thank you, and I look forward to more!
Thanks Jim, Yes indeed, the plan is to finish the series with a video about the work of Abraham Robinson on non-standard analysis as I thought it is too early to mention it now. Thanks again and I hope you will like future videos
Excellent explanations, thank you 👍
Excellent way of presenting the subject. Thanks a lot Tarak Said. Love you for your way of teaching.
Srihari Anne, Newjersey, USA
Thank you so much for your kind words Srihari! I’m truly touched and so glad you enjoyed the presentation. It means a lot to me to know my way of teaching resonated with you. Sending lots of gratitude and love right back to you, all the way to New Jersey :)
So clear. So good!
Amazing, great. ....salute to you sir
I have watched many videos on the calculus that I have found wanting in one or more respects. Poor production value is a big impediment for me when they put no effort into providing visual graphics beyond a white board where they scribble illegible ramblings of their improvised presentation. Another is lack of foundation where they write an equation to explain differentiation. Time out !“//“ I say. What the hell does that equation even mean and why would anyone feel the need to differentiate it? You seem to answer these failings of others who have thrown their hat into the RUclips education ring. I’m liking what I’ve seen thus far and look forward to contributing on patreon the impetus and support you need to produce and release the video series listed in your curriculum.
Thanks for your support, I really appreciate it and I will work on creating a patreon account soon.
I totally agree regarding the need to understand what the equations mean before we work with them and this is the goal of this series. My aim is to break calculus down into small steps in a way that the equations feel natural. I would really appreciate your feedback on future videos so I make sure I am on the right track.
Thanks again :)
Thanks
Thanks a lot for you’re support Michael. It means a lot to me and I really appreciate it :)
Aaaah ! I never thought I would be rediscovering Mathematics at old age. 🤔
Many thanks !
I am glad that you did rediscover mathematics.. No worries :)
Can't wait! I want to support you on patreon!
Thanks for your support. I really appreciate it and it means a lot. I was thinking of starting a patreon account but thought it was too early to do so. You encouraged me to start one. Thank you
great stuff Tarek! Can't wait for more!
Thanks John for all your support, I really appreciate it. Next video will be about the historical motivation for calculus. I hope you'll like it
Underrated Channel
Great channel....hope you will resume your work in the future!
There is a great source for "non-mathematicians" and a gentle introduction to "classic" mathematics for the layman that could come handy to (some of) your listeners: "Mathematics - It's content, methods and meaning" by Lavrent'ev, Alexandrov, Kolmogorov et al...
Thanks ☺️ I will definitely be resuming the work. In fact i am currently working on parts 4 and 5 of the calculus series. I hope you will like them.
I don’t think I have heard about the books before. I will check it out. I am sure it will be handy. Thanks for suggesting it
not studying at the moment, but you have peaked my interest and for that i thank you
That’s great and I’m glad that this peaked your interest :)
Really amazing.............
What a great video, thanks for sharing! Keep doing the great work
Thanks for the support Murat. It really means a lot :)
Your videos are FIRE I love them and learn a lot from them
Thanks for your kind words and I’m really glad you are finding them helpful
Great video Tarek
Thanks Adam :)
wonderful explaining thanks from morocco
Thanks and greetings to Morocco from Australia :)
Amazing explanation,smooth and simple 👍👍👍
Thanks Yasmin. I’m glad you liked it :)
Please bring part 2.
On the way. Already started with it. Hope you’ll like it
Great calculus video!
excellent
Great video , nice information 👏
Keep going 💪
Thanks for your support Bacem. I really appreciate it :)
Excellent!
Masterpiece
Please make more videos.. I love your style
Thanks. Yea I’m working on it. I will be releasing parts 3 and 4 of calculus together soon. I hope you will like them
Nice!
Excellent
Great video!
Thanks :)
❤❤❤❤❤❤❤❤❤❤❤
No other Explanation is as powerful as yours
I thought 3blue1brown is the final limiting point.
Thanks again.. I must say 3blue1brown was a massive inspiration for this channel
Thank you sir!
You are welcome :)
Excelent
Though I am old ie 66 years, I want to learn whole range of mathematical subject from you starting from arithmetic, mensuration, geometry, algebra, trigonometry, co-ordinate geometry and calculus. But you have only 3 videos produced at the rate of one in every 3 months. Please accelerate your production.
It would be my pleasure to help. These videos take a lot of time but I am gradually getting better at it. My aim is to do many more videos on many topics so I will have to find a way to be faster
Belleza de video
Why didn’t you make any mention of “nonstandard analysis,” started by Abraham Robinson, which reinstates the infinitesimal’s role as a logically coherent basis for calculus?
Excellent point, I thought a lot about it and decided to keep it out of the introduction video to keep it simple. I’m planning to do another video later in the series titled calculus in the 20th century where I talk about Robinson’s work. I am thinking it would act like a nice plot twist - a come back of infinitesimals after everyone thought they were forever defeated by limits ;)
@@tareksaid81 I look forward to it! Your videos are great!
My Question of may be 15 years or so, got answered @2:59
I’m glad this video helped you find the answer :)
Fantastic. I never understood why I had to study limits,
Thanks… actually me too at first. But after I learned infinitesimals and understood the evolution of calculus, I began understanding why we use limits. I now believe that calculus should be introduced through infinitesimals. And only after developing an intuitive understanding of calculus that limits should be introduced
Where is part I can't wait please will you add calculations
It’s on the way. Most probably next week. In the next video I’ll be talking about calculus in ancient times and there will be a little bit of calculations but mainly not calculus equations yet. I will talk about those in a later video in the series :)
@@tareksaid81 thank so much visualise videos thank you
What a cliffhanger !!
I tried to release the first two videos together to avoid this but it takes a lot of work. I promise it won't take long :)
Squaring the curves
hungry for part 2
Already started working on it. I hope you’ll like it
Sir kindly upload more videos
Sure. I’m currently working on part 2 and will release it soon
Great
release part 2
It's coming this week
Hi how did you quitte morracoo
Tarek where are you !
Hi Khaled, I know it’s taking me a long time. But planning on releasing the upcoming videos asap 😅
😍
❤
Well done, but why do say "the point of maxima"? Maxima is the plural of maximum, so "the point of maxima" doesn't make sence to me.
You are right. I should have said points (not point) of maxima and minima. Thanks for pointing it out
Infinitesimals or limits, it’s still nothing but magic
Are you have an arabic chanel
No, I don't have channels in other languages at the moment unfortunately. I might add different languages including Arabic when the channel becomes bigger. In the meantime, I noticed that the auto translate is not bad. I recommend trying it if you haven't done so already
2:3 does NOT equal two thirds.
I destroyed hundred coconut and found amazing natural engineering of getting strong product with fiber meterial. I think there no machinary available for domestic use of crushing coconut,it requires very good engineering
Great video!
Thanks Raul :)