History of Calculus: Part 1 - Calculus in a Nutshell

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 :)

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

[AdityaSingh-etlb]

A true masterpiece.. Please bring part 2 of this video as soon as possible...

[nabla_mat]

The cutting/stitching analogy was genius. Great video!

[rezakhadem]

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!

[TenguSteel]

This should be required for all courses in Calculus.

[donjohnson]

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'.

[moularaoul]

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.

[tobiasgertz]

Simple, straight forward, intuitive, content packed. I know quality takes time. You are a hero.

[TelAvivShalom]

You love to what you teach, and you do it with a lot of care… The result is joy for those who learn! Thanks

[tww]

I'm looking forward to part 2. I just saw your video on logarithms and was blown away.

[rextransformation]

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!

[OmegaFalcon]

This is a video I've always wanted!

[nickxyzt]

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.

[MadScientyst]

As a Math history buff...all I can say is keep the expositions coming...😄😄
'Brilliant' cou;d use your talents Tarek!!

[AH-erhk]

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 YouTube.... it is the first time I actually felt like there is a human being on YouTube who does not want the humanity to deteriorate.... appreciate your work! Please let me know if I can support your work in any way.

[pewpewpewpew]

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.

[hygenz]

Superb explanation! Easy to understand 💯
Glad YouTube recommends your videos to me

[WAMTAT]

I've learned more from watching videos like this than I ever have from classes. Thanks for the amazing video.

[osvaldocristo]

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!

[mathswithmrzuber]

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!)

[Nusret]

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.