I hope more people watch your videos very few people explain advanced Mathematics on YT ❤

This is excellent. I wish someone had explained it to me this way when I first started learning calculus almost 60 years ago. Two other things I wish I had known:

1. “Calculus” is short for “the calculus of infinitesimals.” A calculus in general is a way of calculating something, and the calculus of infinitesimals is a way of calculating things using quantities that are infinitely tiny.

2. The rate of change of position with respect to time is velocity, measured in units of length divided by time. The rate of change of velocity with respect to time is acceleration, measured in units of length divided by time, divided by time. This is why acceleration is in units like meters per second per second. That confused me until it finally hit me that it’s (meters/second) per second. (Maybe that was obvious to everybody else, but it wasn’t to me…).

an intellectual tour-de-force.

I want to thank you both for all the hard work and effort you put into these videos. There are countless people—including myself—who find them incredibly helpful. But there are surely also many people who would benefit greatly from them but unfortunately don't know about this channel yet. It definitely deserves more attention.
​I also want to congratulate you on the views and subscribers you already have. I think it's fantastic that you always cite your sources. Calculus is the mathematics of change, and the function describing the growth of my knowledge through your videos is increasing exponentially!

The analogy regarding first and second  derivatives was very smart. New to me. I used to think of velocity and acceleration as an example of what 1st and 2nd derivatives represent. The relation between the function and its derivative was graphically intuitive.
Thank you for taking the time and putting efforts into this.  
Much appreciated.

Have become a big fan since yesterday, can't stop watching your videos and get to work :D

Change is the key concept! I think that sometimes teachers are too ready to make things "easier" by pointing only to the concrete and physical examples. I was so glad to see you use the "discrete derivative", to really highlight that we are focusing on the abstract of change itself, without it being in a physical system!

I sometimes think we do ourselves a disservice by forgetting that Newton called it the "calculus of fluxions". Calculus used to be a word for reckoning in general - the old Romans used small pebbles on their counting boards, and so they talked about "calculos ponere", placing stones. The word calculus is still used in medicine as a term for "stones" within the body (kidney stones, gallstones, and so on). I think the word "calcolo" is used the same way in medicine in Italian today - the broader word for pebbles got replaced with "ciottolo".
The "fluxions" part really shows us that we're thinking about changes - it came from Latin "flūxus"  (which is modern Italian "flusso"), and I think knowing that makes the idea of flowing, and changing, much clearer. Maybe we don't need to rename the whole field of infinitesimal calculus as "fluxions", but it's nice to remind people!

Lastly, I wanted to say that I usually think about infinitesimals like this: It's a quantity so small, that no matter what you do to it, it will never be big enough to be anything other than an infinitesimal. You can multiply by any number, raise it to the highest power possible, make the biggest power tower with it, and even still, you could never ever write it in the form of 0,0000...1. The natural question then might be - what if we multiply epsilon with infinity? And in this case, as you talk about in the next video, you have an indeterminate form. Once something as big as infinity gets mixes together with something as small as an infinitesimal, all the rules stop applying and you have to turn back - otherwise you will only get nonsense from there on.

If it was hard for you when you went right after high school, imagine someone going to college for the first time in their 40s.

I'm so glad I found this video. I've never really studied in my life, but calculus forced me to learn how to study. All my classes suffered because I just couldn't understand calculus.

A dublagem automática do YouTube permite que conteúdos bons de matemática como o seu, cheguem até mim, já que não compreendo sua língua local, continue!

I occasionally grab a book from my vast collection of old math texts a friend donated to me when I was in grad school, and by coincidence, I am currently working through a small book about the difference calculus and sum calculus, which is exactly how you started the video (without mentioning those specific areas of study though).  It is really interesting the way things are expressed in this particular text, and it took a while to get used to. (I can give a reference when I get back to campus on Monday, as that book is at work right now).

I don’t know. I just thought the coincidence was interesting (probably only to me). Although that is probably only interesting to me, I know that engagement helps with the algorithm, so hopefully this comment is supporting the channel.

Great video! Peace out

Honestly, I really do not understand graphs. That is a major issue I had in calc 1. I'm glad to see that it was included in the video.

Great video guys ❤❤

Excellent. Keep going

Thank you!

Thank you

I think intro college physics courses have the most intuitive way of introducing calculus
as we can all relate to a distance a speed and a time period i wish i had
gone through classical mechanics before Calc 1 would have made it much easier for me...

Very nice

Think this pairs well with larry gonick's book "The Cartoon Guide to Calculus"

The discrete method gives less precision because you are using the secant (finite differences), not the slope. For it to be exactly the slope, the separation between points would have to be infinitesimal.