BASIC Calculus – Understand Why Calculus is so POWERFUL!

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[samanthahellawell]

I just wanted to say a Big Thank You to John, so I hope he reads this.
I am just finishing his Algebra 1 course and completed his foundation course before that. At the age of 62 I decided to confront my fear of maths, it was some unfinished business since I realised why I had developed a belief that I couldn’t do it at high school and that I should be able to overcome that. For the past year I have worked hard and have really felt that John was at my side and on my side - even though he does not know me. I have understood everything and to my surprise and delighted I have found that actually, yes, I can do math and moreover I love it!
I love the way he makes such an 13:37 effort to explain things clearly and methodically. He is encouraging whilst at the same time always reminding students about how to not make basic mistakes (which I do but I am getting there).
Now I would like to learn Calculus and have been looking at various videos but this one is the best place to start.
I have loved the Algebra course.
Many thanks, John. Simple the best!

[Ancatdubh]

Thanks for taking the time to make this video, I'm 56 years old and am trying to re-learn math from foundation level up. I see the word calculus often and it still seems like something I could never understand. Perhaps I never will but at least your video gives me an insight and some hope that in the not too distant future I could begin studying calculus, as the simple concepts you outline are easy enough to understand.

[RootlessNZ]

Excellent re-introduction of integral calculus after 60 years. Thank you.

[paulanizan]

It was my favorite math class in high school.

[imagseer]

It's been decades since I did that at school. I think it was non-parametric curves where it lost me. Interesting to revisit the topic so thank you.

[PrinceKumar-qwgm]

pls make same video on basic introduction to algebra

[MeyouNus-ljde]

Calculus Foundations:

Contradictory:
Newtonian Fluxional Calculus
dx/dt = lim(Δx/Δt) as Δt->0

This expresses the derivative using the limiting ratio of finite differences Δx/Δt as Δt shrinks towards 0. However, the limit concept contains logical contradictions when extended to the infinitesimal scale.

Non-Contradictory:
Leibnizian Infinitesimal Calculus
dx = ɛ, where ɛ is an infinitesimal
dx/dt = ɛ/dt

Leibniz treated the differentials dx, dt as infinite "inassignable" infinitesimal increments ɛ, rather than limits of finite ratios - thus avoiding the paradoxes of vanishing quantities.

[Poult]

You just brought back the EUREKA feeling I had when I first learned this. Happy days 😊

[noferblatz]

You really should explain the "dx" symbol. I was an outstanding math student in high school. Then I got to college and had to take calculus, and failed miserably. I tracked it back to this symbol. My lack of understanding of this symbol interfered with my abili8ty to do calculus. And I've never found a satisfactory explanation for it since.

[paulanizan]

Archimedes already developed infinite summation (integration) but unfortunately was killed by Roman rabble. It was rediscovered by Isaac Newton, 2000 years later.

[tomtke]

that big "S" means sum up...
from 2 to 3
integrate means to add a power.. i.e. x^2 becomes x^3

here... (1/3)x^3 + C
at x=3
(1/3)(3^3) + C
=9 + C
at x = 2
(1/3)(2^3) + C
= 8/3 + C
(9+C) - ((8/3)+C)
=9 - 8/3
=(27-8)/3
=19/3
= 6&(1/3)

[gopherspace]

2nd time I've watched you go over this but I still can't get it😂
Thanks for trying 😂
👍👏🙏💪😎🌎

[maryogie]

I never wanted to take Calculus ; it was a required course when I went to college.

[terry_willis]

It appears that calculus is simply a mechanical method. Is this all we have to know to be a certified calculus expert?

[argonwheatbelly]

6⅓ in about 10 seconds in my head. Sorry it took that long. 😞