Great video. It gives a very nice intuition for what's going on. Well done! It might be good to acknowledge that speaking of adding infinitely many quantities that are infinitely small leads to paradoxes. What exactly is an "infinitely small" quantity? The more precise and modern approach that addresses this objection is to introduce the idea of limits, and to consider a succession of subdivisions of the interval [a, b] into a larger and larger number of thinner and thinner rectangular slices. As the number of sub-intervals grows arbitrarily large and the width of each subinterval grows arbitrarily small, the sum of all those "df"s you illustrate becomes arbitrarily close to f(b) - f(a). Speaking of "infinitely small" quantities may well have been how Leibniz and Newton originally conceived of what's going on, and it's worthwhile understanding the history of how ideas developed. But it caused a lot of confusion and consternation until it was put on a solid logical footing. For example, the book "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World" by Amir Alexander gives an interesting account of why the Jesuits in 1632 found the notion so disturbing that they actually banned the teaching of it!
@Foolish Chemist: I’m late to the party - a year late, it seems - but I’m here now and I just have to say how extraordinarily clear and concise this beautifully presented lesson is; and I’m very grateful to you. Very well done and thank you.
oh my fucking god, this is like one of those parts in a movie where everything just connects together in your head leading to a climactic conclusion, JESUS FUCKING CHRIST
300 views? This video is HELLA UNDERRATED. Bro just taught us single variable calculus in 5 minutes.
Algorithm, please bless this channel
Great video. It gives a very nice intuition for what's going on. Well done! It might be good to acknowledge that speaking of adding infinitely many quantities that are infinitely small leads to paradoxes. What exactly is an "infinitely small" quantity? The more precise and modern approach that addresses this objection is to introduce the idea of limits, and to consider a succession of subdivisions of the interval [a, b] into a larger and larger number of thinner and thinner rectangular slices. As the number of sub-intervals grows arbitrarily large and the width of each subinterval grows arbitrarily small, the sum of all those "df"s you illustrate becomes arbitrarily close to f(b) - f(a). Speaking of "infinitely small" quantities may well have been how Leibniz and Newton originally conceived of what's going on, and it's worthwhile understanding the history of how ideas developed. But it caused a lot of confusion and consternation until it was put on a solid logical footing. For example, the book "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World" by Amir Alexander gives an interesting account of why the Jesuits in 1632 found the notion so disturbing that they actually banned the teaching of it!
Finding out people with that math passion spark always makes the derivative of my mood very positive
@Foolish Chemist: I’m late to the party - a year late, it seems - but I’m here now and I just have to say how extraordinarily clear and concise this beautifully presented lesson is; and I’m very grateful to you. Very well done and thank you.
Bro, keep doing what you're doing. Thank you for the great content.
oh my fucking god, this is like one of those parts in a movie where everything just connects together in your head leading to a climactic conclusion, JESUS FUCKING CHRIST
Show us how to use it in chemistry and where the formulas come from, i.e. why it makes sense to use integrals for the formulas
Ty homeslice
lol
Genius sir I haven’t thought this not even my phd teacher I think