Beautiful visualisations ! I love almost all your design choices such as the font, the background color etc. Even the animations where the characters appear from below when writing formulas, wonderful ! Edit: at 20:14, the animation on the bottom right is simply amazing, wow
Very nice video! I took an advanced differential equations class one time that used population models as a framing device. One subject we studied was "delay differential equations", in which the derivative can be based on past values of the variable. Say, f'(t) = a * f(t - 10). In the population model, this could correspond to an animal that takes several years to reach maturity. You could also do something like f'(t) = a * f(t - 10) - b * f(t - 30) to model animals dying of old age. I recall they were a pain to try and solve, but they're neat to simulate.
lol, I had to turn on the subtitles because I thought you were saying "noodles" every time you said "individuals." Great introduction to differential equations.
LMAO, yeah, my accent always gets much worse when I have to speak in a "serious" setting. Had to do several takes for that word. But I'm glad you liked the video!
Very interesting video. The part I can't fully understand is the term XY at 13:26. I don't see how units match. Is there another way of seeing it without introducing a constant with value 1 to fix the units?
Oh, yeah, I ignored units because it's a bit annoying to get right, and I thought, talking about it wouldn't add much. Firstly, X and Y are often relative amounts with respect to a(n unknown) maximum and therefore dimensionless. All parameters then have unit [1/s]. Secondly, if we do want to add units to the numbers of mice and owls -- say [M] and [O], respectively -- then alpha and gamma would still be [1/s]. But beta would be [1/Os] and delta [1/Ms]. The first, for example, could be said to be "the rate with which mice disappear per owlsecond". Which... kinda makes sense? The more owls and the longer the exposure, the fewer the mice. But I find it easier to ignore units altogether for this kind of overview.
Beautiful visualisations ! I love almost all your design choices such as the font, the background color etc. Even the animations where the characters appear from below when writing formulas, wonderful !
Edit: at 20:14, the animation on the bottom right is simply amazing, wow
Thank you so much!!
Oh my gosh that was the best explanation of derivatives I've ever seen! Great use of visuals!
Thank you so much!
Very nice video! I took an advanced differential equations class one time that used population models as a framing device. One subject we studied was "delay differential equations", in which the derivative can be based on past values of the variable. Say, f'(t) = a * f(t - 10). In the population model, this could correspond to an animal that takes several years to reach maturity. You could also do something like f'(t) = a * f(t - 10) - b * f(t - 30) to model animals dying of old age. I recall they were a pain to try and solve, but they're neat to simulate.
lol, I had to turn on the subtitles because I thought you were saying "noodles" every time you said "individuals." Great introduction to differential equations.
LMAO, yeah, my accent always gets much worse when I have to speak in a "serious" setting. Had to do several takes for that word.
But I'm glad you liked the video!
Very interesting video. The part I can't fully understand is the term XY at 13:26.
I don't see how units match. Is there another way of seeing it without introducing a constant with value 1 to fix the units?
Oh, yeah, I ignored units because it's a bit annoying to get right, and I thought, talking about it wouldn't add much.
Firstly, X and Y are often relative amounts with respect to a(n unknown) maximum and therefore dimensionless. All parameters then have unit [1/s].
Secondly, if we do want to add units to the numbers of mice and owls -- say [M] and [O], respectively -- then alpha and gamma would still be [1/s]. But beta would be [1/Os] and delta [1/Ms]. The first, for example, could be said to be "the rate with which mice disappear per owlsecond". Which... kinda makes sense? The more owls and the longer the exposure, the fewer the mice.
But I find it easier to ignore units altogether for this kind of overview.
My birthday isnt for another few score days