kubrikov

Hello!
I did some math animations. Criticize please!

What is Integral (GIF-animation).


Visualization of the integration process (GIF-animation).


What is Derivative (GIF-animation).


Fundamental theorem of calculus (GIF-animation).

alan2here

Excellent, reminds me of "3 blue 1 brown"s Youtube work.

Although, as you request criticism …

"what is derivative" might be better named "what is a derivative" or "what is derivation". And could emphasise that the windows size tends towards 0, that the slope is a proportion of width to height rather than just a difference in height. Often tangent lines are animated here where two tangent approach and become 1 point, but maybe you could get the same point across just by keeping those vertical lines in place after the window has moved on and sliding them gradually together afterwards.

It's just an idea to keep the framing the same and demonstrate how nothing breaks in the derivative as a result of this, but as the process progresses things will look less visually wobbly and more accurate, the natural conclusion and intuition here hopefully being the desired conclusion, that the derivative line is becoming more accurate as a result of this shrinking to the limit.

It does then still suggest that the window repeatedly jumps its own length rather than sliding smoothly, but maybe there effectively the same most of the time, or even at the limit completely equiverlant.