Why Can't We Just Swap LIMIT and INTEGRAL ?!
Audience: undergraduategraduate
Tags: integrationriemannlebesgueuniform-convergencemonotone-convergence-theorem
This video is in french, but it is translated into english thanks to youtube. For people that don't like AI voiceover, they can use the subtitles. We focus on the issue of interchanging limit and integral : but fundamentally, what prevents us from interchanging limit and integral ? This approach, which involves examining what does not work, will be rich in lessons : it will allow us to discover the phenomena of mass loss, but also the 'forbidden law' that governs the theory of integration. By the end of this video, your intuition will be strengthened, and the theorems learned in preparatory classes or undergraduate studies will seem much more natural as we will see how to recreate them.
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Motivation - this is an important topic in calculus and a nice perspective
Clarity - The speaking and graphs were clear
Novelty - It was novel to me!
Memorability - made me thinki about this theorem at a deeper level. Nice work.
Very nicely done! This provides a very natural motivation for these key limit exchange theorems, which I think can certainly be hard to grasp and internalize. I will say, I think with Fatou’s lemma being such a key part of your logic, and not being particularly hard to explain, I think the video might be improved if that lemma was presented with some justification. (That said, naturally this was remedied just by some searching on my part.)
In any case I genuinely think I will carry that idea of why these limit exchanges work the way they do forward with me whenever I have to deal with them, and I am very interested in seeing more from you, and I have subscribed. Thank you very much for participating, and I hope you have a nice rest of your day.
(and apologies for responding in English, my French is very bad and I think it would likely come off wrong if I even attempted)
Fatou’s lemma and regularity hypotheses were brushed under the rug a little, but the intuition is fantastic.
The word “conservation” makes this video especially memorable.
Note that I watched with English voiceover and subtitles.
The pacing felt faster than optimal. This might be due to the language difference. I would have liked if the key equations had stayed on the screen longer. The visuals were great, and the focus on screen was generally obvious.
The content left me dissatisfied. The video didn’t follow the ‘Show, don’t tell’ principle. It did SHOW examples of mass loss, and conditions on the functions that prevent it. Everything else however was only TOLD. That there is no other way to lose mass (this was not even clearly stated), that there is no mass win, that measurability is enough.
Overall the video did not improve my understanding of integration theorems, as I am still missing half the picture presented in the video.
some interesting things, the approach “what we do not want” is really helpful for students.
So bad that “no gain of mass” is not at all explianed, even with some intuition. In my opinion, that is a severe drawback for the video and its pedagogical power.
The topic felt quite novel, and I enjoyed the visuals, which helped guide the examples. However, it felt quite unmotivated and was very hard to follow with French text and AI-translated speech. Also, referencing another video in a “series” doesn’t feel like the best fit for this competition.
Motivation: 5 Novelty: 5 Clarity: 0 Memorability: 5