3blue1brownLine Integrals, Explained Intuitively
In this video, I introduce the concept of a line integral in multivariable calculus by building it up intuitively from integration in single-variable calculus. Math is all about expanding previous knowledge into new domains, after all! I also try to present the intuition behind line integrals, and finally demonstrate a practical calculation of a line integral for an ordinary function: z = x^2 + y^2, over line segment y = x extending from (1,1) to (3,3).
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7
This video was well thought out. There is a strong storyline and the author made a very cohesive argument. I also like the iPad drawing and erasing. That was memorable to me.
Well done!
4.2
Quite standard. Nothing extraordinary.
It was more like a lecture note than showing something interesting.
8.1
Bam ! Good job explained me the perspective I have learned line integrals before but still cannot imagine a picture about it....
5.1
I like the general content of the video, even if it felt a little bit standard. However, I didn't really like the jokes, and the introduction was both not funny to me and didn't tell me at all what the video was actually about or why I should care. Also a minor side note, near the beginning when you were talking at the camera, there were a few awkward pauses. They weren't present at the end though, and the pacing of the rest of the video was good. I liked the use of differentials, since I feel like most textbooks are scared of them, even when they can make things much more intuitive.
8.7
To keep it short : that’s a very nice video ! I haven’t heard about line integration before (but I’m familiar with normal integration), and I have to say that I understood everything ! That was clear, precise, well-motivated, intuitive and very instructive. Good job !
Scale :
- Motivation : 5
- Clarity : 5
- Novelty : 5
- Memorability : 4
---Total : 19
6.5
Okay, the video is good, but I have to ask… is that really how you hold a pencil? I don’t think my thumb is even capable of bending that way! It looks super awkward…
6
There are a lot of handwaving/inaccurate moments throughout the video that don't hold up under stricter scrutiny. For a more general audience, this video is well explained, albeit the intro is very cringe.
6
Sadly you skipped explanation directly to tangent line. I expected you show that distance along the curve tends to tangent... Everything else seems ok.
6.9
Overall, a quite nice introduction to multivariate functions, especially all the comparison to the univariate methods.
Unfortunately, you try to introduce parameter curves as functions, when they aren't (multiple possible y's for x, is not defined for all x, ...). But this is just a minor technical detail, which doesn't impair the main points of the video.