Comments by "vk2ig" (@vk2ig) on "3Blue1Brown" channel.

  1. I have an honours degree in electrical engineering and agree with the sentiments expressed here. For example, we were taught how to solve mesh current or node voltage circuit analysis problems by hand with up to three variables, but by rote using Cramer's Rule. We knew why the matrix and vector elements were what they were, and how to find the determinant of the 3x3 matrix, etc, but not the deeper understanding behind the mathematics. Now I think of a mesh current problem such as [Z]•[I]=[V] (solved by computing [I]=[Z]^(-1)•[V], where [Z] is a square matrix of order N, and [I] and [V] are vectors of N elements) as being a transformation of [I] to [V] where the columns of [Z] are the transformed basis vectors from the "I" space to the "V" space. Overall, I am looking forward to what insights this brings to the more advanced methods such as multi-port network analysis, etc.
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  2. I did my engineering course (given by the Mathematics department) on DEs a long time ago, and all I remember is the phrase "taking the D operator". Where you take it, I can't remember ... out the front of the equation, I believe. Anyway, it was so unrelated to anything we were doing in the rest of the course that sadly, we never used any of it. In fact, our electrical engineering lecturers effectively taught us what DE solving we needed to know using other methods. This led to strange anachronisms such as in 3rd year we were taking a mathematics class for solving the wave equation in two dimensions - on the first day I asked the lecturer if we would be looking at three dimensions, because we were already solving DEs in those situations for electromagnetic wave propagation in waveguides. Looking back on it all, I think we were being taught certain things just so the university administrators could tick an accreditation box somewhere saying "Yes, we've taught them how to solve DEs", but there was little or no thought towards how to teach the subjects in an integrated way (pardon the pun).
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  3. In the second example, the rotated i-hat is in the original j-hat position, so the shear now operates on whatever is in the original j-hat position (i.e. shear operates on the transformed i-hat). The author chose this example to show that, in general, matrix multiplication is not commutative. You could work up another example to show commutativity in a specific case; e.g. scaling by 3 with rotation by +π/2, followed by scaling by 1/3 with rotation by -π/2.
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  4.  @Hecatonicosachoron  Hmmm ... oscillating reactions or osculating reactions? 😁
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  5.  @TCArcticWolves  Thank you. That's just what I needed to round out the "Change of basis" episode and this one.
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  6. L'Hopital's rule would fail for a function f(x)/g(x) if g(x) and its derivative g'(x), when evaluated at x=a, obey g(a)=g'(a)=0.
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  7. If you consider an identity matrix [I] of order 2, then the first column is the transformed i-hat vector, which is identical to i-hat. Likewise, the second column of [I] is the transformed j-hat vector, which is identical to j-hat. Hence the identity matrix "transforms" each basis vector into itself ... in other words, it doesn't change any of the basis vectors, hence it can be considered as an identity transformation. Edit: [I] looks like [ 1 0 ] [ 0 1 ] i-hat is [ 1 ] [ 0 ] and j-hat is [ 0 ] [ 1 ]
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  8. Great explanation of partial derivatives - thanks! Nice how you generated the temperature vs length profile using an odd function summed with a constant (50 degrees C). :)
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  9. And maybe call the third person Cueben?
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