CalcBLUE 2 : Ch. 3.3 : The Derivative : Notation & Examples

One thing to watch out for is the notation, as different texts use different notations for derivates and rates of change. This gives you a survey of such notation in the context of a few examples.

[danieljulian]

6:00 "look at the vector of rates of change of OUTPUTS" (this is what we're interested in finding, but what we're seeing in the video at 6:00 is the vector h of rates of change of INPUTS, the r-dot and theta-dot). [Df] takes the vector h of rates of change of inputs to a vector l (ell) of rates of change of outputs (x-dot, y-dot). We are, a few seconds later) being shown the transformation ("linear combination of the image of the basis vectors").

There is a lot compressed into this few seconds of the video, which I'm only beginning to sort out after some linear algebra study. Isn't this image just of the rates of change? The image vectors are not linear functions (curvilinear coordinates!), but we combine them linearly. It's a wonderful taste of the way math is done after we take off the training wheels, but personally, I haven't fully shed them, and perhaps never will. Isn't the linearity wrapped up in the fact that D is all first-order derivatives?

[achronicstudent]

i cannot understand the geometric explanation. *h* must have had components of 2 and -2 but in the picture at 05:54 it has the components of 2 and -3, did i take that wrong or there is something that i missed?

[buraianmath]

at 6:25 why is the polar grid having y and x marked?

[ProDocentify]

Professor, thank you for your videos! The graphics, the material, the speech - I like these so much!
I wonder, do you make video editing all by yourself? That's a lot of work.

[dr]

Oh, golly, I'm used to a variable dotted to mean the time derivative (partial) & the single right quotation mark after a variable (primed?) to mean some other derivative (partial). Also, I'd expect the r, theta grid to be more like in the right side.