Taylor's MAT267 72573 F16

Tuesday, November 29, 2016

How to learn math

People are asking me how to learn math again. I'm not an expert, but here are a couple of links that might be useful:

Stanford Math 53: How to study math.

Barbara Oakley's Learning How to Learn

Tuesday, November 22, 2016

All about the final exam

Hello Dr. Taylor, I just wanted to confirm where we are going to be taking the final for this class. I am in your MWF class. I assume we take the final exam in the lecture classroom?

Thank you,

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Nope. Per the syllabus (remember that thing?), the final exam will take place in DISCVRY 250 on December 6, from 7:10PM-9:00PM. Plan to be well studied, well rested, wide awake and sober.

Hi Professor, just wondering if you are holding class on Wednesday the 23rd of November. Thanks!

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Yes. The great State of Arizona is paying me to the teach on the 23rd, and so teach I must.

A common point of confusion...

When a problems says to integrate ∫ F.dr along a path, or any path, from point A=(a, b, c) to point
B=(d, e, f), that means that the direction is taken FROM A TO B. For some reason lots of people want to do this in reverse, which means they get the negative of the right answer. In the particular if
F=▽f, lots of people will write ∫ F.dr=f(a, b, c) -f(d, e, f), instead of the correct answer which is
f(d, e, f) -f(a, b, c)

Saturday, November 19, 2016

13.3#11

Hello Professor! I'm a bit stumped here. I am not really sure where to go from this point. My understanding of a conservative vector field is that it is path (in!)dependent, and should turn up the same value for work for any path between two points. (true!)

However, I don't see what I am doing wrong. I have been drawing out the fields and attempting to estimate paths, but I cannot get past these answers. Could you please enlighten me as to what
paths I am thinking of incorrectly?

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Trying to guess about wha their line integrals will be for various paths is *NOT* very helpful, because there are so many possible paths. There are two keys required for these problems. The first is remembering that being path independent/conservative is the same as (if the domain is reasonable) being a gradient. The second is to have a gallery of examples of what gradient fields look like. For example, the gradient of a linear function is always a constant vector field, that is at every point you have the same vector with the same magnitude pointing in the same direction. Do you have any of those? I suggest you look at your favorite quadratic functions and sketch out their gradient fields, there are some of those in the collection above. You should also be able to look at a vector field sketch above, and guess what are the functions F_1 and F_2, and from that understand if
∂F_1/∂y=∂F_2/∂x is possible.

Section 13.4 due date

Hello Professor Taylor!

Quick question: Is section 13.4 meant to be due on Sunday?

Thanks!

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Now it's Friday