2117: "Differentiation and Integration"

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pogrmman
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Re: 2117: "Differentiation and Integration"

Postby pogrmman » Fri Mar 01, 2019 7:17 pm UTC

Quizatzhaderac wrote:This is probably my biggest gap in my calculus instruction: when to actually use these techniques. In class you lean heavily on "we were just taught this technique, so we should probably use it".

pogrmman wrote:As my calculus teacher in high school told us, multiple times: “you can teach a monkey to differentiate, but integration is a skill”.
That seems a perilous thing to say for somebody actively teaching integration.

One student failed? "You can teach a monkey to differentiate, the editorial 'you"; obviously, you (specifically) can't teach that well."

Well, he could actually pull it off because he was (is) a fantastic teacher that did an awesome job addressing that particular gap that you mention — how to recognize when to do different things to integrate. He specifically challenged all of us to think about the “why” as much as the “how”. Obviously, being a high school class, we couldn’t learn the all the reasons behind quite a few of the things we did, but when it was possible, we did.

His main goal was to give us a thorough understanding of the material: often by challenging us a lot. I remember going into the AP worried about how hard it was gonna be, but being stunned by how easy it was. It turns out, whenever we’d been practicing, he’d specifically chosen some of hardest questions from both the AB and BC exams going back like 30 years, even though it was an AB class. When I took multivariable calc in college, I probably had a better understanding of the base material than most other people. The time we’d spent in high school on things like “OK, what actually is an integral? Why do they work the way they do?” and other things along those lines really helped me in college.

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ThAlEdison
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Re: 2117: "Differentiation and Integration"

Postby ThAlEdison » Fri Mar 01, 2019 7:25 pm UTC

Pfhorrest wrote:
GlassHouses wrote:
Pfhorrest wrote:Silicon dioxide has no "ish" about it, that's straight up what most of most stones are made of.

It's not what computer chips are made of, though. That would be highly pure silicon, and silicon is a metalloid, not a rock.

Then all of the jokes about computers being made out of sand fall apart, because sand is mostly silicon dioxide.

Sand could be used as the base for a process that removes the oxygen leaving behind the pure silicon desired.
If such silicon were used in a computer, the computer would have sand as one of it's ingredients, even though no actual sand remained.

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Quizatzhaderac
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Re: 2117: "Differentiation and Integration"

Postby Quizatzhaderac » Fri Mar 01, 2019 10:19 pm UTC

Archgeek wrote:...hilariously pure silicon crystal...
and I though I had a nerdy sense of humor, I don't think I've ever broke out laughing over a crystal.
The thing about recursion problems is that they tend to contain other recursion problems.

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GlassHouses
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Re: 2117: "Differentiation and Integration"

Postby GlassHouses » Fri Mar 01, 2019 10:22 pm UTC

Archgeek wrote:Chips contain plenty of oxide, though. The wafer-thin slices of hilariously pure silicon crystal are very commonly doped with its oxide in order to provide the p-n and n-p junctions that make useful diodes and transistors happen. So at the very least, they certainly contain sand.

Are you sure? This page contains a long list of dopants, but it doesn't mention SiO2.

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Archgeek
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Re: 2117: "Differentiation and Integration"

Postby Archgeek » Fri Mar 01, 2019 11:30 pm UTC

GlassHouses wrote:
Archgeek wrote:Chips contain plenty of oxide, though. The wafer-thin slices of hilariously pure silicon crystal are very commonly doped with its oxide in order to provide the p-n and n-p junctions that make useful diodes and transistors happen. So at the very least, they certainly contain sand.

Are you sure? This page contains a long list of dopants, but it doesn't mention SiO2.

Oh shoot, 'turns out the oxide's used as the dielectric in your standard field-effect transistors, not a dopant, though it's losing popularity of late due to charge loss from quantum tunneling at ever lower process sizes.
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Eebster the Great
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Re: 2117: "Differentiation and Integration"

Postby Eebster the Great » Sat Mar 02, 2019 5:26 pm UTC

As I understand it, metal oxide semiconductor FETs use metal oxide semiconductor material. So for a silicon wafer, you will have a layer of SiO or SiO2 on top of the silicon, which then gets etched to make a working chip.


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