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The math in this video is only understandable if you truly understand calculus, which means that it's likely none of the politicians trying to use these models and not many of the physicians we hear speaking on TV really know what the models are doing. But here is a basic version of how models of the spread of and recovery from viruses are made. It shows a general idea of how a virus might develop and what flattening the curve is. Feel free not to watch it, because it's not for folks who are mathematically faint of heart.
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From:
no subject
My last interaction with differential equations was in 11th grade, when the teacher spent two weeks in my analytical geometry and trig class to prep the students who were going to go on into calc in 12th grade.
I watched most of this video, and while I wouldn't be able to assemble the equations the host did, I did understand enough of what they meant to at least go, 'yep, I follow that.'
It's a story for another time how I didn't end up taking calc (I had planned to), but what resonated about this video and my partial understanding of it relates to the work I ended up doing after high school, particularly the electronics work over the last few decades.
Customers often ask me where I went to school to learn the audio repair biz, and I tell them that I didn't, I am completely self-taught. This surprises most of them, but I elaboate that I was always fascinated by how things work, and well before high school I had read extensively on most basic math and science fields. If you understand the underlying principles of things...
So, when I ended up by chance getting hired to repair major appliances, even though I never worked on, say, a refrigerator before, I knew how they worked. The rest is simply 1) practical application and 2) repetition.
Audio is no different. I loved music, became an audiophile, tinkered with gear for a hobby, eventually started repairing it for a living.
But-- could I design an amplifier? Only with great difficulty, since that's a whole 'nother level of knowledge beyond what I currently know. There'd be a whole lot of trial and error, and the end product might not be optimal.
Would I have been a good engineer if I had gone on to college? Road not taken, no going back, never know. Like being a good doctor, being a good engineer means responsibilities on a whole 'nother level too-- something few people think of when, say, they get into their car, turn the key, and blithely drive off simply assuming that insanely complex, precision machine around them will function properly and not kill them.
One nice thing about the stuff engineers design and I repair is that it very seldom kills or even injures anyone. Yay, audio! :-)
From:
no subject
I was a few years ahead of you, but we didn't have a full course in calculus at my high school, and our school was known for being strong in math and science in the St. Louis area. (Lot's of kids like me who were children of engineers. I purposely did not study engineering in college, so there would be no fight between my brother and I over my father's business.) Having analytic geometry turned out to be extremely useful during my working career, in programming some robotic machinery. We had differential calculus as a part of our "math theory" class as seniors, but not integral calculus. Just in case, I taught myself integral calculus when I was about 40. Didn't actually need any of calculus, but I don't regret learning it.
I thought about being a math major in college. I took analytic geometry again for credit, and breezed through the first part. The second half was diddly special cases that required ponderous, tricky hand calculations. With my undiagnosed dyslexia I had no chance doing the problems consistently, and was lucky to end up with a C in the class. That wasn't worse than most of my friends studying engineering, but it was enough to tell me not to go further formally in math.