What is Calculus Used For? Jeff Heys at TEDxBozeman EIS คณิต กับ ครูโซ่ ยอดหทัย รีศรีคำ

มีนักเรียนคนนึงหลังจากเรียนแคลไปได้ครึ่งเรื่อง เค้าถ้าถามผมว่า อาจารย์ครับนอกจากที่มันจะเอาไปใช้ประโยชน์นอกเหนือจากการหาความชันของเส้นโค้งแล้วมันเอาไปทำอะไรได้อีกครับ คำถามนี้โดนใจผม แสดงว่าเด้กต้องการรู้ลึกๆว่าแคลมันเอาไปทำอะไรได้ในชีวิตประจำวัน ผมในฐานะที่เป็นครู นอกเหนือจากการสอนในเนื้อหาแล้ว ความรู้รอบตัวต้องมีเช่นกัน พูดมานานแล้ว เอาละ ไปดูกันเลยดีว่าว่า แคลทำอะไรได้อีกเยอะเลย สำหรับคนที่ฟังไม่ทัน  ครูถอดคำพูดมาให้

0:09 so i’d like to talk to you about a question that

0:12 i’m guessing most of you have never asked

0:15 uh… but it’s a question that i asked a lot i was an engineering student just up

0:20 the road at montana state university

0:22 ants

0:23 i had to take a lot of calculus courses i’ll so let’s take a lot of math courses

0:26 of high school 0:27 and the question that i kept coming back to his what is all this stuff on using

0:32 or learning

0:34 what does all this calculus used for

0:36 um… and i never

0:38 really got a satisfactory answer intel i went to graduate school in boulder

0:41 colorado

0:43 uh… and the reason why was able to get an answer there is because boulder had a

0:47 very bizarre

0:49 well mean that the sarc data very interesting smoking ordnance the time

0:53 uh… since the mid nineties and the smoking ordinance in boulder was

0:56 basically that if you want to have a smoking area in your restaurant

1:00 it had to be sealed the box had to be completely walled off with the door

1:04 uh… that would open and close 1:06 as you would expect most restaurants didn’t

1:09 really 1:10 uh… have a smoking area because that’s what he reversed too expensive to

1:13 construct 1:14 but if you did and they were buried thick with smoke 1:18 in one of my classes we work asked to develop a mathematical model 1:22 that would allow someone to calculate 1:25 how much smoke would come out of the smoking rooms every time the door was 1:29 open 1:30 uh… or similarly 1:31 allow us to calculate if you were sitting at a table somewhere else in the 1:35 restaurant 1:36 how much smoke would you be exposed to 1:38 this first really sort of it 1:40 transformative assignment for me 1:42 uh… i realized that calculus and mathematical models were useful i could 1:47 use them to calculate something i was interested in when i went into a 1:51 restaurant in 1:52 the waitress wanted to seat neither table like to determine whether or not i 1:56 really wanted said at that table 1:58 based on house 1:59 far close it was to the smoking area 2:02 since that original mathematical model expense 2:05 fifteen or more years developing mathematical models and i sort of come 2:09 to realize that based fit into about three categories 2:13 uh… the first category 2:16 our models that 2:17 predict the future 2:19 euclid once you’re most familiar with 2:21 if you know the current temperature and pressure around the world 2:24 uh… you consult some fairly complicated calculus equations 2:28 and use that solution to predict the weather over the next 2:32 they or we 2:33 four years 2:34 uh… similarly if you want some stocks somebody wants to 2:38 uh… by and option from you to purchase those stocks 2:41 you could solve the black scholes equation it’s another complicated the 2:45 calculus based equation 2:47 that would allow you to predict 2:49 what that stock price is going to do over the next couple months and allow 2:52 you to calculate the price that you should charge for the auction 2:58 well 3:00 difficult models uh… they have a lot of uncertainty on them 3:04 it’s really hard to predict the future 3:07 pics models are largely stay away from 3:16 another category of models uh… our models that we develop to avoid doing 3:20 experiments because the experiments are really really expensive 3:24 so few decades ago wind boeing wanted to design a new aircraft 3:28 what they would do is they would go uh… end of the wind tunnel and they 3:32 would try out the 3:34 old wide range of shapes for the wings for the few slice 3:38 uh… a whole wide range of shapes for the engines 3:41 and they would see what was the most efficient 3:44 that was 3:44 tremendously expensive now what they do is they go into a computer go onto a 3:49 computer 3:50 uh… and they design 3:51 the aircrafts on the computer head of time 3:54 uh… any only test out a couple of the very best designs the wind tunnel 3:58 misstates contends 4:00 of millions understandings dollars 4:03 also if you want to design a billion dollar experiment 4:06 probably a pretty good idea to develop a mathematical model head of time to see 4:10 whether or not that’s money well spent sort of get an idea of whether or not 4:13 that experiment just at work 4:15 in these are difficult models shandling up the ones we create 4:20 the category of models we creates that i’ve worked on for the most part uh… 4:24 our models wear the experiment that would give you the same information 4:28 is unethical 4:30 so wired magazine 4:31 uh… a few months ago 4:33 had a very interesting particle 4:35 the talked about seven experiments 4:37 where if we could do that they would teach us so much about human health and 4:40 human behavior 4:42 but we can’t do them because they’re unethical experiments 4:45 well what i’d like to 4:47 trip highlights for you today is that in some cases there’s an alternative 4:51 to the unethical experiments 4:54 so this is one the first mathematical models ever worked on 4:58 uh… if you took a slice of your ally 5:01 don’t don’t do that but if you did but you would find some tissues in their 5:04 without a new blood vessels the cornea the lands no blood vessels 5:08 your body produces the fluid that circulates in the front part of your eye 5:12 to provide those tissues that nutrients 5:15 that sometimes that circulation fluid gets messed up 5:19 and that leads to glaucoma 5:21 now 5:22 we don’t really understand how all these different forms of walk home it 5:26 developed 5:27 suite two options 5:29 option number one is 5:31 i can get some really 5:33 been pressure transducers maybe a dozen of them in 5:36 and put them in your eye 5:38 aunt i can measure all the forces 5:41 uh… the fluid inside rights for instance 5:45 we have need volunteers for option one 5:48 uh… i can see a very well but i’m guessing there’s not a lot of hands 5:51 so i’ll give you a second option 5:53 we developed a mathematical model that could 5:56 make those same predictions about how barry s forces impacted the eye 6:00 and that model davis insights into the development 6:03 of a couple different forms welcome 6:06 uh… another 6:07 interesting question is 6:09 there’s a lot of unhittable drugs already on the market and more to being 6:12 developed all the time 6:13 for example there tolkien inhale more chemotherapy drugs 6:17 to maximize delivery 6:18 to where you need it most the tumor that’s in your lungs 6:22 but everybody’s airways are different 6:24 your airways are different from a seven year olds especially right 6:29 what size particle and density of particle should you inhale for your 6:33 unique airways 6:34 again there’s two options 6:36 option number one is you get inhale some radioactive particles and using an 6:42 x_-ray we can see where they go 6:44 probably not a good option right 6:46 option number two is we can develop a mathematical model and we’re working on 6:50 the spread of the road it an issue 6:51 uh… that will protect where different size particles will be deposited 6:55 sweeping determine for your unique airway geometry is 6:59 what’s best for you 7:01 uh… another example and that it echo cardioversion once upon a time and 7:05 learns that they have developed micro bubbles that they can inject into the 7:09 bloodstream and using just a standard ultrasound 7:12 they can actually visualize these bubbles 7:15 movin with the bloody in your heart 7:18 they can see what the blood flow 7:20 uh… in your heart looks like 7:22 well 7:24 that’s nice but with the echo cardiologists really wants to know is is 7:28 your heart healthy 7:29 how efficiently is your heart operating 7:32 and they can’t get that information just from looking at some bubbles moving 7:36 around 7:37 uh… honor ultrasound screening 7:39 so what we are working on is combining this very valuable data 7:43 with a mathematical model 7:44 so that we can someday ad 7:47 to this 7:48 sunday at 7:50 to this 7:52 ultrasound display off gauge or inefficiency gates to the echo 7:56 cardiologists vote will be able to use this data uh… more effectively and and 8:01 design treatments 8:03 but i’d like to close 8:05 just with sort of a challenge misses a challenge 8:09 uh… no matter what your ages but especially if you are a jv is seven or 8:13 ten 8:14 which happens to be the ages of my my two children 8:17 i’d like to just challenge you to consider learning math consider it 8:21 learning calculus 8:23 because there are so many things out there that we still need to develop 8:26 mathematical models four 8:28 because the experiment is impossible 8:30 when we’re working on right now for example is 8:33 uh… we’re working on 8:35 higher temperatures hyperthermia 8:38 to kill cancer cells we need better models of that process simply because 8:42 the experiments are too difficult 8:44 so please consider it learning calculus

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