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

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