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Big Picture of Calculus (2010) [video]

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Re: Big Picture of Calculus (2010) [video]

#11

Post by brootstrap »

brightball wrote: post #9

What would be some practical "daily life" applications of calculus? I've been discussing a focus on teaching with applicable examples in a lot of subjects, but this is one where I've been struggling a bit.

Say you want to measure how much energy is hitting the top of our atmosphere in a given day? Triple integral from infinity (the sun) to top of the atmosphere (call it 0).

Examples with classic physics problems are good too. How about F=ma => F=m*dv/dt. Everytime you apply a force to an object calculus magic is there to mathematically describe the process.

Re: Big Picture of Calculus (2010) [video]

#12

Post by jhck »

brightball wrote: post #9

What would be some practical "daily life" applications of calculus? I've been discussing a focus on teaching with applicable examples in a lot of subjects, but this is one where I've been struggling a bit.

In a book review from 1988 [1, p. 892] the mathematician Underwood Dudley claimed:

> First-semester calculus has NO applications.

That said, the central ideas of calculus are firmly grounded in daily life (as Strang points out in the video): Differential calculus is about investigating speed (or, more generally, rate of change), and integral calculus is about investigating area.

[1]: http://www.maa.org/sites/default/files/0002989051112.di99173...

Re: Big Picture of Calculus (2010) [video]

#13

Post by SomeStupidPoint »

brightball wrote: post #9

What would be some practical "daily life" applications of calculus? I've been discussing a focus on teaching with applicable examples in a lot of subjects, but this is one where I've been struggling a bit.

Throwing things is estimating calculus: you pick the velocity to counteract the accelerations the object experiences to get the displacement you desire. Acceleration from air resistance is a function of velocity.

Also, you can measure boobs with integrals and model their jiggle with differential equations.

...I may have been a teenager when I was first learning. But modeling boob motion is apparently serious science and actually gets extremely complex when you try to model the interactions of the different constituent tissues.

Re: Big Picture of Calculus (2010) [video]

#14

Post by mcguire »

quakeguy wrote: post #5
datainplace wrote: post #4

Now I know someone is browsing my Youtube history and posting to HN. Youtube really is the math teacher I never had. Probability Models and Axioms https://www.youtube.com/watch?v=j9WZyLZCBzs The Exponential Function https://www.youtube.com/watch?v=oo1ZZlvT2LQ&t=100s Vector Space https://www.youtube.com/watch?v=ozwodzD5bJM&t=36s Tree cutting fails: https://www.youtube.com/watch?v=JHZkR6UVegY

That last vid made my day, expecting nodes and splitting algorhytms. You clever you! :)

For those of you who don't know, felling trees is incredibly dangerous. They store immense energy in a not terribly structurally safe form. Don't do it if you don't know what you are doing.

Re: Big Picture of Calculus (2010) [video]

#17

Post by Miserlou57 »

alfonsodev wrote: post #7

Thank you for this video, is there a platform that you could aggregate all this resources mapping them to certain knowledge tree ? So that you could have the big picture and then zoom in for specific topics videos. Something like Khan Academy's knowledge map[1], that you could customise to add you own contents, this video for example. [1] https://www.khanacademy.org/exercisedashboard

I worked pretty hard on something like this many years ago. I am not a coder so it was a formidable challenge and I never really got it polished or complete. The goal was to create a blank canvas where anyone could organize instructional content from the web (i.e. KhanAcademy, YouTube, etc) into their own class. Each class topic was structured like a subreddit for each topic, with the best results hopefully filtering to the top

Re: Big Picture of Calculus (2010) [video]

#18

Post by datainplace »

mcguire wrote: post #14
quakeguy wrote: post #5

Earlier quoted context omitted.

That last vid made my day, expecting nodes and splitting algorhytms. You clever you! :)

For those of you who don't know, felling trees is incredibly dangerous. They store immense energy in a not terribly structurally safe form. Don't do it if you don't know what you are doing.

I remembering learning that the most powerful force acting on a building or tree was inertia. Watching videos like this makes that much more clear.

Re: Big Picture of Calculus (2010) [video]

#19

Post by School-Cotton »

brightball wrote: post #9

What would be some practical "daily life" applications of calculus? I've been discussing a focus on teaching with applicable examples in a lot of subjects, but this is one where I've been struggling a bit.

"Calculus" by Tom Apostol has lots and lots of simple physics applications.

I cant think of any obvious applications of calculus to the average non-technical person's daily life. If that's what you mean, you're going to have a bad time, as I think it's a misconception of what math is supposed to be for.

Re: Big Picture of Calculus (2010) [video]

#20

Post by ww2 »

brightball wrote: post #9

What would be some practical "daily life" applications of calculus? I've been discussing a focus on teaching with applicable examples in a lot of subjects, but this is one where I've been struggling a bit.

When you look at the GPS estimated time of arrival, or check the current MPG or mile left for your car.
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