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Big Picture of Calculus (2010) [video]

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

#21

Post by nothis »

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.

My dad always insists on cutting them himself and watching it always gave me a heart attack. That vid is basically what I play through in my head the whole time. So far nothing happened but man.

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

#22

Post by [deleted] »

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

[deleted]

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

#23

Post by semi-extrinsic »

School-Cotton wrote: post #19
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.

Well, there's plenty of applications that may not be "daily life" but rather "you're likely to encounter this at some point". Take the relation between speed and distance traveled, or the difference between marginal cost and per-unit cost.

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

#24

Post by mrcactu5 »

I was a teaching assistant at UC Santa Barbara for 3 years, I can tell you, students might slug through the calculations , but none -- or a precious few -- really get the big picture.

Mostly, it is that calculus pedagogy is a disaster. And it hasn't been updated to include recent advances in technology (such as Data Science)

Strang is an amazing lecturer. I can tell you, that far into your Masters and PhD these same basic issues resurface. There's at least one project I can think of where the entire problem hinges on taking one derivative.

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

#25

Post by espeed »

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.

"The greatest shortcoming of the human race is our inability to understand the exponential function." - Dr. Albert A. Bartlett

That's the thesis of Dr. Bartlett's famous lecture "Arithmetic, Population and Energy": https://www.youtube.com/watch?v=sI1C9DyIi_8

Calculus is foundational for understanding our rapidly changing, data-driven world. It gives us the ability to see.

You can apply calculus anytime you have a quantity that's changing over time, and you want to see where things are going, how things are changing, and when something is going to happen based on its rate of change -- e.g. stocks, startup growth metrics, how an idea is spreading, mass-market adoption, etc -- anytime you have time-series data and you want to see what it means -- make sense out of it, and understand its implications.

See https://en.wikipedia.org/wiki/Calculus#Applications

And Calculus gives you the ability to calculate how lifelong learning can impact your growth over time -- the significance it can have throughout your life/career -- and realize it's never too late to learn anything ;-)

In the words of Prof John Ousterhout: "A little bit of slope makes up for a lot of y-intercept."

https://web.stanford.edu/~ouster/cgi-bin/cs142-spring12/week...

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

#26

Post by dlo »

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.

I'm going to expand the definition of "daily life application" from things you actually use daily to things you experience daily. These could be engaging too!

For example... what are sunspots? How does the plumbing around your house work? How does a car battery work? How does a microwave oven work?

Another thought. If we are unable to find applications for a technique, should we place such an emphasis on teaching it? I look around and see all the very practical (and interesting!) math and science that is not being taught, e.g. signal processing, just because they are nontraditional. It's a shame to me.

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

#27

Post by Meegul »

seycombi wrote: post #6

If you want to get into the details of Calculus Professor Leonard https://www.youtube.com/user/professorleonard57 Herbert Gross MIT Calculus Revisited: Multivariable Calculus https://www.youtube.com/playlist?list=PL1C22D4DED943EF7B Herbert Gross MIT Calculus Revisited: Calculus of Complex Variables https://www.youtube.com/playlist?list=PLD971E94905A70448 Herbert Gross MIT Calculus Revisited: Single Variable Calculus…

Professor Leonard is really great if you need some extra help learning something. He moves slowly enough with the material that it's difficult to get left behind, however that might be too slow for most HNers.

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

#28

Post by empath75 »

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.

The average person is never going to have to use anything but basic arithmetic in 'daily life', but calculus is essentially the mathematics of change, which touches on a huge number of subjects. You can't do any sort of useful physics without it, or machine learning, or statistics, etc, etc.

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

#29

Post by brightball »

dlo wrote: post #26
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.

I'm going to expand the definition of "daily life application" from things you actually use daily to things you experience daily. These could be engaging too! For example... what are sunspots? How does the plumbing around your house work? How does a car battery work? How does a microwave oven work? Another thought. If we are unable to find applications for a technique, should we place such an emphasis on teaching it?…

That's kind've where I was going with it. Basic understanding of the building blocks of society type stuff: power, water, gas, construction, radio, biology, growing food, vehicles, finances, etc.

Thinking back, I just realized the main reason that I was bored to tears in high school wasn't so much that the subjects weren't worth knowing...just that at the time I was being taught formulas without any clear understanding of why it was useful to know it. If you don't know why it's useful to know it, there's very little reason to remember it beyond passing a test.

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

#30

Post by mindcrime »

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

Youtube really is the math teacher I never had.

Same here. I'm on a quest to run myself through the equivalent of a standard Calc I, Calc II, Calc III, Linear Algebra sequence, and I've managed to find great Youtube resources for all of those things (and more). It's times like these that you marvel at how awesome the Internet can be at its best. :-)

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