2/23 class

[Jay McCarthy]

I think that the read and then comment process worked reasonably well
last time, despite my long delays. The next subject, numerical
integration, is much more mathy and much more of the form "scientists
care about integration, but it is hard, what can we do to help them?"

I found some really great slides and then a pretty decent write up of
some basics:

http://butler.cc.tut.fi/~piche/numa/lecture0910.pdf (slides)

http://www2.le.ac.uk/departments/physics/people/mervynroy/lectures/numc.pdf
(section 2 is a write-up)

Can you read these in detail and give your comments & feedback? The
first one is a bit heavy on Matlab code, but I hope that your astute
programmer eyes can see through the language into what is interesting
going on.

I also think it could be interesting to get you to find one
application of integration that you didn't know before hand. (Maybe
try Googling "Why does <field X> need integration?" or something and
try to discover something new.)

<3

Jay

--
Jay McCarthy
http://jeapostrophe.github.io

"Wherefore, be not weary in well-doing,
for ye are laying the foundation of a great work.
And out of small things proceedeth that which is great."
- D&C 64:33

[Lais Baumgratz]

If I'm being honest, I got really confused with the slides. Not just because of the Matlab code, but because of the crazy math that was going on. And also because I feel like it's really hard to actually learn something just reading slides.

But then I read the other text and everything made a lot more sense! (We were supposed to read just section 2, right?)

Since the text mentioned physics already, I searched for "application of integral calculus in biology" and I actually found one application in economics and one in biology.

Say that a company has the functions that represent the Demand and Supply curves. Then, in order to find the consumer surplus, for example, it could use the integration of that pink are of the graph.

As for biology, say you want to obtain an expression for the flux of blood in the blood vessel. Apparently you can also use an integration to figure that out. I didn't quite understood, but it's probably because it's been a while since I took calculus.

Reference: https://www.boundless.com/calculus/textbooks/boundless-calculus-textbook/inverse-functions-and-advanced-integration-3/further-applications-of-integration-15/applications-to-economics-and-biology-101-2817/

[Sean McCoy]

I also found the intricacies of the slides a bit confusing, but the general ideas were pretty clear so I got that out of them at least.

As for an interesting application I didn't know about, consider agriculture - it's possible to calculate the area of irregularly shaped parcels of land if you can find or create equations describing adjacent physical features. Using tools that probably exist to facilitate this process, farmers can draw curves on 2d maps, integrate to calculate the area between them, and determine the sizes of their weirdly-shaped plots of land for the purpose of buying seed or fertilizer. And if their landholdings are not totally flat, like they own part of a mountain or something, they can use multiple integrals to determine areas of things. And actually, come to think of it, this is probably part of how we determine the sizes of really big physical features (mountain ranges, trenches, etc.)

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[blondi...@gmail.com]

I was also really confused by the math in the slides, but it was cool to see some computer science ideas (like Divide and Conquer, etc.) implemented from a mathematical standpoint. The article about numerical integration made much more sense and I liked how it explained the coded algorithms in relation to the mathematical functions. I also think the idea of using a "continuously varying step size" is very interesting. I googled "Why does Wall Street need Integration?" and found that they use integration techniques to develop models for the future of the stock market. 

On Monday, February 23, 2015 at 1:34:08 AM UTC-5, Jay McCarthy wrote:

[James Kelly]

I agree with what's been said about the slides - pretty hard to comprehend them fully because it's mostly just equations. 

I couldn't find too much on this, but I feel like drones would require numerical integration in order to fly smoothly to certain coordinates. It seems like this issue pops up on a few forums.

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[th...@vassar.edu]

I tried foolishly to dive into how integration works in games.  I've heard a lot of buzzwords (Euler,  Verlet, RK4 integration) but not much else, and as far as I can tell it's used in physics games to get an appropriate representation of the velocity, acceleration, path, and position of objects given the fact that they only exist in points between updates of the system (again I may be misconstruing the concept). 

I'd also like to echo the sentiment of confusion at times.  

On Monday, February 23, 2015 at 1:34:08 AM UTC-5, Jay McCarthy wrote:

[isc...@vassar.edu]

Sorry for my super late response. better late than never! :)

I didn't have a lot of questions after I read the write up, but like everyone else I found the slides confusing. 

I looked up integration in meteorology and found that It is used in the hydrostatic equation. The hydrostatic pressure is used to calculate "The pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity" (dictionary.com). Because pressure is not constant, (water pressure increases as depth increases and air pressure decreases with height) in order to calculate how much pressure is being exerted, we must take the integral. 

This is used to estimate how certain particles will react depending on the pressure, and we can then use this to see bigger trends of reactions and ultimately the weather. 

On Monday, February 23, 2015 at 1:34:08 AM UTC-5, Jay McCarthy wrote: