Calculus Final Exam; Applied Calc

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Pobega
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Calculus Final Exam; Applied Calc

Postby Pobega » Sun Dec 02, 2007 5:11 pm UTC

For my final exam for Calculus (One) I need to write a three page paper on a single real life scenario where calculus is applied, using either derivatives or integrals. I've searched the internet but I've been unable to turn up any good projects, and I need this done by the twelvth (!!), so I'm hoping someone here would be able to save my ass and give me a good idea for a project. Preferably something with a link to a website or a nice explanation; I'm good at Calculus, but not THAT good.

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Re: Calculus Final Exam; Applied Calc

Postby SimonM » Sun Dec 02, 2007 5:49 pm UTC

Design a can for a Can of Coke, minimize the amount of metal used (or price of said metal)
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Re: Calculus Final Exam; Applied Calc

Postby Qoppa » Sun Dec 02, 2007 5:59 pm UTC

Did you not do applications at all? Just pick an application question (such as the above) and build on it.

Code: Select all

_=0,w=-1,(*t)(int,int);a()??<char*p="[gd\
~/d~/\\b\x7F\177l*~/~djal{x}h!\005h";(++w
<033)?(putchar((*t)(w??(p:>,w?_:0XD)),a()
):0;%>O(x,l)??<_='['/7;{return!(x%(_-11))
?x??'l:x^(1+ ++l);}??>main(){t=&O;w=a();}

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Re: Calculus Final Exam; Applied Calc

Postby Mathmagic » Sun Dec 02, 2007 6:07 pm UTC

Yeah, usually applications in which you minimize or maximize something (a price, materials used, etc.) are generally easy to describe and explain.
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Re: Calculus Final Exam; Applied Calc

Postby CodeLabMaster » Sun Dec 02, 2007 6:11 pm UTC

The other day when I was at the store, I was buying some bottled water when I noticed some "eco-friendly" bottled water when the bottle was designed a bit differently to lower the amount of plastic used in it's design by 30%. Since its a solid of revolution, they had to keep the volume of a half a liter the same while lowering the surface area and holding to a few constraints like keeping it the same height, having it not budging out too much, and keeping the bottom flat. That sounds like it was a job for calculus.

You could investigate the properties, pros, and cons of changing the shape of a water bottle to help the economy or something similar to that.

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Re: Calculus Final Exam; Applied Calc

Postby Pobega » Sun Dec 02, 2007 6:19 pm UTC

CodeLabMaster wrote:The other day when I was at the store, I was buying some bottled water when I noticed some "eco-friendly" bottled water when the bottle was designed a bit differently to lower the amount of plastic used in it's design by 30%. Since its a solid of revolution, they had to keep the volume of a half a liter the same while lowering the surface area and holding to a few constraints like keeping it the same height, having it not budging out too much, and keeping the bottom flat. That sounds like it was a job for calculus.

You could investigate the properties, pros, and cons of changing the shape of a water bottle to help the economy or something similar to that.


I like this idea very much, I think I'll be using it for my project.

And yes, I did do application Calc, but the essay needs to be three pages long (Which most simplistic problems won't be able to fill). I'm hoping that the idea suggested by CLM will be able to fill all three.

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Re: Calculus Final Exam; Applied Calc

Postby Disco_Inferno » Sun Dec 02, 2007 6:20 pm UTC

You could always do something econ related. Marginal cost is a good way to start, and if something else perks your interest while researching, go with it.

But it seems like you found your topic. I hope you do well.
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Re: Calculus Final Exam; Applied Calc

Postby CodeLabMaster » Sun Dec 02, 2007 6:21 pm UTC

Thanks, I'm glad I could help. If you need anymore ideas for specifics on the project, just let me know.

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Re: Calculus Final Exam; Applied Calc

Postby ikerous » Sun Dec 02, 2007 7:51 pm UTC

Projectile motion, rotational inertia, rocket equation, magnetic field, electric field, calculation of capacitance, calculation of inductance, current in a circuit, force created by * field, power dissipation of a train/resistor/battery, optics, etc

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Re: Calculus Final Exam; Applied Calc

Postby ks_physicist » Sun Dec 02, 2007 8:13 pm UTC

CodeLabMaster wrote:The other day when I was at the store, I was buying some bottled water when I noticed some "eco-friendly" bottled water when the bottle was designed a bit differently to lower the amount of plastic used in it's design by 30%. Since its a solid of revolution, they had to keep the volume of a half a liter the same while lowering the surface area and holding to a few constraints like keeping it the same height, having it not budging out too much, and keeping the bottom flat. That sounds like it was a job for calculus.

You could investigate the properties, pros, and cons of changing the shape of a water bottle to help the economy or something similar to that.


Ozarka. I had my senior physics students do an "applied" lab project where their role was as researchers at a company that produces water bottles. Their 'competitor' was Ozarka, and their task was to verify the claims and quantify the results, comparing the "old" bottles to the "new" ones.

Several of the lab teams did a pretty good job at the analysis, and determined that the new plastic is more dense than the old plastic, but is made much thinner, which combined with the smaller label results in that 30% "reduction" in plastic--by volume.

I'm still waiting for the final written lab reports before writing a summary and sending it in to Ozarka to get a response from their engineers.

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Re: Calculus Final Exam; Applied Calc

Postby Yakk » Sun Dec 02, 2007 8:18 pm UTC

Are you allowed to describe the use of the mathematics?

Because writing mathematics out in English takes a ridiculous number of words. ;)

(This response is a joke: it would be unreadable).
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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Re: Calculus Final Exam; Applied Calc

Postby Herman » Mon Dec 03, 2007 3:22 am UTC

See: Physics.

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Re: Calculus Final Exam; Applied Calc

Postby Qoppa » Mon Dec 03, 2007 3:38 am UTC

"The volume of a cube is given by ecks cubed. Calculating dee by dee ecks of ecks cubed will yield three ecks squared..."

Yeah, that could make it long enough.

Code: Select all

_=0,w=-1,(*t)(int,int);a()??<char*p="[gd\
~/d~/\\b\x7F\177l*~/~djal{x}h!\005h";(++w
<033)?(putchar((*t)(w??(p:>,w?_:0XD)),a()
):0;%>O(x,l)??<_='['/7;{return!(x%(_-11))
?x??'l:x^(1+ ++l);}??>main(){t=&O;w=a();}

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Re: Calculus Final Exam; Applied Calc

Postby Yakk » Mon Dec 03, 2007 4:21 am UTC

Qoppa wrote:"The volume of a cube is given by ecks cubed. Calculating dee by dee ecks of ecks cubed will yield three ecks squared..."

Yeah, that could make it long enough.


The number of cubes that are one foot on each edge that can be made by cutting up our cube which is a given number of feet long is given by taking the length of one edge of your cube, drawing a line that is one foot tall that is perpendicular to the length, and then creating a triangle. Now create a triangle that is similar to that triangle, but with the one foot base corresponding to the length of the side. Now take the non-hypotenuse side that doesn't correspond to the one foot base, and use it as the side corresponding to the one-foot base in yet another similar triangle.

In this last triangle, take the side that the non-hypotenuse and does not correspond to the one-foot base. Now create a rectangular prism that has that as one side, and one foot as the other two defining edges. This shape has the same volume as our original cube.

:)
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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Re: Calculus Final Exam; Applied Calc

Postby Fieari » Mon Dec 03, 2007 11:35 pm UTC

If you're enough of a geek, you can look at D&D and use calculus to determine optimal values of Power Attack (3.5 edition) based on whether you're wielding 1 handed or 2 handed, charging or not, and what the target die roll you need to hit is. You can then use this data to propose alternative models of Power Attack that could produce different results that might be desired... such as making its utility more consistent, instead of sometimes reducing your expected damage output.
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Re: Calculus Final Exam; Applied Calc

Postby Pobega » Mon Dec 17, 2007 12:24 pm UTC

I really need help with this project. If anyone can help me soon (Within a few hours) can you IM me at blockmeharder (AIM) or pobega[at]gmail[dot]com (MSN/Jabber)? I put off this project because of other finals and now I am rushing to finish it hours before the class.

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Re: Calculus Final Exam; Applied Calc

Postby Alexander » Mon Dec 17, 2007 1:38 pm UTC

I'm pretty sure that 'optimization' problems are the big ones that represent Calc 1 work in the field. Fences need to be built, packages need to be optimized for travel, etc. etc. etc. Find something you like and find out why it got designed that way (ever wonder why we don't, for example, pack things in spheres?). Calc 1 sort of really focuses on these things. It would've been a really cool paper to write, if you weren't having a heart attack!

Best of luck. I know this reply is too little, too late. :roll:

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Re: Calculus Final Exam; Applied Calc

Postby Yakk » Mon Dec 17, 2007 2:29 pm UTC

Sorry Pobega. Looks like you are screwed. Shouldn't have put it off nearly this much.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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Re: Calculus Final Exam; Applied Calc

Postby ArmonSore » Wed Dec 19, 2007 2:16 am UTC

Here's the problem you should solve: Your friend in paris really loves chocolate, but doesn't have any! So you decide to take a big cannon and fire said chocolate to said friend at said location. Calculate the speed and direction you would need to fire said chocolate at, in order for it to reach your friend in Paris. Account for wind resistance (you decide whether or not it should be quadratic or linear) and the coriolis force. Treat the bar of chocolate as a point mass with constant mass.

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Re: Calculus Final Exam; Applied Calc

Postby Buttons » Wed Dec 19, 2007 2:52 am UTC

I think I had to do a project like this in high school, where we made up a problem then solved it with calculus. Mine involved kicking Antonin Scalia into next week. And Australia.

That is, finding the velocity with which to launch the Supreme Court justice so that he landed in the Australian Outback one week later. There may have been a story about duck-hunting involved. I was ridiculously political back then.

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Re: Calculus Final Exam; Applied Calc

Postby Yakk » Sun Dec 23, 2007 2:17 am UTC

Point mass? A naked singularity?!
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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Re: Calculus Final Exam; Applied Calc

Postby Pobega » Fri Dec 28, 2007 4:06 pm UTC

Yakk wrote:Sorry Pobega. Looks like you are screwed. Shouldn't have put it off nearly this much.


No need to be so rude and stuck up, I figured everything out but just thought I'd ask for a bit of help here.

I wasn't exactly putting it off, the teacher gave it to us the first and expected it back the seventeenth, while between those two dates I had multiple final exams (Including the final exam in my two Calculus classes!).


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