Need a math topic idea
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Need a math topic idea
I need to come up with a topic in my Calc 2 class to study and write a paper on. I've never had to study and write a paper in a math class before so I'm not sure what kind of research topics I can apply calculus too. We were shown the work of a grad student from a previous semester in which he came up with an equation to predict the growth of a specific species of fish. I just need some simple idea; preferably that an application of integration can be used in.
Re: Need a math topic idea
Population modelling isn't a bad topic to write about.
For an overly simplistic model of a single population you could say the the birthrate and deathrate are directly proportional to the current population. i.e. [imath]\frac{dP}{dt} = (bd)P \;  b,d \in ( 0 , 1)[/imath]. Describe what happens both when [imath]b<d[/imath] and [imath]d<b[/imath], what each of those cases imply and why that means that the model is too simplistic over a large time scale. Then take a look at the logistic function for some more realistic models that you could try plugging some real world data into.
For an overly simplistic model of a single population you could say the the birthrate and deathrate are directly proportional to the current population. i.e. [imath]\frac{dP}{dt} = (bd)P \;  b,d \in ( 0 , 1)[/imath]. Describe what happens both when [imath]b<d[/imath] and [imath]d<b[/imath], what each of those cases imply and why that means that the model is too simplistic over a large time scale. Then take a look at the logistic function for some more realistic models that you could try plugging some real world data into.
Re: Need a math topic idea
There's plenty of calculus to be had in pharmacology. Modeling levels of a drug in the bloodstream offers a lot of options for your topic.
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Re: Need a math topic idea
How long does it have to be? If it can be short: Get an intro diff eq text book, find the chapter with equations of the form dy/dx + f(x)y = g(x), find a word problem, solve it by integration.
Re: Need a math topic idea
If you're interested, the kind of equations Suffusion is referring to is linear, first order.
Computer Science: A place to discuss the spirituality of Pornography Storage Apparatuses and programs, from algorithms to computability.
Formal proofs preferred.
Re: Need a math topic idea
Suffusion of Yellow wrote:How long does it have to be?
Preferably a few pages.

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Re: Need a math topic idea
lncabin wrote:Suffusion of Yellow wrote:How long does it have to be?
Preferably a few pages.
Eh my idea probably won't be long enough then.
 BlackSails
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Re: Need a math topic idea
Have you done taylor series?
If so, perturbation theory might be a good topic.
If so, perturbation theory might be a good topic.
Re: Need a math topic idea
Is your aim to write about maths, or to write about something that you're applying maths to? Given the choice I'd certainly go for the latter but still involve well written mathematics. Quite how much do you even know? Are you comfortable with differential equations or do you want to stick to straight integration? Can you use computerised modelling?
Aside from mathematics, what are you interested in? As you'd know, basically every area of the sciences are pretty calc heavy. Even the humanities such as economics or sociology. If there's anything that you want to write about, then we can probably help you find a way to make it relevant.
edited because word awesomification is annoying.
Aside from mathematics, what are you interested in? As you'd know, basically every area of the sciences are pretty calc heavy. Even the humanities such as economics or sociology. If there's anything that you want to write about, then we can probably help you find a way to make it relevant.
edited because word awesomification is annoying.
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