
#1
Feb2308, 02:53 AM

P: 5

And what is the process called?
Say you have a bunch of data you've collected plotted on a graph, what level of math teaches you to convert this data into a formula that you can play with? I'm in calc 2 right now and we just covered volumes. It's AWESOME! I'm not much of a higher level math person, but this has got me thinking about moving on. But I really don't know what's out there. We are working with such simple equations, but what if I didn't know the equations? Say I plotted the dimensions of 1/2 beer bottle, lengthwise about the xaxis, and wanted to integrate it from 0 to whatever the height is. But the problem is I don't know what formula represents the shape of these dots. I mean I could estimate and do it in sections, but how do I get an equation that represents it perfectly? Thanks a lot! Sorry if this is basic :) 



#2
Feb2308, 03:31 AM

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What we CAN do is to approximate the graph by piecewise "simple" formulas and sew them together. Because polynomials are so nice to work with, it is quite popular to approximate difficult curves by piecewise polynomials. 



#3
Feb2308, 03:46 AM

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Fitting data points to equations is called Mathematical Modeling; also curve fitting. You learn this as early as Introductory Algebra, and you can learn much more of it in Intermediate Algebra and PreCalculus.




#4
Feb2308, 04:11 AM

P: 813

What math level teaches turning data points into equations? 



#5
Feb2308, 04:50 AM

P: 5

actually, after some more searching, I think what I'm looking for is interpolation. That also lead me to info on extrapolation which looks fantastic. 



#6
Feb2308, 06:32 AM

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P: 2,751

If your goal is just to find a mathematical formula to fit the points purely for the purpose of finding the integral then you would be much better off looking at numerical integration techniques like Simpsons rule or RungeKutter. These work directly on the data points (you could say they implicitly interpolate the data points).




#7
Feb2308, 06:36 AM

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#8
Feb2308, 11:10 AM

P: 792

Basic polynomial (3rd degree and lower) curvefitting I did in first year in applied maths, but it was very introductory stuff.




#9
Apr209, 01:19 PM

P: 5

For periodic data use a Sine, Damped Sine, or Lorentzian series as a math model. For nonmonotonic, but not periodic, data I recommend the Lorentzian series. 



#10
Apr209, 02:01 PM

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I second arildno's suggestion of cubic splines (or, generally, Bézier splines).



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