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bugsandin... bugsandin...
 
December 16, 2008 04:37 AM

Where is a Riemann Sum applicable in real life?

Is the use of a Riemann Sum with unevenly spaced intervals ever required in the world of mathematics/engineering? If so, where and how?
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eastwind87 eastwind87
 
 December 16, 2008 05:30 AM
Riemann sums help you approximate the area under a curve. In math class, we typically see polynomial or exponential functions (which are pretty easy to integrate). In real life, however, we rarely see these pretty functions.

For example, it's virtually impossible to find a function that exactly represents the contours of a leaf on a tree outside. If you wanted to find the area of a side of the leaf, you certainly can't rely on plain integration. Riemann sums can help you approximate the area. In terms of even versus uneven intervals, there's really not a huge difference from a mathematical perspective. It really depends on what information you have about the underlying curve.
Source(s):
My bachelor's degree in Applied Mathematics obtained from U.C. Berkeley.

Asker's Rating:
• Thank you for the good example, this will help me stay motivated through AP
Calc class for a few more weeks. :)

Also, thanks to everyone who answered, I appreciate it very much!


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xds xds
 
December 16, 2008 05:39 AM
Gotta say it , if thats a picture of you your freakin beautiful

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gymclothes gymclothes
 
December 16, 2008 04:45 AM
Riemann sums allow you to approximate data from equations that closely model a previous data set.

This probably explains it better than I could: http://www.usna.edu/MathDept/website/courses/calc_labs/area/Application.html

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bugsandins... bugsandins...
 
December 16, 2008 04:55 AM
In this example the subintervals are all evenly spaced, meaning a simpler version of the Riemann Sum formula can be used, but I am looking for an example that has uneven intervals, if I can justify being able to use it, I can learn it better for school.

Thanks for the website though, it is a good reference point!

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gymclothes gymclothes
 
December 16, 2008 05:39 AM
So do you mean a Riemann Integral by any chance then?

A Riemann Integral single point approximations of the Riemann Sum to give you a more accurate approximation than a Riemann Sum.

http://en.wikipedia.org/wiki/Riemann_integral

Here is maybe a bit easier to understand example that shows how to use 3 different methods of Riemann Sums and a Riemann Integral equation:
http://planetmath.org/encyclopedia/ExampleOfEstimatingARiemannIntegral.html

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mibchronic... mibchronic...
 
December 16, 2008 05:32 AM
It think any application of finite element method probably deals with Riemann sums with uneven intervals in some way or another. Finite element method is used all the time in computer modeling where more data points (i.e: more precision) is required in one area than another. You can think of it as approximating a function very accurately in one area (for example where it is very turbulent) and very loosely in another (for example where it is very smooth). http://en.wikipedia.org/wiki/Finite_element_method is a good place to start I guess. You may also be familiar with the FEMLab software.
Source(s):
http://en.wikipedia.org/wiki/Finite_element_method


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