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May 27, 2005
Integration Trick
I have not posted for a few months now, but this has nothing to do with my workload in university. My workload has been a joke. Now, I am alive and well in Halifax, stumbling through a 16-week work term in the Dahn Group. I will be posting more of those long winded IPhO stories shortly.
Before that, however, let me digress and tell you about a neat integration trick I learned from working in the research group.
I was plotting some voltage-current graphs, and wanted to integrate them. These are not your simple Ohmic V-I graphs where the slope is constant, so the task is quite a bit more difficult.
Anyway, the lab here has many computer programs that can do numerical integration, but I needed to select only a portion of the graph, and editing the data file proved to be too much trouble. So, the professor walks in and tells me about a trick.
You see, we have these extremely accurate electronic balances - they are accurate to +/- 1 microgram. Jeff, who is the professor, explains to me how I can make use of this fantastic piece of lab equipment to integrate “as he did back in his day.” Basically, I was to print two copies of the graph in question. I can cut out a rectangle that includes the entire plot and the axes from the first copy, and the area of interest from the second copy. After weighing both cutouts on the balance and calculating some ratios, the result emerges! Much better than using Simpson’s method, right?
Now I just have to petition for the university to let me bring an electronic balance to my final exam instead of a calculator…
Posted by Tout Wang at May 27, 2005 03:31 PM
Comments
You can also colour it in, scan, then dither it to black and white and measure the number of darkened pixels. Thats what they do in Cyber now. :P. Also works with non-connected domains.
Posted by: Oleg Ivrii ![[TypeKey Profile Page]](http://oleg.moltenstudios.com/blog/nav-commenters.gif)
at May 28, 2005 04:56 PM
That's all fine and dandy provided that you know the integral for the whole curve. Of course, being the math guy, I'd say that you should apply a Riemann Sum to the area of interest. That should be more fun. Especially if the function isn't analytic. Or continuous. Or well-behaved.
Posted by: aSo at May 29, 2005 01:47 AM
Wouldn't cutting up things introduce a huge error? Or do you have another equipment for precise cutting...
Posted by: Yufei at May 29, 2005 10:02 AM
If you know Origami, you could also do surface integrals without worrying about the (EG-F^2)^(1/2) thing. :}
Posted by: Max at May 29, 2005 11:58 AM