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How is asymptotic analysis (big o, little o, big theta, big theta etc.) defined for functions with multiple variables?

I know that the Wikipedia article has a section on it, but it uses a lot of mathematical notation which I am unfamiliar with it. I also found the following paper: http://people.cis.ksu.edu/~rhowell/asymptotic.pdf However the paper is very long and provides a complete analysis of asymptotic analysis rather than just giving a definition. Again the frequent usage of mathematical notation made it very hard to understand.

Could someone provide a definition of asymptotic analysis without the complex mathematical notation?

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Could you gave more context for what you're interested in (i.e. what problem you're trying to solve using asymptotic analysis for multiple variables) or perhaps a more detailed description about what notation or concepts you find confusing? –  Antonio Vargas Dec 18 '12 at 0:19
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