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dimensional analysis
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[QUICK DESCRIPTION] By assigning "dimensions" to various quantities in a consistent manner (using units such as "length", "time", or "mass"), one can provide a simple "checksum" that can be used to guard against numerical errors, particularly with regards to exponents. Dimensional analysis can also be used as a shortcut to determine various exponents that would come out at the end of a lengthy calculation, without having to directly calculate the exponents in the intermediate steps of the computation. [PREREQUISITES] Basic physics. [EXAMPLE] Use dimensional analysis to predict the dependence of integrals such as $\int_0^\infty \frac{dx}{a^7+x^7}\ dx$ or $\int_{\R^n} \frac{dy}{|y|^\alpha |x-y|^\beta}$ on the underlying parameter $a$ or $x$. (Give solution here...) [GENERAL DISCUSSION] Dimensional analysis can be interpreted in terms of an underlying ''scale invariance'' of the problem at hand.
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