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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 1

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.