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Dimensional Analysis
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Dimensional Analysis (... called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is a useful technique. The only danger is that you may end up thinking that chemistry is simply a math problem - which it definitely is not.
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Dimensional Analysis is a general method of determining the form of solutions to physical problems. It is illustrated by an example from physics and descriptions of applications to some OR problems. The Ehrhardt power approximation for computing (s,S) inventory policies is examined from this point of view and found to be flawed.
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The real breakthrough in Dimensional Analysis which made it rather central to the Mainstream in mathematics came... with G. W. Bluman (U. British Columbia) and S. Kumei (Shinshu U.), Symmetries and Differential Equations, Springer-Verlag: N.Y. 1989, and the papers on which it was based. They showed that reduction of variables through dimensional analysis for partial differential equations (PDEs) is a special case of reduction from invariance under Lie groups of one-parameter and p-parameter scaling transformations (stretching transformations) in BVPs (boundary value problems), and the one-parameter transformation invariance can be generalized to arbitrary one-parameter Lie groups of point transformations of variables which can be found algorithmically for given differential equations from properties of infinitesimal generators.
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Dimensional Analysis