An Algebra for Scientific Equations with Applications in Computational Problems

Abstract

An algebra for scientific equations is developed which couples a number to a "physical dimension". The physical dimension is viewed as a vector space with some novel properties. In the past, such equations were intuitively used without the development of a formal mathematical theory. Here, the formal theory correlates physical "dimensions" with known mathematical structures unambiguously; all intuitive presuppositions are axiomatically stated. The theory is applied to problems in scientific computing and some novel deductions are made concerning the temperature and the Boltzmann factor.