Application of Partial Differential Equation (PDE) and Integral Calculus to Rock Forming Minerals
DOI:
10.56566/sigmamu.v4i1.428Downloads
Abstract
Chemical reaction in Magma is very complex, because of several anionic and cationic substitutions of different size and charge in the magma and in this case, complex problems require complex solutions. This research was focused on bridging the gap between Bowen and Goldschmidt concepts concerning the problem of elemental substitution and distribution of chemical elements in rocks throughout the time of crystallization with mathematical foundation under thermodynamic change such as Calculus, comprises differentiation, Integration, Cauchy-Riemann equation, Laplace equation and Power series comprises Euler series and Taylor series were applied to predict major minerals encompass the olivine, pyroxene, amphibole, mica, and feldspar, and their associated rocks encompass granite, basalt, andesite, and trachyte and were applied to resolve the problems of rock forming minerals in magma. Findings have shown that, in mathematical context, Bowen’s and Goldschmidt rules were mathematically connected using the Mathematical formulae as; , and Finally the “mathematical connection” between Bowen’s and Goldschmidt concepts was used in this research for a concise explanation of rock forming minerals from the beginning to the end of crystallization and would help the ‘beginners’ especially students of Earth sciences such as Geology, Mineralogy, Petrology and other chemical sciences such as Chemistry.
Keywords:
Application Integral Calculus Partial Differential Equation (PDE)References
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