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Over the years, Mathematics has been widely applied in the fields of science, engineering, and the social sciences to solve a variety of problems.In recent years, Mathematics has also found increasing application in Geology, particularly in Engineering Geology, Rock Mechanics, Soil Mechanics, Geophysics, and Structural Geology. However, relatively little work has been done in the area of Dynamic Geology, such as the study of magma, using applied Mathematics. This book focuses on applying Mathematics to bridge the gap between Bowen's reaction series of rock-forming minerals and Goldschmidt's principle of element substitution-where elements of similar size and charge can replace one another in solid solution under thermodynamic conditions. The result is presented in this volume, Advanced Mathematical Analysis in Dynamic Geology.