Applied Advanced Calculus in Dynamic Geology

Chemical reactions in magma are highly complex due to multiple anionic and cationic substitutions involving minerals of different sizes. Complex problems require complex solutions; in this case the Cauchy-Riemann equations are applied to address issues related to rock-forming minerals in both active and inactive magma. The Cauchy-Riemann conditions must be satisfied at each point Z-Z_0 in every domain of magma M where Z-Z_0 represents a point with variables x and y in the Z-plane of magma R. Here Z is defined as a function of two independent variables x and y such that Z=f(xy). Thus Z is the dependent variable determined by each pair of values of x and y. In the complex plane of magma R each domain M represents a point of nucleation with Z=Z_0 expressed as the function f(xy).