Equivalence transformations for first order balance equations

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The groups of equivalence transformations for a family of first order partial differential equations of balance form are investigated. Equivalence transformations map a specific class of equations involving arbitrary functions or parameters into the same class. In that sense equivalence groups are much more general than symmetry groups. The method of attack to this problem is based on the exterior calculus. The analysis is reduced to determine isovector fields of a closed ideal of the exterior algebra over an appropriate differentiable manifold dictated by the structure of the family of differential equations. The determining equations in terms of the isovector field components are obtained and furthermore their explicit solutions are determined. The results are then applied to a class of Maxwell equations in rigid bodies.