Maxwell's Equations in Arbitrary Coordinate System

The article is devoted to application of tensorial formalism for derivation of different types of Maxwell's equations. The Maxwell's equations are written in the covariant coordinate-free and the covariant coordinate forms. Also the relation between vectorial and tensorial formalisms and differential operators for arbitrary holonomic coordinate system in coordinate form is given. The results obtained by tensorial and vectorial formalisms are verified in cylindrical and spherical coordinate systems.