Differential Forms and Vector Analysis

Usually in this type of calculations one does not write explicitly the unit vectors ei. This makes the notation more economical but is possible only either if the vectors are decomposed into the Cartesian unit vectors ex, ey, ez, or (for vectors decomposed into unit vectors e1(ξ), e2(ξ), e3(ξ) associated with some curvelinear coordinates ξ, ξ, ξ see below), or if no differentiations are involved: for instance, if in the example above C(ξ) = ei(ξ)C (ξ) and B(ξ) = ei(ξ)∂/∂ξ , where the differential operator acts on everything standing to the right of it, then one cannot drop the vectors ei(ξ) because they too should get differentiated.