IEEE Transactions on Education, vol. 40, No. 1, February, 1997, pp.
53-68.
The primary pedagogical advantages of differential forms are the distinct representations of field intensity and flux density, intuitive graphical representations of each of Maxwell's laws, and a simple picture of electromagnetic boundary conditions. Differential forms provide visual models that can help students remember and apply the principles of electromagnetics. Computational simplifications also result from the use of forms: derivatives are easier to employ in curvilinear coordinates, integration becomes more straightforward, and families of related vector identies are replaced by algebraic rules.
The primary pedagogical advantages of differential forms are the distinct representations of field intensity and flux density, intuitive graphical representations of each of Maxwell's laws, and a simple picture of electromagnetic boundary conditions. Differential forms provide visual models that can help students remember and apply the principles of electromagnetics. Computational simplifications also result from the use of forms: derivatives are easier to employ in curvilinear coordinates, integration becomes more straightforward, and families of related vector identies are replaced by algebraic rules.