Stokes theorem for fields with discontinuity surfaces

An expression of the Stokes theorem valid in the presence of discontinuity surfaces spanned by macroscopic EM field vectors is derived. The requirement of continuity for first derivatives of components of the field vector on the contour separating two regions is relaxed. The modification of the Stokes theorem is recommended for studies of EM fields, and for readily determining conditions governing tangential components of the electric field intensity vector and magnetic field intensity vector when dealing with Maxwell field equations in integral form.