The kinematical aspect of the fundamental theorem of calculus

Abstract

Stokes’s theorem and Poincaré’s lemma are two well-known and remarkable aspects of the fundamental theorem of calculus in several variables. With the fanfare accorded to these two aspects, the kinematical aspect of the fundamental theorem of calculus has been unjustly neglected. This aspect, appropriately labeled the transport theorem, has special cases which are well known to workers in continuum mechanics. This paper serves to emphasize the importance of the transport theorem and to briefly survey the other aspects of the fundamental theorem of calculus.