Application of CAS for teaching of integral-transforming theorems

Teaching vector calculus (the integral-transforming theorems, in particular) to students of engineering has got many difficulties. On the one hand complex and deep knowledge of vector algebra (in three dimensions) and calculus (in one and many variables) is necessary for understanding, on the other hand it is difficult to illustrate the concepts of vector calculus exclusively by means of blackboard and chalk. In this paper we demonstrate how the line integral, the surface integral, the theorems of Gauss and Stokes are taught with the help of a MAPLE computer algebra system (CAS). Application of this pedagogical method supports the hypothesis that using of CAS makes it possible to teach those kinds of concepts and theorems which are often used in engineering practice but couldn’t be presented because of lack of time and appropriate preliminary training.