ABSTRACT
This chapter assists the student in the learning process for structural and finite element analysis, in which he must master, not only the numerical techniques available, but also the mathematical skills necessary for the efficient description of the physics of the problem at hand. Following a discussion of the merits of the various notations, the reader is introduced to the ubiquitous Gauss' divergence theorem. This theorem forms the basis of most descriptions of the integral of the rate of change of a variable over a region to its values on the surface of the region. The advantage of the more general formulation by Gauss is in its adaptability to a variety of other physical situations where the concepts of static equilibrium are not available. In structural mechanics it is possible to extend the concept of virtual displacements (forces) to the contragredient principle which succinctly describes the relationship between statically equivalent force systems and their compatible displacements.
