VECTOR ANALYSIS

Most of the Newtonian mechanics and Maxwell's electrodynamics are formulated in terms of the language of vector analysis. In this chapter, the authors introduce the basic properties of scalars, vectors, and their fields. A convenient way to approach vector algebra came with Descartes through the introduction of Cartesian coordinates. Helmholtz theorem says that a vector field is completely and uniquely specified by giving its divergence, curl, and the normal component on the bounding surface. By paying attention to the vector nature of the V operator and by keeping in mind that it is meaningless on its own, we can construct several other useful operators and identities. For a physical understanding of the divergence operator, the authors consider a tangible case like the flow of a fluid. The V 2 operator is called the Laplacian or the Laplace operator, which is one of the most commonly encountered operators in science.