Mathematical Physics and Newtonian Mechanics by Pearson

CHAPTER 2

Vector Calculus

In the present chapter, we have discussed the operations of differentiation and integration of vectors with their geometrical and physical interpretations. These concepts are then utilized in defining gradient of a scalar function and the divergence and curl of a vector function with their significance. Line, surface (flux) and volume integrals of vector field, Gauss-divergence theorem, Stoke-curl theorem, Green’s theorem and Helmholtz theorem (statement only) are then considered. Introduction to Dirac delta function is finally studied.

1. Differentiation of vectors

Suppose, a vector quantity varies with a scalar variable ...