ABSTRACT
More than one variable may be required to label the spatial points and instants within the domain of a tensor field. This chapter speaks on a set of Cartesian coordinates and study the calculus of scalar and vector fields of more than one spatial variable. The rate of change of a tensor field in one of the coordinate directions is just the partial derivative with respect to the coordinate. The notions of the gradient and the directional derivative are readily generalized to scalar functions f(x1, x2, x3) of three variables. In many physical applications of line, surface, and volume integrals, the integrand arises from a vector field u(x1, x2, x3). The extension of the fundamental theorem of calculus to fields of two variables is known as Green's theorem. An important consequence of the divergence and Stokes' theorems is obtained by applying them to small regions of space.
