Advanced Calculus and Vector Field Theory

THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chapters 6 and 7 give the elements of vector field theory, taking the integral definitions of the divergence and curl of a vector field as their starting points; the last chapter surveys very briefly some of the immediate applications of vector field theory to five branches of applied mathematics. Throughout I have given n