20 - Introduction to Vector Analysis

Abstract

This chapter reviews potential functions and the gradients in the understanding of vector analysis. The notion of a vector field is central to the subject of vector analysis. A vector field in R3 is a function whose domain and range are subsets of R3. Vector fields arise in a great number of physical applications. There are, for example, mechanical force fields, magnetic fields, electric fields, velocity fields, and direction fields. The chapter presents Green's theorem in the plane that shows how the line integral of a function around the boundary of a region is related to a double integral over that region. The chapter discusses line integrals in space, surface integrals, Stokes's theorem and the divergence theorem.