Vector Calculus

Abstract

In Chapter 1, we discussed the basic concepts of vector algebra developed in the three common coordinate systems. Through the use of the position and base vectors, we could specify points and vectors in three-dimensional space. We reviewed typical symmetries of vector fields that easily reveal themselves in the cylindrical and spherical coordinate systems. We defined differential quantities such as differential length vectors, differential area vectors, and differential volumes in different coordinate systems. We also learned how to transform the coordinates of a point or the components of a vector from one coordinate system to another.