1.1 INTRODUCTION

The equations of applied mathematics express the relation between measurable quantities of certain defined units. These measurable quantities are classified into two main categories. A class of physical quantity that is completely expressed by only a number is called scalar . Examples of such quantity (scalar) are mass, temperature, time, length, potential, etc. There are, however, other physical quantities that are not expressed only by simple numbers. In addition to numeric representation, direction is required. For example, displacement of a point, the velocity of particle, force, electric field, etc., require a number (scalar) as well as direction to specify them completely. A class of physical quantity that is completely expressed by a number along with direction is called vector . In a three-dimensional coordinate system, a vector may be specified by three scalars expressed along three axes forming the coordinate system. We can carry out the various mathematical operations and calculations with these vector quantities leading to the formulation of vector analysis. Vector analysis is mathematical shorthand. This is used for compact representation of physical quantities and their mathematical processing. In an attempt of systematic study of electromagnetics, this shorthand is inevitable for processing and consequently interpreting results. Therefore, this chapter is dedicated to learning the useful aspects of vectors in view of electromagnetics.