Essentials of Mathematical Methods in Science and Engineering, 2nd Edition

CHAPTER 2VECTOR ANALYSIS

Certain properties in nature such as mass, charge, temperature, are scalars, which can be defined at a point by just giving a single number. In other words, they have only magnitude. Properties such as velocity and acceleration are on the other hand, vector quantities, which have both magnitude and direction. Most of the Newtonian mechanics and Maxwell's electrodynamics are formulated in terms of the language of vector analysis. In this chapter, we introduce the basic properties of scalars, vectors, and their fields.

2.1 VECTOR ALGEBRA: GEOMETRIC METHOD

Abstract vectors are defined as directed line segments. The length of the line segment describes the magnitude of the physical property and the arrow indicates its direction. As long as we preserve their magnitude and direction, we can move abstract vectors freely in space. In this regard, and in Figure 2.1 are equivalent vectors:

(2.1)

Figure 2.1 Abstract vectors.

We can use Latin letters with an arrow to show vector quantities:

(2.2)

As we use in the figures, it is also customary to use boldface ...