Introduction

In this section, we shall give a brief outline of those aspects of vector algebra and vector calculus which are helpful in the study of classical dynamics. Note that the essential purpose of vector algebra is to convert the propositions of Euclidean geometry and trigonometry in three-dimensional space into a convenient algebraic form. In addition, vector calculus allows us to define the velocity and acceleration of a moving point in three-dimensional space, as well as the distance moved by such a point, in a given time interval, along a general curved trajectory. Vector calculus also introduces the concept of a scalar field: e.g., the potential energy associated with a conservative force.

This section is largely based on my undergraduate lecture notes from a course given by Dr. Stephen Gull at the University of Cambridge.