Vector Calculus

Abstract

The physical quantities that we encounter in physics and applied mathematics (e.g., force, temperature, electric field) are represented by mathematical functions of space and time, hence, functions of several variables. For example, for the force F on a particle we may write

$$\text{F} = \,F(x,\,y,\,z,\,t),$$

which shows that the force depends explicitly on the three position coordinates (x, y, z) and the time coordinate t. The force on the particle depends on where the particle is located in space and on when it is at that point.