In this section of the Chapter 2C, we will examine various types of functions and how to differentiate those functions.

• A scalar has magnitude but no direction at a given point. Examples are density, temperature and pressure. However they will be different in different points in space resulting in scalar-valued functions of space. Position vectors in terms of define the space through . Hence density at all points in space is a scalar field.

• A vector at a point defines a quantity, e.g. velocity with a specific magnitude and a direction. Thus at a point , velocity will be in a given direction, e.g. with a magnitude of 30 m/sec. Since this can vary at all points in space specified by , then this velocity field is a vector field.

• A similar argument can be made for higher order tensor fields. Assume that a tensor e.g. (stress at a point ) is given by the tensor

then the stress varies at every point giving different 9 components (6 since it is symmetric), giving the concept of tensor field.