3.Relief Maps A third way to represent a scalar field is to fix one of the dimensions,and then plot the value of the function as a height versus the remaining spatial coordinates,say x and y, that is,as a relief map.Figure 1.2.6 shows such a map for the same function (x,y,0). Figure 1.2.6 A relief map of the scalar field given by Eq.(1.2.3). 1.3 Vector Fields A vector is a quantity which has both a magnitude and a direction in space.Vectors are used to describe physical quantities such as velocity,momentum,acceleration and force, associated with an object.However,when we try to describe a system which consists of a large number of objects (e.g.,moving water,snow,rain,...)we need to assign a vector to each individual object. As an example,let's consider falling snowflakes,as shown in Figure 1.3.1.As snow falls, each snowflake moves in a specific direction.The motion of the snowflakes can be analyzed by taking a series of photographs.At any instant in time,we can assign,to each snowflake,a velocity vector which characterizes its movement. Figure 1.3.1 Falling snow. 1-71-7 3. Relief Maps A third way to represent a scalar field is to fix one of the dimensions, and then plot the value of the function as a height versus the remaining spatial coordinates, say x and y, that is, as a relief map. Figure 1.2.6 shows such a map for the same function ( , ,0) φ x y . Figure 1.2.6 A relief map of the scalar field given by Eq. (1.2.3). 1.3 Vector Fields A vector is a quantity which has both a magnitude and a direction in space. Vectors are used to describe physical quantities such as velocity, momentum, acceleration and force, associated with an object. However, when we try to describe a system which consists of a large number of objects (e.g., moving water, snow, rain,…) we need to assign a vector to each individual object. As an example, let’s consider falling snowflakes, as shown in Figure 1.3.1. As snow falls, each snowflake moves in a specific direction. The motion of the snowflakes can be analyzed by taking a series of photographs. At any instant in time, we can assign, to each snowflake, a velocity vector which characterizes its movement. Figure 1.3.1 Falling snow