However for functions of more than one variable all other variables are treated as if they are constants. The derivatives of f with respect to x or y are written as respectively. The angle is defined as this component divided by the radius of the circle r . The units are radians. Vectors Many physical quantities have a direction as well as a magnitude.
Examples are force velocity and, in electromagnetism, electric and magnetic fields.
We describe such quantities using vectors. At each point in space we can imagine an arrow whose length gives the magnitude of the quantity it describes and whose direction corresponds to the direction of the quantity. In dealing with vectors it is often convenient to describe a vector in terms of components. Because space has three-dimensions, three components lying along three orthogonal directions are required to describe any vector. The most common system is the Cartesian one where the three directions are the x, y and z-axes.