At any given point in space, an electric or magnetic field possesses two properties, a magnitude and a direction. In general, these properties vary (continuously) from point to point. It is conventional to represent such a field in terms of its components measured with respect to some conveniently chosen set of Cartesian axes (i.e., the conventional -, -, and -axes). Of course, the orientation of these axes is arbitrary. In other words, different observers may well choose different coordinate axes to describe the same field. Consequently, electric and magnetic fields may have different components according to different observers. We can see that any description of electric and magnetic fields is going to depend on two seperate things. Firstly, the nature of the fields themselves, and, secondly, our arbitrary choice of the coordinate axes with respect to which we measure these fields. Likewise, Maxwell's equations--the equations which describe the behaviour of electric and magnetic fields--depend on two separate things. Firstly, the fundamental laws of physics which govern the behaviour of electric and magnetic fields, and, secondly, our arbitrary choice of coordinate axes. It would be helpful if we could easily distinguish those elements of Maxwell's equations which depend on physics from those which only depend on coordinates. In fact, we can achieve this by using what mathematicians call vector field theory. This theory enables us to write Maxwell's equations in a manner which is completely independent of our choice of coordinate axes. As an added bonus, Maxwell's equations look a lot simpler when written in a coordinate-free manner. In fact, instead of eight first-order partial differential equations, we only require four such equations within the context of vector field theory.