Abstract: Sir Isaac Newton, one of the greatest scientists and mathematicians of all time, introduced the notion of a vector to define the existence of gravitational forces, the motion of the planets ...

In the study of electromagnetics one often needs to perform line, surface, and volume integrations. The evaluation of these integrals in a particular coordinate system requires the knowledge of ...

Therefore we can express the arc length of the graph of a vector--valued function as an integral of the magnitude of its derivative. Note that we are actually integrating a scalar--function here, not ...

Electromagnetics is a field theory, so most quantities have direction as well as magnitude. The electric field $\vec E$, magnetic field intensity $\vec H$, flux ...