23CURVES, SURFACES, AND VOLUMES
Electrodynamics is a geometric subject. Curves, surfaces, and volumes play a dual role in electromagnetic theory. They serve as the places where electric charge and current can reside, and they play an essential role in the formulation of the Maxwell equations, the modern expression of how electric and magnetic fields are created and how they evolve in time.
Before we can explore the Maxwell equations, we’ll need data types for curves, surfaces, and volumes—we’ll build them in this chapter. A curve can be specified by giving a function from a single real parameter to a position in space. A surface can be specified ...
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