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A.1 Scalar and Vector Fields

The laws of Physics, the boundary conditions, and the initial conditions that make the phys-
ical model yield the mathematical model that has to be solved to find the unknowns of the
problem—the physical quantities of interest (e.g., temperature, velocity, pressure, electric
potential, magnetic potential, species concentration). Qualitatively the physical quantities
may be scalar and vector, and the mathematical physics is concerned with the solution of
the problems where they occur.