ABSTRACT
This chapter describes the process of using the basic principles of physics, combined with appropriate boundary condition, initial conditions, and approximations, to form a complete and well-posed mathematical model of a system. A physical system is characterized by its material properties and geometry as well as the physical processes occurring within the system. Action or displacement from equilibrium is caused by external forces or stimuli acting on the system. For engineers and applied mathematicians, the ultimate purpose of mathematics is to describe and predict the behavior of physical systems. The basic steps involve the translation of the physical processes acting on a system into a mathematical model, followed by the solution of the model equations. Order-of-magnitude or dimensional analysis can be used to perform this estimation. A classic example is boundary layer theory in fluid mechanics, where an order-of-magnitude analysis can be used to show that streamwise diffusion-type terms can be neglected compared with streamwise advection terms.
