Mathematical modeling plays a fundamental role in the description of a large part of phenomena in the applied sciences and in several aspects of technical and industrial activity.
By a mathematical model, we mean a set of equations and/or other mathematical relations capable of capturing the essential features of a complex natural or artificial system, to describe, forecast, and control its evolution. The applied sciences are not confined to the classical ones; in addition to physics and chemistry, the practice of mathematical modeling heavily affects disciplines like finance, biology, ecology, medicine, and sociology.
In the industrial activity such as aerospace or naval projects, nuclear reactors, combustion problems, production and distribution of electricity, traffic control, etc., the mathematical modeling, involving the analysis and the numerical simulation and followed by experimental tests, has become a common procedure, necessary for innovation, and also motivated by economic factors. All of this is made possible by the enormous computational power now available.
In general, the construction of a mathematical model is based on two main ingredients: general laws and constitutive relations. In this unit, we shall deal with general rules coming from real-life problems such as continuum mechanics, physics, chemistry, biology, ecology, medicine, etc. This is in deep relationship with the Saudi Vision 2030.