ABSTRACT
This chapter illustrates the mathematical modeling process by considering various systems that are modeled in terms of partial differential equations. It focuses on the heat, wave, and potential equations that are important in many scientific and engineering applications. Burger's equation was introduced as a one-dimensional model for turbulence and has since found applications in the study of shock wave, wave transmission, traffic flow, and so on. The chapter presents a brief overview of nonlinear wave equations. An in-depth treatment of wave phenomena in fluids requires a knowledge of fluid mechanics. Waves on the oceans are generated by various causes. First, there are waves generated by winds blowing on the ocean surface. Then, there are waves due to tidal forces exerted by the gravitational interaction with the Sun and Moon systems. Finally, there are those that are generated as a result of earthquakes or other natural catastrophes. This last category of waves is referred to as tsunamis.
