ABSTRACT
Differential equations are developed mathematically upon the fundamental theorem of calculus according to the laws of thermodynamics in terms of mass, force, momentum, and energy conservation, as well as other relevant laws and principles. This chapter revisits some of the partial differential equations (PDEs) to find out how a “differential unit” is selected and how the laws of physics and thermodynamics are applied. It shows how differential equations are developed and describes the development of several one-dimensional PDEs. The chapter also illustrates that PDEs sometimes are of the same mathematical type even though they govern problems of different physics, thus suggesting that for countless real-world problems one may only need to deal with limited types of governing differential equations.
