Partial Differential Equations

The theory of partial differential equation (PDE) is one of the most important fields of study in mathematics. In fact PDEs frequently occur in many branches of physics, engineering and other sciences. For example, most physical phenomena electricity, mechanics, optics, can be described in general by PDEs. In contrast to ordinary differential equations, where the unknown function depends only on one variable, in the PDEs the unknown function depends on several variables. The derivatives in this equation represent natural things, such as velocity, acceleration, force and current. This explain why most of the natural laws of physics, such as Maxwell's equations, Newton's law of cooling, The Navier-Stokes equations and Schrodinger's equation of Quantum mechanics can be stated in terms of PDEs, that is these laws describe physical phenomena by relation space and time derivatives.