User:Jalenlthomas/New sandbox


 * For this article I would like to add some more information to the introduction section at the start of the section.
 * From what I have read there could be a few more steps that could be added to simplify the introduction of the partial differential equations page.
 * I would like to add some of the specific partial differential equations to go along with the links for them towards the end of the page.
 * I would like to add these because they show the practicality of the PDEs in terms of how they apply in the real world.
 * I think I could also add some images in order to give a few more details and graphs about how partial differential equations work and look like.

Article

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function.

(My additon: PDE's appear frequently throughout all areas of engineering, mathematics and even physics as well. They appear in different subjects of financing, biology, chemistry, and various computer sciences. Some of the history of partial differential equations a huge amount of analysis of the PDEs in many different facets and approaches. During the 19th century for example, finding explicit solutions was accomplished through the use of the classical approach. Because of the importance of PDE's in physics when these advancements occured for PDEs this coincided with advancements in physics as these equations allowed the subject to progress in its own right.)

The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability.[citation needed] Among the many open questions are the existence and smoothness of solutions to the Navier–Stokes equations, named as one of the Millennium Prize Problems in 2000.