Search results
- DictionaryPar·tial dif·fer·en·tial e·qua·tion/ˈpärSHəl ˌdifəˈren(t)SHəl əˈkwāZHən/
noun
- 1. an equation containing one or more partial derivatives.
Powered by Oxford Languages
In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. 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 x 2 − 3 x + 2 = 0 .
Partial Differential Equation Definition. A Partial Differential Equation commonly denoted as PDE is a differential equation containing partial derivatives of the dependent variable (one or more) with more than one independent variable. A PDE for a function u (x 1 ,……x n) is an equation of the form.
Partial differential equations are widely used in engineering and physics to model natural phenomena such as heat transfer, wave propagation, diffusion, and electrostatics. Partial differential equations consist of an unknown multivariable function and its partial derivatives.
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time. This is a self-published text book with excellent coverage and solid mathematics and theory to support applications.
In this course we shall consider so-called linear Partial Differential Equations (P.D.E.’s). This chapter is intended to give a short definition of such equations, and a few of their properties.
Nov 18, 2021 · Differential equations containing partial derivatives with two or more independent variables are called partial differential equations (pdes). These equations are of fundamental scientific interest but are substantially more difficult to solve, both analytically and computationally, than odes.
A partial differential equation is an equation that involves an unknown function of more than one independent variable and one or more of its partial derivatives. Examples of partial differential equations are [latex]\large{u_t=c^{2}\,(u_{xx}+u_{yy})}[/latex] (heat equation in two dimensions) [latex]\large{u_{tt}=c^{2}\,(u_{xx}+u_{yy})}[/latex]
