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- DictionaryPar·tial dif·fer·en·tial e·qua·tion/ˈpärSHəl ˌdifəˈren(t)SHəl əˈkwāZHən/
noun
- 1. an equation containing one or more partial derivatives.
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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 x2 − 3x + 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.
A partial differential equationis an equation for a function which depends on more than one independent variable which involves the independent variables, the function, and partial derivatives of the function:
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.
1: First Order Partial Differential Equations; 2: Second Order Partial Differential Equations; 3: Trigonometric Fourier Series; 4: Sturm-Liouville Boundary Value Problems; 5: Non-sinusoidal Harmonics and Special Functions; 6: Problems in Higher Dimensions; 7: Green's Functions and Nonhomogeneous Problems; 8: Complex Representations of Functions
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]
Partial differential equations are differential equations that contains unknown multivariable functions and their partial derivatives. Front Matter. 1: Introduction. 2: Equations of First Order. 3: Classification. 4: Hyperbolic Equations. 5: Fourier Transform. 6: Parabolic Equations. 7: Elliptic Equations of Second Order. Bibliography.
Equations involving one or more partial derivatives of a function of two or more independent variables are called partial differential equations (PDEs). Well known examples of PDEs are the following equations of mathematical physics in which the notation: u =∂u/∂x, u xy=∂u/∂y∂x, u xx=∂2u/ ∂x2, etc., is used:
partial differential equation, in mathematics, equation relating a function of several variables to its partial derivatives. A partial derivative of a function of several variables expresses how fast the function changes when one of its variables is changed, the others being held constant (compare ordinary differential equation).
