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第186行：
第186行： − + − {{main|Partial differential equation}} 第193行：
第192行： − 偏微分方程函数是一种包含未知多变量函数及其偏导数的微分方程函数。(这与处理单变量函数及其导数的常微分方程不同。)偏微分方程用于描述涉及多个变量函数的问题，或者以封闭形式求解，或者用于创建相关的计算机模型。+ 第201行：
第200行： − 偏微分方程可以用来描述自然界中各种各样的现象，如声音、热量、静电、电动力学、流体流动、弹性或量子力学。这些看起来截然不同的物理现象可以用偏微分方程类似地形式化。正如常微分方程经常对一维动力系统进行建模一样，偏微分方程经常对多维系统进行建模。随机偏微分方程推广了随机性建模的偏微分方程。+ − −
→Partial differential equations
===Partial differential equations===
===Partial differential equations===
偏微分方程
A [[partial differential equation]] (''PDE'') is a differential equation that contains unknown [[Multivariable calculus|multivariable function]]s and their [[partial derivatives]]. (This is in contrast to [[ordinary differential equations]], which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant [[computer model]].
A [[partial differential equation]] (''PDE'') is a differential equation that contains unknown [[Multivariable calculus|multivariable function]]s and their [[partial derivatives]]. (This is in contrast to [[ordinary differential equations]], which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant [[computer model]].
A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (This is in contrast to ordinary differential equations, which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant computer model.
A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (This is in contrast to ordinary differential equations, which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant computer model.
'''<font color="#ff8000">偏微分方程 Partial Differential Equation</font><font>'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程用于描述涉及多元函数的问题，或者以封闭形式求解，或者用于创建相关的计算机模型。
PDEs can be used to describe a wide variety of phenomena in nature such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. Stochastic partial differential equations generalize partial differential equations for modeling randomness.
PDEs can be used to describe a wide variety of phenomena in nature such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. Stochastic partial differential equations generalize partial differential equations for modeling randomness.
偏微分方程可以用来描述自然界中各种各样的现象，如声音、热量、静电、电动力学、流体流动、弹性或量子力学。这些看起来截然不同的物理现象可以用相似的偏微分方程表达。正如常微分方程经常对一维动力系统进行建模一样，偏微分方程经常对多维系统进行建模。随机偏微分方程推广了偏微分方程在随机性建模上的应用。
===Non-linear differential equations===
===Non-linear differential equations===