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第5行：
第5行： − 二维方程[用第三维表示温度的热方程]的解的可视化+ 第11行：
第11行： − 在数学中，偏微分方程函数是包含未知多变量函数及其偏导数的微分方程函数。偏微分方程用于描述涉及多个变量函数的问题，可以手工求解，也可以用于创建计算机模型。常微分方程是一种特殊情况，它处理单变量函数及其导数。+ 第19行：
第19行： − 偏微分方程可以用来描述各种各样的现象，如声音，热量，扩散，静电，电动力学，流体动力学，弹性，重力和量子力学。这些看起来截然不同的物理现象可以用类似的偏微分方程来形式化。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。偏微分方程在随机偏微分方程中得到了推广。+
无编辑摘要
A visualisation of a solution to the two-dimensional [[heat equation with temperature represented by the third dimension]]
A visualisation of a solution to the two-dimensional [[heat equation with temperature represented by the third dimension]]
二维热传导方程解的可视化，图中第三个维度表示温度的大小。
In [[mathematics]], a '''partial differential equation''' ('''PDE''') is a [[differential equation]] that contains unknown [[Multivariable calculus|multivariable functions]] and their [[partial derivative]]s. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a [[computer model]]. A special case is [[ordinary differential equation]]s (ODEs), which deal with functions of a single variable and their derivatives.
In [[mathematics]], a '''partial differential equation''' ('''PDE''') is a [[differential equation]] that contains unknown [[Multivariable calculus|multivariable functions]] and their [[partial derivative]]s. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a [[computer model]]. A special case is [[ordinary differential equation]]s (ODEs), which deal with functions of a single variable and their derivatives.
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.
在数学中，'''<font color = #ff8000"">偏微分方程函数 Partial Differential Equation<\font>是包含未知多元函数及其偏导数的微分方程。偏微分方程用于描述涉及多元函数的问题，可以通过人为求解，也可以通过创建计算机模型来求解。常微分方程是偏微分方程一种特殊情况，它处理的是一元函数及其导数。
PDEs can be used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, gravitation and quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, gravitation and quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
偏微分方程可以用来描述各种各样的物理现象，如声音，热量，扩散，静电，电动力学，流体力学，弹性力学，重力和量子力学。这些看起来截然不同的物理现象却可以用类似的偏微分方程来描述。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。随机偏微分方程是偏微分方程的一种推广。