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第37行：
第37行： − 函数的偏微分方程是形式的方程+ 第45行：
第45行： − 数学 f 左(x1，ldots xn; u，frac { partial x1} ， ldots frac { partial x1} ; frac { partial ^ 2 u }部分 x1} ， ldots frac { partial ^ 2 u }部分 x1} ; ldots frac1 partial x1}右)0。 数学+ − 第53行：
第52行： − 如果偏微分方程是线性函数及其导数，则偏微分方程称为线性函数。线性偏微分方程的常见例子包括热方程、波动方程、拉普拉斯方程、亥姆霍兹方程方程、 Klein-Gordon 方程和 Poisson 方程。+ 第61行：
第60行： − 一个相对简单的 PDE 是+
→Introduction
A partial differential equation (PDE) for the function is an equation of the form
A partial differential equation (PDE) for the function is an equation of the form
对于函数{{math|''u''(''x''<sub>1</sub>,… ''x<sub>n</sub>'')}}，它的的偏微分方程形式是：
<math>f \left (x_1, \ldots x_n; u, \frac{\partial u}{\partial x_1}, \ldots \frac{\partial u}{\partial x_n}; \frac{\partial^2 u}{\partial x_1 \partial x_1}, \ldots \frac{\partial^2 u}{\partial x_1 \partial x_n}; \ldots \right) = 0.</math>
<math>f \left (x_1, \ldots x_n; u, \frac{\partial u}{\partial x_1}, \ldots \frac{\partial u}{\partial x_n}; \frac{\partial^2 u}{\partial x_1 \partial x_1}, \ldots \frac{\partial^2 u}{\partial x_1 \partial x_n}; \ldots \right) = 0.</math>
<math>f \left (x_1, \ldots x_n; u, \frac{\partial u}{\partial x_1}, \ldots \frac{\partial u}{\partial x_n}; \frac{\partial^2 u}{\partial x_1 \partial x_1}, \ldots \frac{\partial^2 u}{\partial x_1 \partial x_n}; \ldots \right) = 0.</math>
If is a linear function of and its derivatives, then the PDE is called linear. Common examples of linear PDEs include the heat equation, the wave equation, Laplace's equation, Helmholtz equation, Klein–Gordon equation, and Poisson's equation.
If is a linear function of and its derivatives, then the PDE is called linear. Common examples of linear PDEs include the heat equation, the wave equation, Laplace's equation, Helmholtz equation, Klein–Gordon equation, and Poisson's equation.
如果偏微分方程是函数及其导数的线性方程，则偏微分方程称为线性函数。线性偏微分方程的常见例子包括热方程、波动方程、拉普拉斯方程、亥姆霍兹方程方程、 Klein-Gordon 方程和 Poisson 方程。
A relatively simple PDE is
A relatively simple PDE is
一个相对简单的偏微分方程是：