108
个编辑
更改
→Notation
== Notation ==
== Notation ==
符号
In PDEs, it is common to denote partial derivatives using subscripts. That is:
In PDEs, it is common to denote partial derivatives using subscripts. That is:
<math>u_x = \frac{\partial u}{\partial x}</math>
<math>u_x = \frac{\partial u}{\partial x}</math>
: <math>u_{xx} = \frac{\partial^2 u}{\partial x^2} </math>
: <math>u_{xx} = \frac{\partial^2 u}{\partial x^2} </math>
<math>u_{xx} = \frac{\partial^2 u}{\partial x^2} </math>
<math>u_{xx} = \frac{\partial^2 u}{\partial x^2} </math>
: <math>u_{xy} = \frac{\partial^2 u}{\partial y\, \partial x} = \frac{\partial}{\partial y } \left(\frac{\partial u}{\partial x}\right). </math>
: <math>u_{xy} = \frac{\partial^2 u}{\partial y\, \partial x} = \frac{\partial}{\partial y } \left(\frac{\partial u}{\partial x}\right). </math>
<math>u_{xy} = \frac{\partial^2 u}{\partial y\, \partial x} = \frac{\partial}{\partial y } \left(\frac{\partial u}{\partial x}\right). </math>
<math>u_{xy} = \frac{\partial^2 u}{\partial y\, \partial x} = \frac{\partial}{\partial y } \left(\frac{\partial u}{\partial x}\right). </math>
Especially in physics, del or nabla () is often used to denote spatial derivatives, and for time derivatives. For example, the wave equation (mentioned below) can be written as
Especially in physics, del or nabla () is often used to denote spatial derivatives, and for time derivatives. For example, the wave equation (mentioned below) can be written as
特别是在物理学中，[[del]]或nabla ({{math|∇}})经常用来表示空间导数和时间导数。例如，波动方程(下面提到的)可以写成
<math>\ddot u=c^2\nabla^2u</math>
<math>\ddot u=c^2\nabla^2u</math>
<math>\ddot u=c^2\Delta u</math>
<math>\ddot u=c^2\Delta u</math>
where is the Laplace operator.
where is the Laplace operator.
其中{{math|Δ}}代表拉普拉斯算子
== Classification ==
== Classification ==