LaTex数学公式（三）复杂公式示例

1

\int _{b}^{a} f'( x) dx=f( b) -f( a)

效果：

$$\int _{b}^{a} f'( x) dx=f( b) -f( a)$$

1

\underbrace{\frac{1}{4} W_{\mu \nu } \cdot W^{\mu \nu } -\frac{1}{4} B_{\mu \nu } B^{\mu \nu } -\frac{1}{4} G_{\mu \nu }^{a} G_{a}^{\mu \nu }}_{\mathrm{kinetic\ energies\ and\ self-interactions\ of\ the\ gauge\ bosons}}

效果：

$$\underbrace{\frac{1}{4} W_{\mu \nu } \cdot W^{\mu \nu } -\frac{1}{4} B_{\mu \nu } B^{\mu \nu } -\frac{1}{4} G_{\mu \nu }^{a} G_{a}^{\mu \nu }}_{\mathrm{kinetic\ energies\ and\ self-interactions\ of\ the\ gauge\ bosons}}$$

1

\Vert x+y\Vert \geq \bigl|\Vert x\Vert -\Vert y\Vert \bigr|

效果：

$$\Vert x+y\Vert \geq \bigl|\Vert x\Vert -\Vert y\Vert \bigr|$$

1
2

\nabla \cdot \mathbf{D} =\rho \ \mathrm{and} \ \nabla \cdot \mathbf{B} =0\
\nabla \times \mathbf{E} =-\frac{\partial \mathbf{B}}{\partial t} \ \mathrm{and} \ \nabla \times \mathbf{H} =\mathbf{J} +\frac{\partial \mathbf{D}}{\partial t}

效果：

$$\nabla \cdot \mathbf{D} =\rho \ \mathrm{and} \ \nabla \cdot \mathbf{B} =0$$
$$\nabla \times \mathbf{E} =-\frac{\partial \mathbf{B}}{\partial t} \ \mathrm{and} \ \nabla \times \mathbf{H} =\mathbf{J} +\frac{\partial \mathbf{D}}{\partial t}$$

1

y=\frac{\sum\limits _{i} w_{i} y_{i}}{\sum\nolimits _{i} w_{i}} \ \ ,i=1,2...k

$$y=\frac{\sum\limits _{i} w_{i} y_{i}}{\sum\nolimits _{i} w_{i}} \ \ ,i=1,2...k$$

1

e=\lim\limits _{n\rightarrow \infty }\left( 1+\frac{1}{n}\right)^{n}

效果：

$$e=\lim\limits _{n\rightarrow \infty }\left( 1+\frac{1}{n}\right)^{n}$$

1

\dot{x}_{i} =a_{i} x_{i'} -( d+a_{i0} +a_{i1}) x_{i} +rx_{i}( f_{i} -\phi )

效果：

$$\dot{x}_{i} =a_{i} x_{i'} -( d+a_{i0} +a_{i1}) x_{i} +rx_{i}( f_{i} -\phi )$$