LaTex数学符号+代码运行结果

\[
\Gamma_{ij}^{k}
=\frac{1}{2}(\frac{\partial g_{il}}{\partial u^j}
+\frac{\partial g_{jl}}{\partial u^i}
-\frac{\partial g_{ij}}{\partial u^l})
\]

\[\sum_{i,j,k=1}^{\infty}{x_{i_{j_{k}}}}\]

\[\frac{f(x)}{g(x)}\]

\[\frac{x}{y}+\frac{f(x)}{g(x)}\]

\[\lim_{x\rightarrow x^0}f(x)=A\]
\[\lim_{x\rightarrow x_0}f(x)=A\]
$\int^a_dc_b f(x)dx$\(\int^a_dc_b f(x)dx\)
\[\int^a_dc_b f(x)dx\]

\[\sum_{i=1}^{\infty} x_i\]
\[\sqrt[5]{x^4-3x+1}\]

Errors=\(\sqrt{\frac{\sum_{j=1}^{M}[predictior(j)-real(j)]^2}{M}}\)

\[\iint_{\Omega}f(x,y)dxdy\]
\[\iiint_{\Gamma}f(x,y,z)dxdydz\]

\[
\left|\begin{array}{cccc}
1 & 6 & 9 \\
7 & 90 & f(x)\\
9 & \psi(x) & g(x)
\end{array}\right|
\]

\[
\left[\begin{array}{cccc}
1 & 6 & 9 \\
7 & 90 & f(x)\\
9 & \psi(x) & g(x)
\end{array}\right]
\]

\[
\left(\begin{array}{cccc}
1 & 6 & 9 \\
7 & 90 & f(x)\\
9 & \psi(x) & g(x)
\end{array}\right)
\]


\[
\left(\begin{array}{llll}
1 & 6 & 9 \\
7 & 90 & f(x)\\
9 & \psi(x) & g(x)
\end{array}\right)
\]


\[
\left(\begin{array}{rrrrr}
1 & 6 & 9 \\
7 & 90 & f(x)\\
9 & \psi(x) & g(x)
\end{array}\right)
\]

\[
\begin{cases}
\ u_{tt}(x,t)= b(t)\triangle u(x,t-4)&\\
\ \hspace{42pt}- q(x,t)f[u(x,t-3)]+te^{-t}\sin^2 x, & t \neq t_k; \\
\ u(x,t_k^+) - u(x,t_k^-) = c_k u(x,t_k), & k=1,2,3\ldots ;\\
\ u_{t}(x,t_k^+) - u_{t}(x,t_k^-) =c_k u_{t}(x,t_k), &k=1,2,3\ldots\ .
\end{cases}
\]
\[
q(x,t)=
\begin{cases}(t-k+1)x^2,\quad \ \ &
t\in\big(k-1,k-\dfrac{1}{2}\big],\\
(k-t)x^2, \quad \ \ & t\in\big(k-\dfrac{1}{2},k\big],
\end{cases}
\]

代码运行结果：