[QuantEcon]MATLAB混编FORTRAN语言

$$
N(d) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^d \exp(-t^2/2) \;dt
$$

1. mathwork

复制代码

$$
x=\pi \,k-\frac{\pi }{4}\mathrm{}\mathrm{\ \ for\ all\ \ }\mathrm{}k\mathrm{}\mathrm{\ \ with\ \ }\mathrm{}k\in \mathbb{Z}\wedge 1\le k
$$

$$
\left[\begin{array}{l}
m\frac{{{d^2}x}}{{d{t^2}}} = T\left( t \right)\frac{{x\left( t \right)}}{r}\\
m\frac{{{d^2}y}}{{d{t^2}}} = T\left( t \right)\frac{{y\left( t \right)}}{r} - mg\\
x{\left( t \right)^2} + y{\left( t \right)^2} = {r^2}
\end{array}\right]
$$

$$
-\frac{\mathrm{sin}\left(x\right)}{2\,{\mathrm{sin}\left(\frac{x}{2}\right)}^2 -1}
$$

$$
\begin{array}{l}
\left(\begin{array}{ccc}
\frac{b-1}{{\left(a-1\right)}\,\sigma_2 } & 0 & 0\\
\frac{1}{\sigma_2 } & 0 & 0\\
0 & 0 & 0\\
0 & 0 & 1\\
0 & \frac{f-1}{\sigma_1 \,{\left(e-1\right)}} & 0\\
0 & \frac{1}{\sigma_1 } & 0
\end{array}\right)\\
\mathrm{}\\
\textrm{where}\\
\mathrm{}\\
\;\;\sigma_1 =\sqrt{\frac{{{\left(f-1\right)}}^2 }{{{\left(e-1\right)}}^2 }+1}\\
\mathrm{}\\
\;\;\sigma_2 =\sqrt{\frac{{{\left(b-1\right)}}^2 }{{{\left(a-1\right)}}^2 }+1}
\end{array}
$$

$$
\begin{array}{l}
\left(\begin{array}{ccc}
\frac{b-1}{{\left(a-1\right)}\,\sigma_2 } & 0 & 0\\
\frac{1}{\sigma_2 } & 0 & 0\\
0 & 0 & 0\\
0 & 0 & 1\\
0 & \frac{f-1}{\sigma_1 \,{\left(e-1\right)}} & 0\\
0 & \frac{1}{\sigma_1 } & 0
\end{array}\right)\\
\mathrm{}\\
\textrm{where}\\
\mathrm{}\\
\;\;\sigma_1 =\sqrt{\frac{{{\left(f-1\right)}}^2 }{{{\left(e-1\right)}}^2 }+1}\\
\mathrm{}\\
\;\;\sigma_2 =\sqrt{\frac{{{\left(b-1\right)}}^2 }{{{\left(a-1\right)}}^2 }+1}
\end{array}
$$

$$
\left(\begin{array}{ccc}
z & \frac{1}{{\mathrm{hy}}^2 }-2\,z & z\\
\frac{1}{{\mathrm{hx}}^2 }-2\,z & 4\,z-\frac{2}{{\mathrm{hx}}^2 }-\frac{2}{{\mathrm{hy}}^2 } & \frac{1}{{\mathrm{hy}}^2 }-2\,z\\
z & \frac{1}{{\mathrm{hy}}^2 }-2\,z & z
\end{array}\right)
$$

$$
d\,\frac{\partial^4 }{\partial x^4 }\;u\left(x,y\right)+2\,d\,\frac{\partial^2 }{\partial y^2 }\;\frac{\partial^2 }{\partial x^2 }\;u\left(x,y\right)+d\,\frac{\partial^4 }{\partial y^4 }\;u\left(x,y\right)
$$

$$
\left(\begin{array}{cccccc}
\frac{1}{360} & h & h & h & h & \frac{\partial^6 }{\partial x^6 }\;u\left(x,y\right)+5\,\frac{\partial^2 }{\partial y^2 }\;\frac{\partial^4 }{\partial x^4 }\;u\left(x,y\right)+5\,\frac{\partial^4 }{\partial y^4 }\;\frac{\partial^2 }{\partial x^2 }\;u\left(x,y\right)+\frac{\partial^6 }{\partial y^6 }\;u\left(x,y\right)
\end{array}\right)
$$

$$
\left(\begin{array}{cccccc}
\frac{1}{360} & h & h & h & h & \frac{\partial^6 }{\partial x^6 }\;u\left(x,y\right)+5\,\frac{\partial^2 }{\partial y^2 }\;\frac{\partial^4 }{\partial x^4 }\;u\left(x,y\right)+5\,\frac{\partial^4 }{\partial y^4 }\;\frac{\partial^2 }{\partial x^2 }\;u\left(x,y\right)+\frac{\partial^6 }{\partial y^6 }\;u\left(x,y\right)
\end{array}\right)
$$