Installation for windows 7

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Tutorial 1

In TexMaker, type

\documentclass[11pt]{article}
\begin{document}
This is my first LaTex document.
Suppose we are given a rectangle with side 
lengths $(x+1)$ and $(x+3)$.Then the equation $A=x^2+4X+3$ represents the area of the rectangle.
Suppose we are given a rectangle with side 
lengths $(x+1)$ and $(x+3)$.Then the equation $$A=x^2+4X+3$$ represents the area of the rectangle.
\end{document}

It shows:

\documentclass[11pt]{article}

\begin{document}
This is my first LaTex document.

Suppose we are given a rectangle with side
lengths $(x+1)$ and $(x+3)$.Then the equation $A=x^2+4X+3$ represents the area of the rectangle.

Suppose we are given a rectangle with side
lengths $(x+1)$ and $(x+3)$.Then the equation $$A=x^2+4X+3$$ represents the area of the rectangle.
\end{document}

Tutorial 2

In TexMaker, type

\documentclass[11pt]{article}
\begin{document}
superscripts: $$2x^3$$
$$2x^{34}$$
$$2x^{3x+4}$$
$$2x^{3x^4+5}$$
subscripts: 
$$x_1$$
$$x_{12}$$
$${x_1}_2$$
greek letters:
$$\pi$$
$$\alpha$$
$$A=\pi r^2$$
trig functions:
$$y=\sin{x}$$
log functions:
$$\log_5{x}$$
$$\ln{x}$$
square roots:
$$\sqrt{2}$$
$$\sqrt[3]{2}$$
$$\sqrt{x^2+y^2}$$
$$\sqrt{1+\sqrt{x}}$$
fractions:
About $\displaystyle{\frac{2}{3}}$ of the glass is full.
$$\frac{x}{x^+x+1}$$
$$\frac{\sqrt{x+1}}{\sqrt{x-1}}$$
$$\frac{1}{1+\frac{1}{x}}$$
$$\sqrt{\frac{x}{x^2+x+1}}$$
\end{document}

Note : In hexo, need to use

subscripts: 
$$x\_1$$
$$x\_{12}$$
$${x\_1}\_2$$

It shows:

\documentclass[11pt]{article}

\begin{document}

superscripts: $$2x^3$$
$$2x^{34}$$
$$2x^{3x+4}$$
$$2x^{3x^4+5}$$

subscripts:
$$x_1$$
$$x_{12}$$
$${x_1}_2$$

greek letters:
$$\pi$$
$$\alpha$$
$$A=\pi r^2$$

trig functions:
$$y=\sin{x}$$

log functions:
$$\log_5{x}$$
$$\ln{x}$$

square roots:
$$\sqrt{2}$$
$$\sqrt[3]{2}$$
$$\sqrt{x^2+y^2}$$
$$\sqrt{1+\sqrt{x}}$$

fractions:

About $\displaystyle{\frac{2}{3}}$ of the glass is full.

$$\frac{x}{x^+x+1}$$

$$\frac{\sqrt{x+1}}{\sqrt{x-1}}$$

$$\frac{1}{1+\frac{1}{x}}$$

$$\sqrt{\frac{x}{x^2+x+1}}$$
\end{document}

Paper formula

$Z{normal}=[z{normal1}, z{normal2}…z{normal_n}]\in R^{n\times m}$

\begin{equation}
\label{eq:xznormal}
x{normal} = \frac{z{normali}-\bar{z}{normali}}{\sigma(z{normal_i})}
\end{equation}

$\bar{z}_{normali}$
$z{normali}$
$\sigma(z{normali})$
$x{normal}$

\begin{equation}
\label{eq:snormalk}
s_{normalk} = W{normalk}\cdot x{normal_i}
\end{equation}

$W_{normalk}\in R^{k\times m}$
$x{normal_i}\in R^{m\times 1}$

\begin{equation}
\label{eq:snormale}
s_{normale} = W{normale}\cdot x{normal_i}
\end{equation}

$W_{normal_e}\in R^{(d-k)\times m}$

$E{normal}$
${I^2}{normal}$
${I^2}_{normal_e}$

\begin{equation}
\label{eq:inormal}
{I^2}{normal}= s{normalk}^T\cdot s{normalk}
\end{equation}
\begin{equation}
\label{eq:inormale}
I{normale}^2= s{normale}^T\cdot s{normale}
\end{equation}
\begin{equation}
\label{eq:xase}
X{normal}= A{normal}\cdot S{normal}+E_{normal}
\end{equation}

$E_{normal}$

\begin{equation}
\label{eq:enormal}
E{normal}=T{normal}\cdot P{normal}^T+F{normal}
\end{equation}

$E{normal}=[e{normal1}, e{normal2}…e{normal_m}]\in R^{n\times m}$

$T{normal}^2$
$Q{normal}$

\begin{equation}
\label{eq:t2normal}
T{normal}^2=e{normali}^T\cdot P{normal}\cdot \Lambda ^{-1}\cdot P{normal}^T\cdot e{normali}
\end{equation}
\begin{equation}
\label{eq:qnormal}
Q{normal}= r{normal}^T r{normal}
\end{equation}

$r{normal}=(I-P{normal}\cdot P{normal}^T )\cdot e{normal_i}\in R^{m\times 1}$
$I\in R^{m\times m}$

\begin{equation}
\label{eq:inputmatrix}
X{normal}= [{I^2}{normal},I_{normale}^2,T{normal}^2,Q_{normal}]
\end{equation}

$Z{fault}=[z{fault1}, z{fault2}…z{faultm}]\in R^{n\times m}$
$X{fault}=[x_{fault1}, x{fault2}…x{faultm}]\in R^{n\times m}$
Calculate Statistics
$y{normal}=0$

\begin{equation}
\label{eq:ifault}
{I^2}{fault}= s{faultk}^T\cdot s{faultk}
\end{equation}
\begin{equation}
\label{eq:ifaulte}
I{faulte}^2= s{faulte}^T\cdot s{faulte}
\end{equation}
\begin{equation}
\label{eq:t2fault}
T{fault}^2=e_{faulti}^T\cdot P{fault}\cdot \Lambda ^{-1}\cdot P{fault}^T\cdot e{faulti}
\end{equation}
\begin{equation}
\label{eq:qfault}
Q{fault}= r{fault}^T r{fault}
\end{equation}

\begin{equation}
\label{eq:inputmatrixf}
X{fault}= [{I^2}{fault},I_{faulte}^2,T{fault}^2,Q_{fault}]
\end{equation}

\begin{equation}
\label{eq:inew}
{I^2}{new}= s{newk}^T\cdot s{newk}
\end{equation}
\begin{equation}
\label{eq:inewe}
I{newe}^2= s{newe}^T\cdot s{newe}
\end{equation}
\begin{equation}
\label{eq:t2new}
T{new}^2=e_{newi}^T\cdot P\cdot \Lambda ^{-1}\cdot P^T\cdot e{newi}
\end{equation}
\begin{equation}
\label{eq:qnew}
Q{new}= r{new}^T r{new}
\end{equation}

$X{new}= [{I^2}{new},I_{newe}^2,T{new}^2,Q_{new}]$

\multicolumn{1}{c}{ICA-PCA-SVM} &
\multicolumn{1}{c}{PCA-RVM} &
\multicolumn{1}{c}{ICA-RVM} &
\multicolumn{1}{c}{Proposed Method}

& ICA-SVM & ICA-PCA-SVM & PCA-RVM & ICA-RVM & ICA-PCA-RVM