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Latex Maths

[latexpage]

you may always place a LaTeX expression within shortcodes everywhere on the site. Attribute tags are allowed: [latex attrs]…[/latex].

Misplaced & x^2 + y^2 &= 1 y &= \sqrt{1 – x^2}

At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
\[
f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\]
where $h$ is some step.
Then we interpolate points $\{(x_k,f_k)\}$ by polynomial
\begin{equation} \label{eq:poly}
P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}
\end{equation}
Its coefficients $\{a_j\}$ are found as a solution of system of linear equations:
\begin{equation} \label{eq:sys}
\left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}
Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}).
Here is reference to non-existing equation (\ref{eq:unknown}).

For the display environments, equation numbering is automatic, but this may be overridden and the number set explicitly with \tag{..} placed within the display expression.

A number of options may be set for an expression with attribute tags such as size, color, background, align, as arguments of \quicklatex{} placed within the expression:

\[
\quicklatex{color=”#00ff00″ size=25}
\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1}
\]
 

Compilation of an expression may be suppressed, showing instead the LaTeX source, by preceding the expression with a !.

For mathematical graphs you may use tikzpicture and pgfplots, e.g. :

\begin{tikzpicture}
[+preamble]
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
[/preamble]
\begin{axis}
\addplot3[surf,domain=0:360,samples=40] {cos(x)*cos(y)};
\end{axis}
\end{tikzpicture}