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## Formulas with LaTeX

LaTeX is most often used for medium-to-large technical or scientific documents. It is extremely useful to write complex formulas with a simple syntax. You can learn learn how to write LaTeX here.

#### For the new Koenig editor

For inline equations, simply surround the LaTex math with a backslash and parentheses: $$LaTex$$. For example a simple function inline:   $$f(x)=(x+a)(x+b)$$.

To get a large and centred expression, surround the LaTex math with a backslash and square brackets: $LaTex$. For example, the Taylor series expansion for the function $$e^x$$ is given by:

$e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots = \sum_{n\geq 0} \frac{x^n}{n!}$

#### For the old Markdown editor

In Markdown, you will have to escape some of the control characters, as explained here. Usually, all that needs to be escaped are the surrounding backslashes. To get the same expressions as above, surround the LaTex with double backslashes: \$$LaTex \$$ and \$LaTex \$.

#### How Formulas look like

See how the delimiters are of reasonable size in these examples (either with the new koenig editor or markdown):

$\left(a+b\right)\left[1-\frac{b}{a+b}\right]=a\,,$

$\sqrt{|xy|}\leq\left|\frac{x+y}{2}\right|,$

even when there is no matching delimiter

$\int_a^bu\frac{d^2v}{dx^2}\,dx =\left.u\frac{dv}{dx}\right|_a^b -\int_a^b\frac{du}{dx}\frac{dv}{dx}\,dx.$

whereas vector problems often lead to statements such as

$u=\frac{-y}{x^2+y^2}\,,\quad v=\frac{x}{x^2+y^2}\,,\quad\text{and}\quad w=0\,.$

Arrays of mathematics are typeset using one of the matrix environments as in

$\begin{bmatrix} 1 & x & 0 \\ 0 & 1 & -1 \end{bmatrix}\begin{bmatrix} 1 \\ y \\ 1 \end{bmatrix} =\begin{bmatrix} 1+xy \\ y-1 \end{bmatrix}.$ $\begin{pmatrix} 2 & 3 & 4\\ 5 & 6 & 7\\ 8 & 9 & 10 \end{pmatrix} v = 0$