# mathjax

display vzorec $$a = 5$$

ted zkusime inline: $a = 5$, ale mozna je default backslash a (zavorky): $a = \sqrt{2}$

Klasicka kvadraticka rovnice: $x_{1,2} = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

pm $\pm$ plusminus

sqrt $\sqrt{2}$ druha odmocnica

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

in, ni, notin, forall, exists $\in \ni \notin \forall \exists$

$\arccos \cos \csc \exp \ker \limsup \min \sinh \arcsin \cosh \deg \gcd \lg \ln \Pr \sup \arct an \cot \det \hom \lim \log \sec \tan \arg \coth \dim \inf \liminf \max \sin \tanh$

# Derivatives, Limits, Sums and Integrals

The expressions $$\frac{du}{dt} and \frac{d^2 u}{dx^2}$$ are obtained in LaTeX by typing \frac{du}{dt} and \frac{d^2 u}{dx^2} respectively. The mathematical symbol $\partial$ is produced using \partial.

Thus the Heat Equation $$\frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} \right)$$ is obtained in LaTeX by typing

 \frac{\partial u}{\partial t}
= h^2 \left( \frac{\partial^2 u}{\partial x^2}
+ \frac{\partial^2 u}{\partial y^2}
+ \frac{\partial^2 u}{\partial z^2} \right)

To obtain mathematical expressions such as $$\lim_{x \to +\infty}, \inf_{x > s} and \sup_K$$ in displayed equations we type

\lim_{x \to +\infty}, \inf_{x > s} and \sup_K

respectively.

Thus to obtain $$\lim_{x \to +\infty} \frac{3x^2 +7x^3}{x^2 +5x^4} = 3.$$ (in LaTeX) we type  \lim_{x \to +\infty} \frac{3x^2 +7x^3}{x^2 +5x^4} = 3.

To obtain a summation sign such as $$\sum_{i=1}^{2n}$$ we type \sum_{i=1}^{2n}.

Thus $$\sum_{k=1}^n k^2 = \frac{1}{2} n (n+1).$$ is obtained by typing

    \sum_{k=1}^n k^2 = \frac{1}{2} n (n+1).