Informatics1-2017/Practice7

A MathWikiből
A lap korábbi változatát látod, amilyen Kkovacs (vitalap | szerkesztései) 2017. október 30., 06:53-kor történt szerkesztése után volt.
(eltér) ←Régebbi változat | Aktuális változat (eltér) | Újabb változat→ (eltér)

Tartalomjegyzék

Latex mathematical formulas

Formulas

Reproduce the following in latex:


\begin{align}
a_{11}x_1 + a_{12}x_2 + \ldots + a_{1n}x_n &\leq b_1\\
a_{21}x_1 + a_{22}x_2 + \ldots + a_{2n}x_n &\leq b_2\\
&\vdots\\
a_{m1}x_1 + a_{m2}x_2 + \ldots + a_{mn}x_n &\leq b_m
\end{align}


where x_i \geq 0 \, \forall i=1,2,\ldots,n. The form of the objective function:



z = c_1x_1 + c_2x_2 + \ldots + c_nx_n \Rightarrow \mathop{max} \text{ or } \mathop{min}


The same with vectors and matrices:



\begin{align}
\overrightarrow{x} &\geq 0\\
A\overrightarrow{x} &\leq \overrightarrow{b}\\
z=\overrightarrow{c}^T\overrightarrow{x}&\Rightarrow\mathop{max} \text{ or } \mathop{min}
\end{align}

Matrices, tables

Try the tabular environment with different aligns! Create a 3x3 matrix with all kinds of brackets. Try to do an nxn matrix as well for example, try to create this formula from wikipedia: matrix.

Reproduce this table (matrix):


\begin{array}{c|cccc|c}
  & x_1 & x_2 & \cdots & x_n & \overrightarrow{b}\\\hline
u_1 & a_{11} & a_{12} & \cdots & a_{1n} & b_1\\
u_2 & a_{21} & a_{22} & \cdots & a_{2n} & b_2\\
\vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\
u_m & a_{m1} & a_{m2} & \cdots & a_{mn} & b_m\\\hline
-z & c_1 & c_2 & \cdots & c_n & 0
\end{array}


Theorems, definitions

Let's do some theorems. For that append this to the preamble:

\newtheorem{mydef}{Definition}
  • Create a new threorem style environment!
  • Try the different styles (remark, theorem, definition)!

Labels, references

Create references to your theorems:

\begin{theorem}\label{thm:sample_thm}
Theorem text
\end{theorem}
 
In Theorem \ref{thm:sample_thm} we...

Floating pictures

\begin{figure}[p]
    \centering
    \includegraphics[width=0.8\textwidth]{image.png}
    \caption{Awesome Image}
    \label{fig:awesome_image}
\end{figure}

Change the placement (h,t,p,b,!,H)!

BibTeX

BibTeX is a package to create nice looking bibliographies. Create a test bibliography using these sites: http://www.bibtex.org/Using/, https://en.wikibooks.org/wiki/LaTeX/Bibliography_Management.

Személyes eszközök