Yo enseño Física...

{jatex}\documentclass[12pt,landscape]{article} \usepackage{multicol} \usepackage{calc} \usepackage{ifthen} \usepackage[landscape]{geometry} % To make this come out properly in landscape mode, do one of the following % 1. % pdflatex latexsheet.tex % % 2. % latex latexsheet.tex % dvips -P pdf -t landscape latexsheet.dvi % ps2pdf latexsheet.ps % If you're reading this, be prepared for confusion. Making this was % a learning experience for me, and it shows. Much of the placement % was hacked in; if you make it better, let me know... % 2008-04 % Changed page margin code to use the geometry package. Also added code for % conditional page margins, depending on paper size. Thanks to Uwe Ziegenhagen % for the suggestions. % 2006-08 % Made changes based on suggestions from Gene Cooperman. % To Do: % \listoffigures \listoftables % \setcounter{secnumdepth}{0} % This sets page margins to .5 inch if using letter paper, and to 1cm % if using A4 paper. (This probably isn't strictly necessary.) % If using another size paper, use default 1cm margins. \ifthenelse{\lengthtest { \paperwidth = 11in}} { \geometry{top=.5in,left=.5in,right=.5in,bottom=.5in} } {\ifthenelse{ \lengthtest{ \paperwidth = 297mm}} {\geometry{top=1cm,left=1cm,right=1cm,bottom=1cm} } {\geometry{top=1cm,left=1cm,right=1cm,bottom=1cm} } } % Turn off header and footer \pagestyle{empty} % Redefine section commands to use less space \makeatletter \renewcommand{\section}{\@startsection{section}{1}{0mm}% {2ex plus -.5ex minus -.2ex}% {0.5ex plus .2ex}%x {\normalfont\small\bfseries}} \renewcommand{\subsection}{\@startsection{subsection}{2}{0mm}% {2ex plus -.5ex minus -.2ex}% {0.5ex plus .2ex}% {\normalfont\footnotesize\bfseries}} \renewcommand{\subsubsection}{\@startsection{subsubsection}{3}{0mm}% {-1ex plus -.5ex minus -.2ex}% {1ex plus .2ex}% {\normalfont\tiny\bfseries}} \makeatother % Define BibTeX command \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}} % Don't print section numbers \setcounter{secnumdepth}{0} \setlength{\parindent}{0pt} \setlength{\parskip}{0pt plus 0.5ex} % ----------------------------------------------------------------------- \begin{document} \raggedright \footnotesize \begin{tabular}{@{}p{\linewidth / 4} @{}p{\linewidth / 4} @{}p{\linewidth / 4} @{}p{\linewidth / 4}@{}} \begin{center} \large{\textbf{Formulario de F\'{i}sica}}\\ \tiny{\'{U}ltima actualizaci\'{o}n: \today} \end{center} \section{Movimiento en l\'{i}nea recta} \begin{tabular}{@{}p{\linewidth}@{}} \textbullet Velocidad media \\ \hspace{0.5em} $v_{media} = \frac{s}{t_2 - t_1} = \frac{x_2 - x_1}{t_2 - t_1} = \frac{\Delta x}{\Delta t}$ \\ \\ \textbullet Velocidad instant\'{a}nea \\ \hspace{0.5em} $v = lim_{t_2 - t_1 \rightarrow 0}\frac{x_2 - x_1}{t_2 - t_1} = \frac{dx}{dt}$ \\ \\ \textbullet Aceleraci\'{o}n media \\ \hspace{0.5em} $a_{med} = \frac{v_2 - v_1}{t_2 - t_1}$ \\ \\ \textbullet Aceleraci\'{o}n instant\'{a}nea \\ \hspace{0.5em} $a_{inst} = \frac{dv}{dt}$ \\ \\ \end{tabular} \vspace{-1.5em} \subsection{MUA} \begin{tabular}{@{}p{\linewidth}@{}} \hspace{0.5em} $v_{med} = \frac{x-x_0}{t}$ \\ \\ \hspace{0.5em} $v_{med} = \frac{v+v_0}{2}$ \\ \\ \hspace{0.5em} $a_{med} = \frac{v-v_0}{t}$ \\ \\ \textbullet Velocidad final \\ \hspace{0.5em} $v = v_{0} + at$ \\ \\ \textbullet Posici\'{o}n final \\ \hspace{0.5em} $x = x_0 + v_{0}t + \frac{1}{2}at^2$ \\ \\ \textbullet Velocidad final independiente de t \\ \hspace{0.5em} $v_x^2 = v_{0}^2 + 2a(x - x_0)$ \\ \\ \textbullet Posici\'{o}n final independiente de a \\ \hspace{0.5em} $x = (\frac{v_{0} + v}{2})t + x_0$ \\ \\ \end{tabular} \vspace{-1.5em} % SECOND COLUMN PAGE TABLE & \section{Movimiento de proyectiles} \begin{tabular}{@{}p{\linewidth}@{}} \textbullet Componente de v en x \\ \hspace{0.5em} $v_{x} = v\cos\theta$ \\ \\ \textbullet Componente de v en y \\ \hspace{0.5em} $v_{y} = v\sin\theta$ \\ \\ \textbullet Velocidad en x \\ \hspace{0.5em} $v_x = v_0\cos\theta$ \\ \\ \textbullet Posici\'{o}n en x \\ \hspace{0.5em} $x = x_0 + v_0\cos\theta t$ \\ \\ \textbullet Velocidad en y \\ \hspace{0.5em} $v_y = v_0\sin\theta + gt$ \\ \\ \textbullet Posici\'{o}n en y \\ \hspace{0.5em} $y = y_0 + v_0\sin\theta t + \frac{1}{2}gt^2$ \\ \\ \textbullet (Componente) Vector velocidad \\ \hspace{0.5em} $ v = \sqrt{v_x^2 + v_y^2}$ \\ \\ \textbullet Direcci\'{o}n del proyectil (\'{a}ngulo) \\ \hspace{0.5em} $tan\theta = \frac{v_y}{v_x}$ \\ \\ \end{tabular} \vspace{-1.5em} \subsection{Altura y rango m\'{a}ximo} \begin{tabular}{@{}p{\linewidth}@{}} \textbullet Tiempo en alcanzar altura m\'{a}xima \\ \hspace{0.5em} $t_{h_{max}} = \frac{v_0\sin\theta}{g}$ \\ \\ \textbullet Altura m\'{a}xima \\ \hspace{0.5em} $h_{max} = \frac{v_0^2\sin^2\theta}{2g}$ \\ \\ \textbullet Tiempo en llegar al m\'{a}ximo alcance \\ \hspace{0.5em} $t_{R} = 2t_{h_{max}}$ \\ \\ \textbullet M\'{a}ximo alcance \\ \hspace{0.5em} $R = \frac{v_0^2\sin2\theta}{g}$ \\ \\ \end{tabular} \vspace{-1.5em} % THIRD COLUMN PAGE TABLE & \section{Movimiento circular uniforme} \begin{tabular}{@{}p{\linewidth}@{}} \textbullet R es el radio de la circunferencia \\ \hspace{0.5em} $ a_{rad} = \frac{v^2}{R} = \frac{4\pi^2R}{T^2}$ \\ \\ \textbullet T: tiempo en recorrer 1 vez la circunferencia \\ \hspace{0.5em} $v = \frac{2\pi R}{T} = \frac{d}{t}$ \\ \\ \end{tabular} \vspace{-1.5em} \section{Leyes de Newton} \begin{tabular}{@{}p{\linewidth}@{}} \textbullet $\theta$ respecto al eje x \\ \hspace{0.5em} $F_x = F \cos\theta$ \\ \hspace{0.5em} $F_y = F \sin\theta$ \\ \\ \textbullet $\theta$ respecto al eje y \\ \hspace{0.5em} $F_x = F \sin\theta$ \\ \hspace{0.5em} $F_y = F \cos\theta$ \\ \\ \textbullet Principio de superposici\'{o}n \\ \hspace{0.5em} $F_T = \sum{F}$ \\ \\ \textbullet Primera Ley de Newton \\ \hspace{0.5em} $ \sum{F} = 0$ \\ \\ \textbullet Segunda Ley de Newton \\ \hspace{0.5em} $F_T = ma$ \\ \hspace{0.5em} $F_{Tx} = ma_x$ \\ \hspace{0.5em} $F_{Ty} = ma_y$ \\ \\ \textbullet Tercera Ley de Newton \\ \hspace{0.5em} $F_{accion} = F_{reaccion}$ \\ \hspace{0.5em} $w = mg$ \\ \\ \textbullet Trabajo ($N \cdot m = Joules$) \\ \hspace{0.5em} $W = F (x - x_0) = Fs$ \\ \hspace{0.5em} $W_x = Fs_x \cos\theta$ \\ \hspace{0.5em} $W_y = Fs_y \sin\theta $ \\ \\ \textbullet Teorema del trabajo-energ\'{i}a \\ \hspace{0.5em} $W=\frac{1}{2}mv^2 - \frac{1}{2}mv_0^2 = K_2 - K_1$ \\ \\ \textbullet Energ\'{i}a Cin\'{e}tica \\ \hspace{0.5em} $K = \frac{1}{2}mv^2$ \\ \\ \end{tabular} \vspace{-1.5em} % FOURTH COLUMN PAGE TABLE & \section{Vectores} \begin{tabular}{@{}p{\linewidth}@{}} \hspace{0.5em} $F_x = F \cos\theta$ \\ \hspace{0.5em} $F_y = F \sin\theta$ \\ \hspace{0.5em} $\vec{F} = \vec{F_x} + \vec{F_y} = F\cos\theta_{\hat{i}} + F\sin\theta_{\hat{j}}$ \\ \hspace{0.5em} $F = \sqrt{F_x^2 + F_y^2}$ \\ \hspace{0.5em} $\theta = \tan^{-1} \frac{F_y}{F_x}$ \\ \\ \textbullet Distancia entre dos puntos en el espacio \\ \hspace{0.5em} $\left|P_1P_2\right| = $ \\ \hspace{0.8em} $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$ \\ \\ \textbullet Vector unitario \\ \hspace{0.5em} $\hat{u} = \frac{\vec{QP}}{\left\|\vec{QP}\right\|} = \frac{P-Q}{\left\|P-Q\right\|}$ \\ \hspace{0.5em} $\vec{T} = T\hat{u}$ \\ \\ \textbullet Cosenos directores \\ \hspace{0.5em} $\theta_x = \cos^{-1}\frac{F_x}{F}$ \\ \\ \hspace{0.5em} $\theta_y = \cos^{-1}\frac{F_y}{F}$ \\ \\ \hspace{0.5em} $\theta_z = \cos^{-1}\frac{F_z}{F}$ \\ \\ \end{tabular} \vspace{-1.5em} \end{tabular} \vspace{-1.5em} \end{document}{/jatex}