Ayuda:Fórmulas Matemáticas

De Wikillerato

(Diferencias entre revisiones)

Revisión de 11:59 6 nov 2007

Ayuda A continuación ofrecemos un cuadro de referencia con nociones básicas y ejemplos que sirven de ayuda para escribir fórmulas utilizando el código LaTeX.

Tabla de contenidos

1 Básicos
2 Subíndices, superíndices, integrales
3 Fracciones, matrices, multilíneas
4 Alfabetos
5 Añadiendo paréntesis a grandes expresiones
6 Espaciado
7 Colores
8 Ejemplos

Básicos

Acentos
`\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}`	$\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}$
`\check{a} \bar{a} \ddot{a} \dot{a}`	$\check{a} \bar{a} \ddot{a} \dot{a}$
Funciones estándar
`\sin a \cos b \tan c`	$\sin a \cos b \tan c$
`\sec d \csc e \cot f`	$\sec d \csc e \cot f$
`\arcsin h \arccos i \arctan j`	$\arcsin h \arccos i \arctan j$
`\sinh k \cosh l \tanh m \coth n`	$\sinh k \cosh l \tanh m \coth n$
`\lim u \limsup v \liminf w \min x \max y`	$\lim u \limsup v \liminf w \min x \max y$
`\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g`	$\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g$
Derivadas
`\nabla \partial x dx \dot x \ddot y`	$\nabla \partial x dx \dot x \ddot y$
Conjuntos
`\forall \exists \emptyset \varnothing`	$\forall \exists \emptyset \varnothing$
`\in \ni \notin \subset \subseteq \supset \supseteq`	$\in \ni \notin \subset \subseteq \supset \supseteq$
`\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus`	$\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus$
`\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup`	$\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup$
Operadores
`+ \oplus \bigoplus \pm \mp -`	$+ \oplus \bigoplus \pm \mp -$
`\times \otimes \bigotimes \cdot \circ \bullet \bigodot`	$\times \otimes \bigotimes \cdot \circ \bullet \bigodot$
`\star * / \div \frac{1}{2}`	$\star * / \div \frac{1}{2}$
Lógica
`\land \wedge \bigwedge \bar{q} \to p`	$\land \wedge \bigwedge \bar{q} \to p$
`\lor \vee \bigvee \lnot \neg q \And`	$\lor \vee \bigvee \lnot \neg q \And$
Raíces
`\sqrt{2} \sqrt[n]{x}`	$\sqrt{2} \sqrt[n]{x}$
Relaciones
`\sim \approx \simeq \cong`	$\sim \approx \simeq \cong$
`\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto`	$\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto$
Geometría
`\Diamond \Box \triangle \angle \perp \mid \nmid \\| 45^\circ`	$\Diamond \Box \triangle \angle \perp \mid \nmid \\| 45^\circ$
Flechas
`\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow`	$\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow$
`\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft`	$\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft$
`\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow`	$\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow$
`\Longrightarrow \Uparrow \Downarrow \Updownarrow`	$\Longrightarrow \Uparrow \Downarrow \Updownarrow$
`\nLeftrightarrow \longleftrightarrow`	$\nLeftrightarrow \longleftrightarrow$
Especial
`\eth \S \P \% \dagger \ddagger \ldots \cdots`	$\eth \S \P \% \dagger \ddagger \ldots \cdots$
`\smile \frown \wr \triangleleft \triangleright \infty \bot \top`	$\smile \frown \wr \triangleleft \triangleright \infty \bot \top$
`\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar`	$\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar$
Otros
`\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown`	$\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown$
`\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge`	$\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge$
`\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes`	$\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes$
`\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant`	$\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant$
`\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot`	$\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot$
`\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox`	$\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox$
`\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot`	$\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot$
`\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq`	$\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq$
`\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork`	$\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork$
`\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq`	$\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq$
`\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid`	$\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid$
`\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \ngtr`	$\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \ngtr$
`\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq`	$\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq$
`\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq`	$\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq$
`\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq`	$\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq$

Subíndices, superíndices, integrales

	Sintaxis	Cómo se verá
	Sintaxis	HTML	PNG
Superíndice	`a^2`	a²	$a^2$
Subíndice	`a_2`	>a₂	$a_2$
Agrupar	`a^{2+2}`	a^{2 + 2}	$a^{2+2}$
Agrupar	`a_{i,j}`	a_i,j	$a_{i,j}$
Combinar superíndice y subíndice	`x_2^3`	$x_2^3$
Superíndices y subíndices, anteriores, posteriores, arriba y abajo	`\sideset{_1^2}{_3^4}\prod_a^b`	$\sideset{_1^2}{_3^4}\prod_a^b$
	`{}_1^2\!\Omega_3^4`	${}_1^2\!\Omega_3^4$
Apilar	`\overset{\alpha}{\omega}`	$\overset{\alpha}{\omega}$
	`\underset{\alpha}{\omega}`	[Unparseable or potentially dangerous latex formula. Error 3 ]
	`\overset{\alpha}{\underset{\gamma}{\omega}}`	$\overset{\alpha}{\underset{\gamma}{\omega}}$
	`\stackrel{\alpha}{\omega}`	$\stackrel{\alpha}{\omega}$
Derivadas ( forzando el PNG)	`x', y, f', f`	$x', y'', f', f''$
Subrayado, línea superior, vectores	`\hat a \ \bar b \ \vec c`	$\hat a \ \bar b \ \vec c$
	`\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}`	$\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}$
	`\overline{g h i} \ \underline{j k l}`	$\overline{g h i} \ \underline{j k l}$
Flechas	`A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C`	$A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C$
Llaves superiores	`\overbrace{ 1+2+\cdots+100 }^{5050}`	$\overbrace{ 1+2+\cdots+100 }^{5050}$
Llaves inferiores	`\underbrace{ a+b+\cdots+z }_{26}`	$\underbrace{ a+b+\cdots+z }_{26}$
Sumatorios	`\sum_{k=1}^N k^2`	$\sum_{k=1}^N k^2$
Productorio	`\prod_{i=1}^N x_i`	$\prod_{i=1}^N x_i$
Coproduct	`\coprod_{i=1}^N x_i`	$\coprod_{i=1}^N x_i$
Límite	`\lim_{n \to \infty}x_n`	$\lim_{n \to \infty}x_n$
Integral	`\int_{-N}^{N} e^x\, dx`	`\int_{-N}^{N} e^x\, dx`
Integral doble	`\iint_{D}^{W} \, dx\,dy`	$\iint_{D}^{W} \, dx\,dy$
Integral triple	`\iiint_{E}^{V} \, dx\,dy\,dz`	$\iiint_{E}^{V} \, dx\,dy\,dz$
Integral de línea	`\oint_{C} x^3\, dx + 4y^2\, dy`	$\oint_{C} x^3\, dx + 4y^2\, dy$
Intersecciones	`\bigcap_1^{n} p`	$\bigcap_1^{n} p$
Uniones	`\bigcup_1^{k} p`	$\bigcup_1^{k} p$