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LaTeX Formula Template Reference

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Physical

Formulas	LaTeX	Formulas	LaTeX
	\sum {{{ \vec{F} }_i}} = \frac{{d \vec{v}}}{{dt}} = 0		\vec{F} = m \vec{a} = m \frac{{{d^2} \vec{r} }}{{d{t^2}}}
	{{ \vec{F} }_{12}} = - {{ \vec{F} }_{21}}	${E_p} = -\frac{{GMm}}{r} $	{E_p} = -\frac{{GMm}}{r}
	\vec{F} = k \frac{{Qq}}{{{r^2}}} \hat{r}		\oint_L { \vec{E} } \cdot { \rm{d}} \vec{l} = 0
	d \vec{B} = \frac{{{ \mu _0}}}{{4 \pi }} \frac{{Idl \times \vec{r} }}{{{r^3}}} = \frac{{{ \mu _0}}}{{4 \pi }} \frac{{Idl \sin \theta }}{{{r^2}}}	$d \vec{F}= Id \vec{l} \times \vec{B} $	d \vec{F}= Id \vec{l} \times \vec{B}
$E = n{{ \Delta \Phi } \over {\Delta {t} }} $	E = n{{ \Delta \Phi } \over {\Delta {t} }}		\mathop \Phi \nolimits_e = \oint { \vec{E} \cdot {d \vec{S}} = {1 \over {{\varepsilon _0}}}\sum {q} }
	\oint { \vec{E} \cdot {d\vec{l}} = - {{d{\varphi _B}} \over {dt}}}		\oint { \vec{B} \cdot {d \vec{l}} = { \mu _0}} I + { \mu _0}{I_d}
$Q = I ^ { 2 } R \mathrm { t } $	Q = I ^ { 2 } R \mathrm { t }	$F = G{{Mm} \over {{r^2}}} $	F = G{{Mm} \over {{r^2}}}
${E_k} = hv - {W_0} $	{E_k} = hv - {W_0}	$\lambda = \frac{{ \frac{{{c^2}}}{v}}}{{ \frac{{m{c^2}}}{h}}} = \frac{h}{{mv}} = \frac{h}{p} $	\lambda = \frac{{ \frac{{{c^2}}}{v}}}{{ \frac{{m{c^2}}}{h}}} = \frac{h}{{mv}} = \frac{h}{p}
$\Delta {x} \Delta {p} \ge \frac{h}{{4 \pi }} $	\Delta {x} \Delta {p} \ge \frac{h}{{4 \pi }}	$l = {l_0} \sqrt {1 - {{( \frac{v}{c})}^2}} $	l = {l_0} \sqrt {1 - {{( \frac{v}{c})}^2}}
${y_0} = A \cos ( \omega {t} + { \varphi _0}) $	{y_0} = A \cos ( \omega {t} + { \varphi _0})	$y(t) = A \cos ( \frac{{2 \pi {x}}}{ \lambda } + \varphi )$	y(t) = A \cos ( \frac{{2 \pi {x}}}{ \lambda } + \varphi )
$\begin{array}{l} \nabla \cdot \mathbf{E} =\cfrac{\rho}{\varepsilon _0} \\ \nabla \cdot \mathbf{B} = 0 \\ \nabla \times \mathbf{E} = -\cfrac{\partial \mathbf{B}}{\partial t } \\ \nabla \times \mathbf{B} = \mu _0\mathbf{J} + \mu _0\varepsilon_0 \cfrac{\partial \mathbf{E}}{\partial t } \end{array} $	\begin{array}{l} \nabla \cdot \mathbf{E} =\cfrac{\rho}{\varepsilon _0} \\ \nabla \cdot \mathbf{B} = 0 \\ \nabla \times \mathbf{E} = -\cfrac{\partial \mathbf{B}}{\partial t } \\ \nabla \times \mathbf{B} = \mu _0\mathbf{J} + \mu _0\varepsilon_0 \cfrac{\partial \mathbf{E}}{\partial t } \end{array}	$\begin{array}{l} {\huge \oiint}_\mathbb{S} \mathbf{E} \cdot\mathrm{d}s= \cfrac{Q}{\varepsilon_0} \\ {\huge \oiint}_\mathbb{S} \mathbf{B} \cdot\mathrm{d}s= 0 \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{E} \cdot \mathrm{d}l=-\cfrac{\mathrm{d}\Phi _{\mathbf{B}}}{\mathrm{d}t } \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{B} \cdot \mathrm{d}l=\mu_0I+ \mu_0 \varepsilon_0\cfrac{\mathrm{d}\Phi _{\mathbf{E}}}{\mathrm{d}t } \end{array} $	\begin{array}{l} {\huge \oiint}_\mathbb{S} \mathbf{E} \cdot\mathrm{d}s= \cfrac{Q}{\varepsilon_0} \\ {\huge \oiint}_\mathbb{S} \mathbf{B} \cdot\mathrm{d}s= 0 \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{E} \cdot \mathrm{d}l=-\cfrac{\mathrm{d}\Phi _{\mathbf{B}}}{\mathrm{d}t } \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{B} \cdot \mathrm{d}l=\mu_0I+ \mu_0 \varepsilon_0\cfrac{\mathrm{d}\Phi _{\mathbf{E}}}{\mathrm{d}t } \end{array}
$\begin{array}{l} \nabla \cdot \mathbf{D} =\rho _f \\ \nabla \cdot \mathbf{B} = 0 \\ \nabla \times \mathbf{E} = -\cfrac{\partial \mathbf{B}}{\partial t } \\ \nabla \times \mathbf{H} = \mathbf{J}_f + \cfrac{\partial \mathbf{D}}{\partial t } \end{array} $	\begin{array}{l} \nabla \cdot \mathbf{D} =\rho _f \\ \nabla \cdot \mathbf{B} = 0 \\ \nabla \times \mathbf{E} = -\cfrac{\partial \mathbf{B}}{\partial t } \\ \nabla \times \mathbf{H} = \mathbf{J}_f + \cfrac{\partial \mathbf{D}}{\partial t } \end{array}	$\begin{array}{l} {\huge \oiint}_\mathbb{S} \mathbf{D} \cdot\mathrm{d}s= Q_f \\ {\huge \oiint}_\mathbb{S} \mathbf{B} \cdot\mathrm{d}s= 0 \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{E} \cdot \mathrm{d}l=-\cfrac{\mathrm{d}\Phi _{\mathbf{B}}}{\mathrm{d}t } \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{H} \cdot \mathrm{d}l=I_f+\cfrac{\mathrm{d}\Phi _{\mathbf{D}}}{\mathrm{d}t } \end{array} $	\begin{array}{l} {\huge \oiint}_\mathbb{S} \mathbf{D} \cdot\mathrm{d}s= Q_f \\ {\huge \oiint}_\mathbb{S} \mathbf{B} \cdot\mathrm{d}s= 0 \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{E} \cdot \mathrm{d}l=-\cfrac{\mathrm{d}\Phi _{\mathbf{B}}}{\mathrm{d}t } \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{H} \cdot \mathrm{d}l=I_f+\cfrac{\mathrm{d}\Phi _{\mathbf{D}}}{\mathrm{d}t } \end{array}

Chemical

Formulas	LaTeX	Formulas	LaTeX
	\ce{SO4^2- + Ba^2+ -> BaSO4 v}		\ce{A v B (v) -> B ^ B (^)}
	\ce{Hg^2+ ->[I-] $\underset{\mathrm{red}}{\ce{HgI2}}$ ->[I-] $\underset{\mathrm{red}}{\ce{[Hg^{II}I4]^2-}}$}		\ce{Zn^2+ <=>[+ 2OH-][+ 2H+] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$ <=>[+ 2OH-][+ 2H+] $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$}
	\ce{H2O}\quad \ce{Sb2O3} \quad\ce{H+} \\\ce{CrO4^2-} \quad\ce{[AgCl2]-} \\\quad\ce{Y^99+} \quad\ce{Y^{99+}}		\ce{2H2O} \quad\ce{0.5 H2O} \\\ce{1/2H2O} \quad\ce{(1/2)H2O} \quad\ce{$n$ H2O}
	\ce{^{227}_{90}Th+} \quad\ce{^227_90Th+} \quad\ce{^{0}_{-1}n^{-}} \quad\ce{^0_-1n-}		\ce{H^3 HO}
	\ce{A <--> B} \ce{A <=> B} \ce{A <=>> B} \ce{A <<=> B}		\ce{A ->[H2O] B} \ce{A ->[{上方文字}][{下方文字}] B}
	\ce{$K = \frac{[\ce{Hg^2+}][\ce{Hg}]}{[\ce{Hg2^2+}]}$}\quad\ce{$K = \ce{\frac{[Hg^2+][Hg]}{[Hg2^2+]}}$}

Others

Formulas	LaTeX	Formulas	LaTeX
$x\tfrac{a}{b} $	x\tfrac{a}{b}	$\mathrm{d}t $	\mathrm{d}t
$\frac{\mathrm{d} y}{\mathrm{d} x} $	\frac{\mathrm{d} y}{\mathrm{d} x}	$\partial t $	\partial t
$\frac{\partial y}{\partial x} $	\frac{\partial y}{\partial x}	$\nabla\psi $	\nabla\psi
$ \frac{\partial^2}{\partial x_1\partial x_2}y $	\frac{\partial^2}{\partial x_1\partial x_2}y	$\cfrac{1}{a + \cfrac{7}{b + \cfrac{2}{9}}} =c $	\cfrac{1}{a + \cfrac{7}{b + \cfrac{2}{9}}} =c
	\begin{equation}x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4} } } }\end{equation}	${f}^{(n)} $	{f}^{(n)}
${f}'' $	{f}''	$\sqrt[2]{3} $	\sqrt[2]{3}
$_{a}^{d}x$	_{a}^{d}x	$x_{a}^{d} $	x_{a}^{d}
$_{a}^{d}x_{a}^{d} $	_{a}^{d}x_{a}^{d}	$36.5^{\circ} $	36.5^{\circ}
$\lim_{x \to \infty} $	\lim_{x \to \infty}	$\lim_{x \to 0} $	\lim_{x \to 0}
$\textstyle \lim_{x \to 0} $	\textstyle \lim_{x \to 0}	$\max_{x} f$	\max_{x} f
$\log_{2}{5} $	\log_{2}{5}	$\lg_{2}{4} $	\lg_{2}{4}
$\ln_{2}{10} $	\ln_{2}{10}	$\sin^{-1} \alpha $	\sin^{-1} \alpha
$\sum_{a}^{b} $	\sum_{a}^{b}	$ {\textstyle \sum_{a}^{b}} $	{\textstyle \sum_{a}^{b}}
$\prod_{a}^{b} $	\prod_{a}^{b}	$ {\textstyle \prod_{a}^{b}} $	{\textstyle \prod_{a}^{b}}

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