LaTeX初級テンプレート

LaTeX友の会さんの書込 (2006/08/14(Mon) 02:46)

+-------------------------- -------------- ---------------------------+ + $\text{\LaTeX}$ 初級テンプレート by $\text{\LaTeX}$ 友の会・事務局since 2006-08-06 + +-------------------------- -------------- ---------------------------+ +「原稿の表示」からご自分で必要な部分をコピー＆ペーストし,「<ｔex>」,「</ｔex>」で括って下さい．《Tでなく，半角のtを使ってね》 +「このテンプレート」の説明は，《Re: LaTeX初級テンプレート：使用説明》 2006/08/14(Mon) 02:50 No.11308 をご覧下さい． --------------------------- -------------- ---------------------------+ ■1■ 文中の数式と，別行立ての数式 --------------------------- ◇原稿の表示◇ ---------------------------+ 中学で最初に知る式は<Tex>y=ax+b</Tex>で，少したつと双曲線の式； <Tex> y=a/x=frac{a}{x}, </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+ 中学で最初に知る式は y=ax+b で，少したつと双曲線の式；

$y=a/x=\frac{a}{x},$

--------------------------- -------------- ---------------------------+ ■2■ 上下の添え字 --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex> x^2+y^2=r^2, && _nmathrm{C}_r = frac{n!}{(n-r)!r!}, </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$x^2+y^2=r^2, && _n\mathrm{C}_r = \frac{n!}{(n-r)!r!},$

--------------------------- -------------- ---------------------------+ ■3■ 式の番号 --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex> y=asin(omega t). tag{888a} </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$y=a\sin(\omega t). \tag{888a}$

--------------------------- -------------- ---------------------------+ ■4■ 微分 --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex>dot x = x^{prime} = dx/dt =frac{d x(t)}{d t} =frac{d}{d t}left(x(t)right),</Tex> <Tex>ddot x = x^{prime prime} = d^2 x/d t^2 =frac{d^2 x(t)}{d t^2} =frac{d^2}{d t^2}left(x(t)right).</Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\dot x = x^{\prime} = d x/d t=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right),$

$\ddot x = x^{\prime \prime} = d^2 x/d t^2=\frac{d^2 x(t)}{d t^2}=\frac{d^2}{d t^2}\left(x(t)\right).$

--------------------------- -------------- ---------------------------+ ■5■ 積分（簡易横並び：区切り記号→「&&」) --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex>int f(x)dx, && g(x)=int^{x} f(x')dx', && int_{alpha}^{beta} f(x)dx.</Tex> <Tex> intmspace{-11mu}int f(x,y) mspace{2mu}dx mspace{2mu}dy, && oint_{C} f(z)dz.</Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\int f(x)dx, && g(x)=\int^{x} f(x')dx', && \int_{\alpha}^{\beta} f(x)dx.$

$\int\mspace{-11mu}\int f(x,y)\mspace{2mu}dx \mspace{2mu}dy,&& \oint_{C} f(z)dz.$

--------------------------- -------------- ---------------------------+ ■6■ 偏微分 --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex>frac{partial f(x,y)}{partial x} =partial_{x}f(x,y)=f_{x}(x,y),</Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\frac{\partial f(x,y)}{\partial x}=\partial_{x}f(x,y)=f_{x}(x,y),$

--------------------------- -------------- ---------------------------+ ■7■ ベクトル（簡易横並び：区切り記号→「&&」) --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex> vec r = xvec e_x +yvec e_y+zvec e_z, && mathbf{r}=xmathbf{i}+ymathbf{j}+zmathbf{k},&& cosleft(angle mathrm{AOB}right)= frac{overrightarrow{mathrm{OA}}cdotoverrightarrow{mathrm{OB}}} {|\overrightarrow{\mathrm{OA}}|cdot|overrightarrow{mathrm{OB}}|}. </Tex> <Tex> vec A = A_xvec e_x +A_yvec e_y+A_zvec e_z, && mathbf{A}=A_xmathbf{i}+A_{y}mspace{3mu}mathbf{j}+A_zmathbf{k},</Tex> <Tex> vec A = A_xvec e_x +A_yvec e_y+A_zvec e_z, && mathbf{A}=A_xmathbf{i}+A_{y}mspace{3mu}mathbf{j}+A_zmathbf{k},</Tex> <Tex> vec Acdotvec B equiv A_xB_x +A_yB_y +A_zB_z. && text{(inner product or dot product)}</Tex> <Tex> vec A times vec B equiv begin{vmatrix}vec e_{x} & vec e_{y} & vec e_{z} \ A_x & A_y & A_z \ B_x & B_y & B_z end{vmatrix}. && text{(outer product or cross product)} </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\vec r = x\vec e_x +y\vec e_y+z\vec e_z, &&\mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k},&&\cos\left(\angle \mathrm{AOB}\right)=\frac{\overrightarrow{\mathrm{OA}}\cdot\overrightarrow{\mathrm{OB}}}{|\overrightarrow{\mathrm{OA}}|\cdot|\overrightarrow{\mathrm{OB}}|}.$

$\vec A = A_x\vec e_x +A_y\vec e_y+A_z\vec e_z, &&\mathbf{A}=A_x\mathbf{i}+A_{y}\mspace{3mu}\mathbf{j}+A_z\mathbf{k},$

$\vec A\cdot\vec B \equiv A_xB_x +A_yB_y +A_zB_z. && \text{(inner product or dot product)}$

$\vec A \times \vec B \equiv\begin{vmatrix}\vec e_{x} & \vec e_{y} & \vec e_{z} \\ A_x & A_y & A_z \\B_x & B_y & B_z\end{vmatrix}. && \text{(outer product or cross product)}$

--------------------------- -------------- ---------------------------+ ■8■ nabla演算子 --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex>overrightarrow{bigtriangledown} equiv frac{partial}{partial x}vec e_{x} +frac{partial}{partial y}vec e_{y} +frac{partial }{partial z}vec e_{z}.</Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\overrightarrow{\bigtriangledown} \equiv \frac{\partial}{\partial x}\vec e_{x}+\frac{\partial}{\partial y}\vec e_{y}+\frac{\partial }{\partial z}\vec e_{z}.$

--------------------------- -------------- ---------------------------+ ■9■ grad(gradient:勾配), div(divergence:発散), rot(rotation:回転) --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex> mathrm{grad}f(vec r)=overrightarrow{bigtriangledown} f(vec r) =frac{partial f(vec r)}{partial x}vec e_{x} +frac{partial f(vec r)}{partial y}vec e_{y} +frac{partial f(vec r)}{partial z}vec e_{z}, </Tex> <Tex> mathrm{div}vec E(vec r,t)= overrightarrow{bigtriangledown} cdot vec E(vec r,t) =frac{partial E_{x}(vec r,t)}{partial x} +frac{partial E_{y}(vec r,t)}{partial y} +frac{partial E_{z}(vec r,t)}{partial z}, </Tex> <Tex> mathrm{rot} vec H(vec r,t) = overrightarrow{bigtriangledown} times vec H(vec r,t) =begin{vmatrix}vec e_{x} & vec e_{y} & vec e_{z}\ dfrac{partial}{partial x} & dfrac{partial}{partial y} & dfrac{partial}{partial z} \ H_{x}(vec r,t) & H_{y}(vec r,t) & H_{z}(vec r,t) end{vmatrix}. </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\mathrm{grad}\ f(\vec r)=\overrightarrow{\bigtriangledown} f(\vec r)=\frac{\partial f(\vec r)}{\partial x}\vec e_{x}+\frac{\partial f(\vec r)}{\partial y}\vec e_{y}+\frac{\partial f(\vec r)}{\partial z}\vec e_{z},$

$\mathrm{div}\ \vec E(\vec r,t)= \overrightarrow{\bigtriangledown} \cdot \vec E(\vec r,t)=\frac{\partial E_{x}(\vec r,t)}{\partial x}+\frac{\partial E_{y}(\vec r,t)}{\partial y}+\frac{\partial E_{z}(\vec r,t)}{\partial z},$

$\mathrm{rot}\ \vec H(\vec r,t)= \overrightarrow{\bigtriangledown} \times \vec H(\vec r,t)=\begin{vmatrix}\vec e_{x} & \vec e_{y} &\vec e_{z}\\ \dfrac{\partial}{\partial x} &\dfrac{\partial}{\partial y} &\dfrac{\partial}{\partial z} \\H_{x}(\vec r,t) & H_{y}(\vec r,t) &H_{z}(\vec r,t) \end{vmatrix}.$

--------------------------- -------------- ---------------------------+ ■10■ Laplacian(ラプラシアン：ラプラスの演算子) --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex>bigtriangleup Psi(vec r) equiv left( frac{partial^2}{partial x^2} +frac{partial^2}{partial y^2} +frac{partial^2}{partial z^2}right) Psi(vec r) = overrightarrow{bigtriangledown}^2 Psi(vec r) = mathrm{div}cdotmathrm{grad}Psi(vec r)</Tex> <Tex> bigtriangleup Psi(vec r) &=0 && leftarrow text{Laplace equation} & Psi(vec r): text{harmonic function} \ bigtriangleup Phi(vec r) & = q(vec r) && leftarrow text{Poisson's equation} </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\bigtriangleup \equiv \left( \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\right) = \overrightarrow{\bigtriangledown}^2 = \mathrm{div}\cdot\mathrm{grad}$

$\bigtriangleup \Psi(\vec r) &=0 && \leftarrow \text{Laplace equation} & \Psi(\vec r): \text{harmonic function} \\\bigtriangleup \Phi(\vec r) & = q(\vec r) && \leftarrow \text{Poisson's equation}$

--------------------------- -------------- ---------------------------+ ■11■ 複素数 --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex> z=x+mathrm{i}y=rmathrm{e}^{+mathrm{i}theta} =rleft(cos(theta)+mathrm{i}sin(theta)right), </Tex> <Tex> bar z=x-mathrm{i}y=rmathrm{e}^{-mathrm{i}theta} =rleft(cos(theta)-mathrm{i}sin(theta)right), </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$z=x+\mathrm{i}y=r\mathrm{e}^{+\mathrm{i}\theta}=r\left(\cos(\theta)+\mathrm{i}\sin(\theta)\right),$

$\bar z=x-\mathrm{i}y=r\mathrm{e}^{-\mathrm{i}\theta}=r\left(\cos(\theta)-\mathrm{i}\sin(\theta)\right),$

--------------------------- -------------- ---------------------------+ ■12■ オイラの公式とその逆公式（左波括弧，アレイ環境：区切り＝"＆"） --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex> left{ begin{array}{l c} mathrm{e}^{mathrm{i}theta} & =cos(theta)+mathrm{i}sin(theta),\ mathrm{e}^{-mathrm{i}theta} & =cos(theta)-mathrm{i}sin(theta). end{array} right. </Tex> <Tex> left{ begin{array}{l c} cos(theta) &= dfrac{mathrm{e}^{mathrm{i}theta}+mathrm{e}^{-mathrm{i}theta}}{2},\ sin(theta) &= dfrac{mathrm{e}^{mathrm{i}theta}-mathrm{e}^{-mathrm{i}theta}}{2mathrm{i}}, end{array} right. </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\left\{ \begin{array}{l c}\mathrm{e}^{\mathrm{i}\theta} & =\cos(\theta)+\mathrm{i}\sin(\theta),\\\mathrm{e}^{-\mathrm{i}\theta} & =\cos(\theta)-\mathrm{i}\sin(\theta).\end{array} \right.$

$\left\{ \begin{array}{l c}\cos(\theta) &=\dfrac{\mathrm{e}^{\mathrm{i}\theta}+\mathrm{e}^{-\mathrm{i}\theta}}{2},\\\sin(\theta) &=\dfrac{\mathrm{e}^{\mathrm{i}\theta}-\mathrm{e}^{-\mathrm{i}\theta}}{2\mathrm{i}},\end{array} \right.$

--------------------------- -------------- ---------------------------+ ■13■ 指数関数と双曲線関数 --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex> left{ begin{array}{l c} mathrm{e}^{x} & =cosh(x)+sinh(x),\ mathrm{e}^{-x} & =cosh(x)-sinh(x), end{array} right. </Tex> <Tex> left{ begin{array}{lcc} cosh(x) &= dfrac{mathrm{e}^{x}+mathrm{e}^{-x}}{2} & ,\ sinh(x) &= dfrac{mathrm{e}^{x}-mathrm{e}^{-x}}{2} & ,\ tanh(x) &= dfrac{sinh(x)}{cosh(x)} &= dfrac{mathrm{e}^{x}-mathrm{e}^{-x}} {mathrm{e}^{x}+mathrm{e}^{-x}}. </Tex> --------------------------- ◇TeXの表示◇ ----------------------------+

$\left\{ \begin{array}{l c}\mathrm{e}^{x} & =\cosh(x)+\sinh(x),\\\mathrm{e}^{-x} & =\cosh(x)-\sinh(x),\end{array} \right.$

$\left\{ \begin{array}{lcc}\cosh(x) &= \dfrac{\mathrm{e}^{x}+\mathrm{e}^{-x}}{2}, & \\\sinh(x) &= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{2}, & \\\tanh(x) &= \dfrac{\sinh(x)}{\cosh(x)}&= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{\mathrm{e}^{x}+\mathrm{e}^{-x}}.\end{array} \right.$

--------------------------- -------------- ---------------------------+ ■14■ 良く使うギリシャ文字 --------------------------- ◇原稿の表示◇ ---------------------------+ <pre> alpha eta nu tau beta theta xi upsilon gamma iota phi delta kappa pi chi epsilon lambda rho psi zeta mu sigma omega

Gamma Theta Xi Upsilon Delta Lambda Pi Phi Sigma Psi

Omega

varGammavarThetavarXivarUpsilon varDeltavarLambda varPivarPhi varSigma varPsi

varOmega

</pre>--------------------------- ◇TeXの表示◇ ----------------------------+

$\begin{array}{cc|cc|cc|cc|}alpha &\alpha &eta &\eta &nu &\nu &tau &\tau \\beta &\beta &theta &\theta &xi &\xi &upsilon &\upsilon \\gamma &\gamma &iota &\iota &omicron & &phi &\phi \\delta &\delta &kappa &\kappa &pi &\pi &chi &\chi \\epsilon &\epsilon &lambda &\lambda &rho &\rho &psi &\psi \\zeta &\zeta &mu &\mu &sigma &\sigma &omega &\omega \\\cline{1-8}\text{Gamma} &\Gamma &\text{Theta} &\Theta &\text{Xi} &\Xi &\text{Upsilon} &\Upsilon \\\text{Delta} &\Delta &\text{Lambda} &\Lambda &\text{Pi} &\Pi &\text{Phi} &\Phi\\\cline{1-4}& & & &\text{Sigma} &\Sigma &\text{Psi} &\Psi \\\cline{5-6}& & & & & &\text{Omega} &\Omega \\\cline{1-8}varGamma &\varGamma &varTheta &\varTheta &varXi &\varXi &varUpsilon &\varUpsilon \\varDelta &\varDelta &varLambda &\varLambda &varPi &\varPi &varPhi &\varPhi\\\cline{1-4}& & & &varSigma &\varSigma &varPsi &\varPsi \\\cline{5-6}& & & & & &varOmega &\varOmega \\\cline{1-8}\end{array}$

--------------------------- -------------- ---------------------------+

Re: LaTeX初級テンプレート：使用説明

LaTeX友の会さんのレス (2006/08/14(Mon) 02:50)

○使い方○

■【LaTeX初級テンプレート】No.11307 ■ ←について説明します．

・ $\text{\LaTeX}$ 友の会は，上記の $\text{\LaTeX}$ 初級テンプレートを製作・維持・管理します．

・・初級テンプレート：公開日：2006-08-14

・ $\text{\LaTeX}$ 友の会には，誰でもが参加でき，自由に意見を付けられます．

・資料の引用は，「数学用語の使い方」と「TeXでの表し方」のスレッド； 1) 2006/08/04(Fri) 20:16 No.11108 と， 2) 2006/08/05(Sat) 11:26 No.11132 とに，基づいています．

・・テンプレートや友の会にご意見などをお持ちの方は，上記No.11108 のスレッドに追加ください．

●文責： $\text{\LaTeX}$ 友の会・事務局編集人/ｍNeji，2006-08-14.

Re: LaTeX初級テンプレート：準備室

LaTeX友の会さんのレス (2006/08/14(Mon) 02:51)

○準備室○

--------------------------- -------------- ---------------------------+ ■15■ 記号 --------------------------- ◇原稿の表示◇ ---------------------------+ <pre> pm circbulletcdot alephhbarReIm inftyemptysetforallexists capcup vee wedge subset supsetsqsubsetsqsupset subseteq supseteqvdash dashv in notin ninotni parallel perpsim simeq equivapproxproptoneq le llgegg </pre>--------------------------- ◇TeXの表示◇ ----------------------------+

$\begin{array}{cc|cc|cc|cc|}pm & \pm & circ & \circ & bullet & \bullet & cdot & \cdot \\aleph & \aleph & hbar & \hbar & Re & \Re & Im & \Im \\infty & \infty & emptyset & \emptyset & forall & \forall & exists & \exists \\cap & \cap & cup & \cup & vee & \vee & wedge & \wedge \\subset & \subset & supset & \supset & sqsubset & \sqsubset & sqsupset & \sqsupset \\subseteq & \subseteq & supseteq & \supseteq & vdash & \vdash & dashv & \dashv \\in & \in & notin & \notin & ni & \ni & not\cdot ni & \not\ni \\parallel & \parallel & perp & \perp & sim & \sim & simeq & \simeq \\equiv & \equiv & approx & \approx & propto & \propto & neq & \neq \\le & \le & ll & \ll & ge & \ge & gg & \gg \\\cline{1-8}\end{array}$

--------------------------- -------------- ---------------------------+ ■16■ 矢印と点 --------------------------- ◇原稿の表示◇ ---------------------------+ <pre>getslongleftarrow Leftarrow Longleftarrow tolongrightarrow RightarrowLongrightarrow

leftrightarrowlongleftrightarrow LeftrightarrowLongleftrightarrow mapstolongmapsto hookleftarrow hookrightarrow

賢いdots(カンマ区切り)dotsc (commas) 賢いdots(二項演算子)dotsb (binary op. or relations) 賢いdots(多項並べ)dotsm (multiplications) 賢いdots(多重積分)dotsi (integrals)

</pre>--------------------------- ◇TeXの表示◇ ----------------------------+

$\begin{array}{cc|cc|}gets &\gets &longleftarrow &\longleftarrow \\Leftarrow &\Leftarrow &Longleftarrow &\Longleftarrow \\to &\to &longrightarrow &\longrightarrow \\Rightarrow &\Rightarrow &Longrightarrow &\Longrightarrow \\\cline{1-4}leftrightarrow &\leftrightarrow&longleftrightarrow &\longleftrightarrow \\Leftrightarrow &\Leftrightarrow&Longleftrightarrow &\Longleftrightarrow \\mapsto &\mapsto &longmapsto &\longmapsto \\ hookleftarrow &\hookleftarrow &hookrightarrow &\hookrightarrow \\\cline{3-4}rightleftharpoons &\rightleftharpoons \\\cline{1-4}dots &a_1,a_2,\dots,a_n. &dotsc &a_1,\dotsc \\dots &a_1 + a_2 + \dots + a_n &dotsb &a_1 + \dotsb \\dots &a_1 a_2 \dots a_n &dotsm &a_1 \dotsm \\dots &\int \dots \int &dotsi &\int \dots\end{array}$

--------------------------- -------------- ---------------------------+

$\mathrm{J}_{\lambda}(z)=\frac{1}{2\mathrm{\pi}}\int_{\mathrm{L}}\mathrm{e}^{-\mathrm{i}z\sin(\zeta)+\mathrm{i}\lambda\zeta}\mathrm{d}\zeta$

$J_{\lambda}(z)=\frac{1}{2\mathit{\pi}}\int_{L}e^{-iz\sin(\zeta)+i\lambda\zeta}d\zeta$

+-------------------------- -------------- ---------------------------+ =====倉庫===== --------------------------- -------------- ---------------------------+ ■■ --------------------------- ◇原稿の表示◇ ---------------------------+ <Tex></Tex> --------------------------- ◇TeXの表示◇ ----------------------------+ $> ! Paragraph ended before \align* was complete. >$

Re: LaTeX初級テンプレート

LaTeX友の会さんのレス (2006/08/14(Mon) 04:58)

○予備のページ○

$\Delta \Psi(\vec r) &=0 && \leftarrow \text{Laplace equation} & \Psi(\vec r): \text{harmonic function} \\\Delta \Phi(\vec r) & = q(\vec r) && \leftarrow \text{Poisson's equation}$

$\begin{array}{llll}\Delta \Psi(\vec r) &=0 &\leftarrow \text{Laplace equation} & \Psi(\vec r)=\text{harmonic function} \\\Delta \Phi(\vec r) & = q(\vec r) &\leftarrow \text{Poisson's equation} & \\\end{array}$

手書きの場合，

$y=h(t) \qquad (3)'$

は勿論動きます．

この場合のソースは <Tex> y=h(t) qquad (3)' </Tex>

しかし，この版では，tag{3}を使う場合括弧の中にしか入りません．

$y=x \tag{3}\\y=z \tag{3'}\\y=w \tag{3`}$

上の場合，

テスト

CO さんのレス (2006/08/15(Tue) 12:46)

これはテストです．

$\left(\begin{array}{cc}A^{1}\\ A^{2}\\\end{array}\right)=\left(\begin{array}{cc}g^{11} & g^{12} \\g^{21} & g^{22} \\\end{array}\right)\left( \begin{array}{cc} A_{1}\\ A_{2}\\ \end{array} \right)$

ああ，本日は曇天なり．テスト．1234567 $> ! Paragraph ended before \align* was complete. >$

[home] [掲示板] [ページの先頭]