#rst2hooktail_source ================================================================= LaTeX初級テンプレート ================================================================= - by LaTeX友の会・事務局 since 2006-08-06 .. csv-table:: 数式のテンプレート :header: "表示項目", "原稿表示", "TeX表示" "分数 式番号","y=a/x=\\frac{a}{x} \\tag{88}"," $y=a/x=\frac{a}{x} \tag{88} $ " "上付添え字","x^2+y^2=r^2"," $x^2+y^2=r^{2}$ " "下付添え字 ","_{\\it n}\\mathrm{C}_{\\it r} = \\frac{n!}{(n-r)!r!},"," $_{\it n}\mathrm{C}_{\it r} = \frac{n!}{(n-r)!r!},$ " "1次微分","\\dot x^{\\prime} = dx/dt =\\frac{d x(t)}{d t} =\\frac{d}{d t}\\left(x(t)\\right),"," $ \dot x = x^{\prime} = d x/d t=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right), $ " "2次微分","\\ddot x^{\\prime \\prime} = d^{2}x/dt^{2} =\\frac{d^{2} x(t)}{d t^{2}} =\\frac{d}{d t^{2}}\\left(x(t)\\right),"," $ \ddot x = x^{\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), $ " "積分 ","\\int f(x)dx, \\ g(x)=\\int^{x} f(x')dx', \\ \\int_{\\alpha}^{\\beta} f(x)dx."," $ \int f(x)dx, \ g(x)=\int^{x} f(x')dx', \ \int_{\alpha}^{\beta} f(x)dx. $ " "面積分,線積分 \\rm≡\\mathrm","\\int\\mspace{-11mu}\\int_{S} f(x,y)\\mspace{2mu}{\\rm d}x \\mspace{2mu}\\rm d}y, \\quad \\oint_{C} f(z){\\rm d}z."," $ \int\mspace{-11mu}\int_{S} f(x,y) \mspace{2mu}{\rm d} x \mspace{2mu}{\rm d}y, \quad \oint_{C} f(z){\rm d}z. $ " "偏微分 ","\\frac{\\partial f(x,y)}{\\partial x} =\\partial_{x}f(x,y)=f_{x}(x,y),"," $ \frac{\partial f(x,y)}{\partial x} =\partial_{x}f(x,y)=f_{x}(x,y), $ " "2点間のヴェクタ(上の長い矢) ","\\cos\\left(\\angle \\mathrm{AOB}\\right)= \\frac{\\overrightarrow{\\mathrm{OA}}\\cdot \\overrightarrow{\\mathrm{OB}}}{| \\overrightarrow{\\mathrm{OA}}| \\cdot|\\overrightarrow{\\mathrm{OB}}|}. "," $ \cos\left(\angle \mathrm{AOB}\right)=\frac{\overrightarrow{\mathrm{OA}}\cdot\overrightarrow{\mathrm{OB}}}{|\overrightarrow{\mathrm{OA}}|\cdot|\overrightarrow{\mathrm{OB}}|}.$ " "ヴェクタ(上→,太斜体) \\bm≡\boldmath","\\vec A &= A_x\\vec e_x +A_y\\vec e_y +A_z\\vec e_z, \\\\ \\bm{A} &=A_x\\bm{i} +A_{y}\\mspace{3mu}\\bm{j} +A_z\\bm{k},","$ \vec A &= A_x\vec e_x +A_y\vec e_y+A_z\vec e_z, \\ \bm{A} &=A_x\bm{i}+A_{y}\mspace{3mu}\bm{j}+A_z\bm{k}.$" "ヴェクタ内積 dot-product","\\vec A\\cdot\\vec B \\equiv A_xB_x +A_yB_y +A_zB_z.","$\vec A\cdot\vec B &\equiv A_xB_x +A_yB_y +A_zB_z. \\ &\text{(inner product or dot product)} $" "ヴェクタ外積 cross-product","\\vec A \\times \\vec B &\\equiv \\begin{vmatrix}\\vec e_{x} & \\vec e_{y} & \\vec e_{z} \\\\ A_x & A_y & A_z \\\ B_x & B_y & B_z \\end{vmatrix}.","$\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)} $" "nabla演算子 ","\\overrightarrow{\\bigtriangledown} \\equiv \\frac{\\partial}{\\partial x}\\vec e_{x} +\\frac{\\partial}{\\partial y}\\vec e_{y} +\\frac{\\partial }{\\partial z}\\vec e_{z}, \\quad \\nabla \\equiv \\frac{\\partial}{\\partial x}\\bm{e}_{x} +\\frac{\partial}{\\partial y}\\bm{e}_{y} +\\frac{\\partial }{\\partial z}\\bm{e}_{z}. ","$ \overrightarrow{\bigtriangledown} &\equiv \frac{\partial}{\partial x}\vec e_{x} +\frac{\partial}{\partial y}\vec e_{y} +\frac{\partial }{\partial z}\vec e_{z}, \\ \nabla &\equiv \frac{\partial}{\partial x}\bm{e}_{x} +\frac{\partial}{\partial y}\bm{e}_{y} +\frac{\partial }{\partial z}\bm{e}_{z}. $" "gradient:勾配","\\mathrm{grad}\\ f(\vec r)=\\overrightarrow{\\bigtriangledown} f(\\vec r) =\\frac{\\partial f(\\vec r)}{\\partial x}\\vec e_{x} +\\frac{\\partial f(\\vec r)}{\\partial y}\\vec e_{y} +\\frac{\partial f(\\vec r)}{\\partial z}\\vec e_{z},","$ \mathrm{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}, $" "divergence:発散","\\mathrm{div}\\ \\vec E(\\vec r,t)= \\overrightarrow{\\bigtriangledown} \\cdot \\vec E(\\vec r,t) =\\frac{\\partial E_{x}(\\vec r,t)}{\\partial x} +\\frac{\\partial E_{y}(\\vec r,t)}{\\partial y} +\\frac{\\partial E_{z}(\\vec r,t)}{\\partial z},","$\mathrm{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}, $ " "rotation:回転","\\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}.","$\mathrm{rot}\ \vec H(\vec r,t)= \overrightarrow{\bigtriangledown} \times \vec H(\vec r,t) =\begin{vmatrix}\vec e_{x} & \vec e_{y} & \vec e_{z}\\ \dfrac{\partial}{\partial x} & \dfrac{\partial}{\partial y} & \dfrac{\partial}{\partial z} \\ H_{x}(\vec r,t) & H_{y}(\vec r,t) & H_{z}(\vec r,t) \end{vmatrix}.$" "Laplacian(ラプラシアン:ラプラスの演算子)","\\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}.","$\bigtriangleup &\equiv \left( \frac{\partial^2}{\partial x^2} +\frac{\partial^2}{\partial y^2} +\frac{\partial^2}{\partial z^2}\right)\\ &= \overrightarrow{\bigtriangledown}^{2} \\ &= \mathrm{div}\cdot\mathrm{grad}.$" "ラプラスの方程式 <br>ポアッソンの方程式","\\bigtriangleup \\Psi(\vec r) &=0 && \\leftarrow \text{Laplace eq.} & \\Psi(\vec r): \quad \\text{harmonic function} \\\\ \bigtriangleup \\Phi(\vec r) & = q(\vec r) && \leftarrow \\text{Poisson's equation}","$\bigtriangleup \Psi(\vec r) &=0 && \leftarrow \text{Laplace eq.} \quad \Psi(\vec r): \text{harmonic function} \\ \bigtriangleup \Phi(\vec r) & = q(\vec r) && \leftarrow \text{Poisson's equation}$" "複素数 成分により表示","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).","$z=x+\mathrm{i}y=r\mathrm{e}^{+\mathrm{i}\theta} =r\left(\cos(\theta)+\mathrm{i}\sin(\theta)\right), \\ \bar z=x-\mathrm{i}y=r\mathrm{e}^{-\mathrm{i}\theta} = r\left(\cos(\theta)-\mathrm{i}\sin(\theta)\right),$" "オイラの公式","\\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.","$\left\{ \begin{array}{l c} \mathrm{e}^{\mathrm{i}\theta} & =\cos(\theta)+\mathrm{i}\sin(\theta), \\ \mathrm{e}^{-\mathrm{i}\theta} & =\cos(\theta)-\mathrm{i}\sin(\theta).\end{array} \right.$" "オイラの逆公式","\\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.","$\left\{ \begin{array}{l c} \cos(\theta) &=\dfrac{\mathrm{e}^{\mathrm{i}\theta} +\mathrm{e}^{-\mathrm{i}\theta}}{2},\\ \sin(\theta) &=\dfrac{\mathrm{e}^{\mathrm{i}\theta} -\mathrm{e}^{-\mathrm{i}\theta}}{2\mathrm{i}}, \end{array} \right.$" "指数関数と双曲線関数","\\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.","$\left\{ \begin{array}{l c} \mathrm{e}^{x} &=\cosh(x)+\sinh(x), \\ \mathrm{e}^{-x} &=\cosh(x)-\sinh(x), \end{array} \right. \\ \left\{ \begin{array}{lcc} \cosh(x) &=\dfrac{\mathrm{e}^{x}+\mathrm{e}^{-x}}{2}, & \\ \sinh(x) &= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{2}, & \\ \tanh(x) &= \dfrac{\sinh(x)}{\cosh(x)} &= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}} {\mathrm{e}^{x}+\mathrm{e}^{-x}}. \end{array} \right.$" .. csv-table:: Greek letters :header: "See/Type", "See/Type", "See/Type", "See/Type" "$\alpha$ \\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" "$\Gamma$ \\Gamma", "$\Theta$ \\Theta", "$\Xi$ \\Xi", "$\Upsilon$ \\Upsilon" "$\Delta$ \\Delta", "$\Lambda$ \\Lambda", "$\Pi$ \\Pi", "$\Phi$ \\Phi" " ", " ", "$\Sigma$ \\Sigma", "$\Psi$ \\Psi" " ", " ", " ", "$\Omega$ \\Omega" "$\varGamma$ \\varGamma", "$\varTheta$ \\varTheta", "$\varXi$ \\varXi", "$\varUpsilon$ \\varUpsilon" "$\varDelta$ \\varDelta", "$\varLambda$ \\varLambda", "$\varPi$ \\varPi", "$\varPhi$ \\varPhi" " ", " ", "$\varSigma$ \\varSigma", "$\varPsi$ \\varPsi" " ", " ", " ", "$\varOmega$ \\varOmega" .. csv-table:: 数学記号 :header: "See", "Type", "意味", "例" "$\mathbb{N}$", "\\mathbb{N}", "自然数の全体", "$1,2,\dots$" "$\mathbb{Z}$","\\mathbb{Z}", "整数全体", "$0,\pm1,\pm2,\dots$" "$\mathbb{Q}$","\\mathbb{Q}", "有理数全体", "$\pm 2/3$" "$\mathbb{R}$","\\mathbb{R}", "実数全体", "$\sqrt{2}, \pi, e=\mathrm{e}^{1}$" "$\mathbb{C}$","\\mathbb{C}", "複素数全体", "\mathrm{e}^{\mathrm{i}\pi}-1=0$" @@author:mNeji@@ @@accept: 2006-08-28@@ @@category: script@@ @@id: latexTemplate@@