Wikidot 當中的 LaTex 數學式 (範例集)
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基本範例
\begin{align} f(n) = \sum^{N-1}_{k=0} F(k) e^{i 2 \pi k} \frac{n}{N} \end{align}
基本範例
\begin{align} e = lim_{n \rightarrow \infty}\; 1+\frac{1}{1!}+\frac{1}{2!}+...+\frac{1}{n!} \end{align}
基本範例
\begin{align} e = lim_{n \rightarrow \infty} (1+\frac{1}{x})^x \end{align}
複雜範例
\begin{split} \mathbf{T n} &= \left[T_{ij} \mathbf{e}_i \otimes \mathbf{e}_j \right] n_k \mathbf{e}_k \\ & = T_{ij} n_k \left(\mathbf{e}_i \otimes \mathbf{e}_j\right) \mathbf{e}_k \\ & = T_{ij} n_j \mathbf{e}_i \end{split}
多行範例
\begin{eqnarray} f'(x) & = & \frac{d f(x)}{dx} = c_1+c_2*2*x+c_3*3*x^2+c_4*4*x^3+... \\ f''(x) & = & \frac{d f'(x)}{dx} = c_2*2*1+c_3*3*2*x+c_4*4*3*x^2+... \\ f'''(x) & = & \frac{d f''(x)}{dx} = c_3*3*2*1+c_4*4*3*2*x+... \\ ... \\ f^k(x) & = & \frac{d f^{k-1}(x)}{dx} = c_k k!+c_{k+1} (k+1)! x+... \end{eqnarray}
矩陣範例
\begin{align} \left[ \begin{array}{ccc} T_{11} & T_{12} & T_{13} \\ T_{21} & T_{22} & T_{23} \\ T_{31} & T_{32} & T_{33} \end{array} \right] \end{align}
矩陣範例
\begin{align} \left\{ \begin{array}{c} t_1 \\ t_2 \\ t_3 \end{array} \right\} = \left[ \begin{array}{ccc} T_{11} & T_{12} & T_{13} \\ T_{21} & T_{22} & T_{23} \\ T_{31} & T_{32} & T_{33} \end{array} \right] \left\{ \begin{array}{c} n_1 \\ n_2 \\ n_3 \end{array} \right\} \end{align}
範例(8)\begin{align} \int_1^x \frac{1}{x} dx = 1 \end{align}
範例(9)\begin{align} \frac{d}{dx} e^x = e^x \end{align}
範例(10)\begin{align} e^x = 1+\frac{1}{1!} x + \frac{2}{2!} x^2 + ... \frac{n}{n!} x^n+ ... \end{align}
範例(11)\begin{equation} e^{i x} = cos(x) + i*sin(x) \end{equation}
範例(12)\begin{align} f(x) = c_0 + c_1 x + c_2 x^2 + ...+ c_k x^k+...=\sum_{k=0}^\infty c_k x^k \end{align}
範例(13)\begin{align} c_k = \frac{f^k(0)}{k!} \end{align}
範例(14)\begin{align} f(x) = f(0) + \frac{f'(0)}{1!} x +...+ \frac{f^k (0)}{k!} x^k+...=\sum^{\infty}_{k=0} \frac{f^k(0)}{k!} x^k \end{align}
範例(15)\begin{align} f(x) = f(a) + \frac{f'(a)}{1!} x +...+ \frac{f^{k(a)}}{k!} x^k+...= \sum^\infty_{k=0} \frac{f^k(a)}{k!} x^k \end{align}
範例(16)\begin{align} e^{i x} = 1 + i \frac{x}{1!} - \frac{x^2}{2!} - i \frac{x^3}{3!} + ... \end{align}
範例(17)\begin{align} cos(x) = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} + ... \end{align}
範例(18)\begin{align} sin(x) = \frac{x}{1!} - \frac{x^3}{3!} + \frac{x^5}{5!} + ... \end{align}
範例(19)\begin{equation} e^{i x} = cos(x) + i * sin(x) \end{equation}
範例(20)\begin{align} f(x) = \frac{a_0}{2} + \sum^{\infty}_{n=- \infty} a_n cos(n x)+ b_n sin(n x) \end{align}
範例(21)\begin{equation} cos(n x) + i * sin(n x) = e^{i n x} \end{equation}
範例(22)\begin{align} f(x) = \sum^{\infty}_{n=-\infty} F_n e^{i n x} \end{align}
範例(23)\begin{align} F_t = \frac{1}{2\pi} \int^{\pi}_{-\pi} f(x) e^{i t x} dx \end{align}
範例
範例(24)\begin{align} f(t) = \int^\infty_{- \infty} F(x) e^{i 2 \pi x t} dt \end{align}
範例
\begin{eqnarray} f(x) = \left\{ \begin{array}{c} 1 \qquad x \in Z \\ 0 \qquad x \notin Z \end{array} \right. \end{eqnarray}
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page revision: 13, last edited: 08 Oct 2012 02:10
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