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author | Norbert Preining <norbert@preining.info> | 2021-02-08 03:01:14 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2021-02-08 03:01:14 +0000 |
commit | 314f2cf58d8c42409e06e1c52de09b77d6e5fe09 (patch) | |
tree | aed06f32ad00ff26fb839b9fd650b51b2443a3fb /macros/latex/contrib/easybook/doc/pages/chapter2.tex | |
parent | e068841d2fc2976d094b382e4dd5e4d6df455506 (diff) |
CTAN sync 202102080301
Diffstat (limited to 'macros/latex/contrib/easybook/doc/pages/chapter2.tex')
-rw-r--r-- | macros/latex/contrib/easybook/doc/pages/chapter2.tex | 25 |
1 files changed, 14 insertions, 11 deletions
diff --git a/macros/latex/contrib/easybook/doc/pages/chapter2.tex b/macros/latex/contrib/easybook/doc/pages/chapter2.tex index 49e9d1e824..bf2bbf7798 100644 --- a/macros/latex/contrib/easybook/doc/pages/chapter2.tex +++ b/macros/latex/contrib/easybook/doc/pages/chapter2.tex @@ -1,16 +1,18 @@ % Chapter 2 -\documentclass[../easybook-demo]{subfiles} -\begin{document} \chapter{定理盒子} -\begin{outline}\index{zhaiyao@摘要盒子} +\begin{outline} +\index{zhaiyao@摘要盒子} \item 这是一个摘要盒子。 \item 它的标题是可选参数,默认标题是摘要。 \end{outline} -\section{定理}\index{d@定理} -\begin{theorem}[(高斯公式\footnote{选自高等数学公式。})]\label{theorem:gauss formula}\index{d@定理!g@高斯公式} +\section{定理} +\index{d@定理} +\begin{theorem}[(高斯公式\footnote{选自高等数学公式。})] +\label{theorem:gauss formula} +\index{d@定理!g@高斯公式} 设空间闭区域$\Omega$是由分片光滑的闭曲面$\Sigma$围成,若函数$P(x,y,z)$,$Q(x,y,z)$,$R(x,y,z)$在$\Omega$上具有一节连续偏导数,则有 \begin{align} \iiint_\Omega\left(\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial x}\right)\mathrm{d}V & =\oiint_\Sigma P\mathrm{d}y\mathrm{d}z+Q\mathrm{d}z\mathrm{d}x+R\mathrm{d}x\mathrm{d}y @@ -20,7 +22,8 @@ 这里$\Sigma$是整个边界曲面$\Omega$的外侧,$\cos\alpha,\cos\beta,\cos\gamma$是$\Sigma$在点$(x,y,z)$处的法向量的方向余弦。引用这个公式如\cref{theorem:gauss formula}。 \end{theorem} -\begin{definition}[(Stokes formula)]\index{d@定理!s@Stokes formula} +\begin{definition}[(Stokes formula)] +\index{d@定理!s@Stokes formula} Let $\Gamma$ be a piecewise smooth directed closed curve, $\Sigma$ is a piecewise smooth directed surface bounded by $\Gamma$, the side of $\Gamma$ and the positive direction of $\Sigma$ According to the right-hand rule, if the function $P(x,y,z)$, $Q(x,y,z)$, $R(x,y,z)$ has a first-order continuous deviation on the curve $\Sigma$ Derivative, then \begin{multline} \iint_\Sigma\left(\frac{\partial R}{\partial y}-\frac{\partial Q}{\partial z}\right)\mathrm{d}y\mathrm{d}z+\left(\frac{\partial P}{\partial z}-\frac{\partial R}{\partial x}\right)\mathrm{d}z\mathrm{d}x+\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)\mathrm{d}x\mathrm{d}y @@ -55,14 +58,16 @@ The Stokes formula is an extension of the basic calculus formula in the case of 这是一个证明,末尾自动添加证明结束符。 \end{proof} -\begin{mybox}*[My title]\index{z@自定义盒子} +\begin{mybox}*[My title] +\index{z@自定义盒子} \zhlipsum*[3][name = aspirin] \tcblower \zhlipsum*[8][name = aspirin] \end{mybox} \zhlipsum*[3][name = aspirin] -\begin{exercise}[black][1.][习题]\index{x@习题环境} +\begin{exercise}[black][1.][习题] +\index{x@习题环境} \item 设$w = f(x+y+z,xyz)$,$f$具有二阶连续偏导数,求$\dfrac{{\partial w}}{{\partial x}}$和$\dfrac{{{\partial ^2}w}}{{\partial x\partial z}}$。 \item 已知$y = y(x)$在任意点$x$处的增量$\Delta y = \dfrac{y\Delta x}{1+x^2}+\alpha$,其中$\alpha$是$\Delta x$的高阶无穷小($\Delta x\to 0$时),$y(0) = \pi$,则$y(1) = \uline{\mbox{\hspace{2em}}}$。 \item 设函数$f(x)$在$(-\infty,+\infty)$上有定义,则下述命题中正确的是 \mbox{(\hspace{1.5em})} @@ -72,6 +77,4 @@ The Stokes formula is an extension of the basic calculus formula in the case of \task 若$f''(x_0) = 0$,则$(x_0,f(x_0))$是曲线$y = f(x)$的拐点坐标。 \task 若$f'(x_0) = 0$, $f''(x_0) = 0$,$f'''(x_0)\ne 0$,则$x_0$一定不是$f(x)$的极值点。 \end{tasks} -\end{exercise} - -\end{document}
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