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-rw-r--r--macros/latex/contrib/easybook/doc/pages/chapter2.tex25
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} \ No newline at end of file
+\end{exercise} \ No newline at end of file