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changelog/index.html

@@ -1039,6 +1039,10 @@ <h1 id="changelog">Changelog<a class="headerlink" href="#changelog" title="Perma
 <div class="heti-skip">
 <h2 id="2025">2025 年<a class="headerlink" href="#2025" title="Permanent link">¶</a></h2>
 <ul>
+<li><span style="font-family: var(--md-code-font-family)">02-09 <a href="https://github.com/ZJU-Turing/TuringCourses/commit/72c549bb07edae33f90e055507707a6d09fcea9e">72c549b</a> </span>docs: 更新思政、<a href="https://zju-turing.github.io/TuringCourses/political/modern_history/">史纲</a>、军理和<a href="https://zju-turing.github.io/TuringCourses/math_phys/math_analysis1/">数分</a>一内容，添加24年<a href="https://zju-turing.github.io/TuringCourses/math_phys/math_analysis1/">数分</a>回忆卷 (<a href="https://github.com/ZJU-Turing/TuringCourses/pull/220">#220</a>)<ul>
+<li>🔗 <a href="https://zju-turing.github.io/TuringCourses/political/military_theory/">军事理论</a> <a href="https://zju-turing.github.io/TuringCourses/political/morality_law/">思想道德与法治</a> </li>
+</ul>
+</li>
 <li><span style="font-family: var(--md-code-font-family)">02-07 <a href="https://github.com/ZJU-Turing/TuringCourses/commit/2e48360185216bd2a61f719cb4f3d564d622a55b">2e48360</a> </span>docs: 添加短学期数据要素市场相关内容 (<a href="https://github.com/ZJU-Turing/TuringCourses/pull/218">#218</a>)<ul>
 <li>🔗 <a href="https://zju-turing.github.io/TuringCourses/short_term/data_market/">数据要素市场概论</a> </li>
 </ul>

math_phys/math_analysis1/index.html

@@ -1102,7 +1102,7 @@
 <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M20.71 7.04c.39-.39.39-1.04 0-1.41l-2.34-2.34c-.37-.39-1.02-.39-1.41 0l-1.84 1.83 3.75 3.75M3 17.25V21h3.75L17.81 9.93l-3.75-3.75L3 17.25Z"></path></svg>
 </a>
 <div class="admonition warning">
-<p class="admonition-title">1709276023</p>
+<p class="admonition-title">1739034124</p>
 </div>
 <h1 id="ih">数学分析（甲）Ⅰ（H）<a class="headerlink" href="#ih" title="Permanent link">¶</a></h1>
 <h2 id="_1">课程学习内容<a class="headerlink" href="#_1" title="Permanent link"><span><span class="heti-spacing"> </span>¶</span></a></h2>
@@ -1131,6 +1131,7 @@ <h2 id="_3">历年回忆卷<a class="headerlink" href="#_3" title="Permanent lin
 <li><a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892021%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7.pdf">（<span>21<span class="heti-spacing"> </span></span>级）<span>2021<span class="heti-spacing"> </span></span>秋冬期末回忆卷</a> ｜ <a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892021%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7%E8%A7%A3%E7%AD%94.pdf">解答</a></li>
 <li><a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892022%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7.pdf">（<span>22<span class="heti-spacing"> </span></span>级）<span>2022<span class="heti-spacing"> </span></span>秋冬期末回忆卷</a> ｜ <a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892022%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7%E8%A7%A3%E7%AD%94.pdf">解答</a></li>
 <li><a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892023%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7.pdf">（<span>23<span class="heti-spacing"> </span></span>级）<span>2023<span class="heti-spacing"> </span></span>秋冬期末回忆卷</a> ｜ <a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892023%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7%E8%A7%A3%E7%AD%94.pdf">解答</a></li>
+<li><a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892024%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7.tex">（<span>24<span class="heti-spacing"> </span></span>级）<span>2024<span class="heti-spacing"> </span></span>秋冬期末回忆卷</a> ｜ <a href="%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%EF%BC%88%E7%94%B2%EF%BC%89I%EF%BC%88H%EF%BC%892024%E7%A7%8B%E5%86%AC%E6%9C%9F%E6%9C%AB%E5%9B%9E%E5%BF%86%E5%8D%B7%E8%A7%A3%E7%AD%94.pdf">解答</a></li>
 </ul>
 <h2 id="_4">课程学习建议与相关推荐书目<a class="headerlink" href="#_4" title="Permanent link"><span><span class="heti-spacing"> </span>¶</span></a></h2>
 <div class="admonition warning">
@@ -1140,13 +1141,13 @@ <h2 id="_4">课程学习建议与相关推荐书目<a class="headerlink" href="#
 <p><em>《高等数学》同济大学出版社</em> 这本书过于简单，不建议学</p>
 </div>
 <h3 id="0">第<span class="heti-skip"><span class="heti-spacing"> </span>0<span class="heti-spacing"> </span></span>级【不想挂科呜呜呜，如何从零开始迎接考试周】<a class="headerlink" href="#0" title="Permanent link">¶</a></h3>
-<p>作为一门<span class="heti-skip"><span class="heti-spacing"> </span>5.5<span class="heti-spacing"> </span></span>学分的大课，无论从知识的重要性还是单纯对绩点的考量，这门课虽然难度在大一上所有课程中最大，但也不是松懈放弃的理由。如果你很后悔在秋学期的数分学习过于摆烂，在冬学期建议各位抓住计算题，并确保自己知道最常用的一些定理，可以在考场中默写出来。在考试前掌握了极限、泰勒公式、不定积分和定积分的简单计算，并至少知道柯西收敛定理、闭区间上的相关性质、求导链式法则、微分中值定理、黎曼积分、<span>A-D<span class="heti-spacing"> </span></span>判别法这些定理，相信通过考试考到<span class="heti-skip"><span class="heti-spacing"> </span>60<span class="heti-spacing"> </span></span>分以上是没问题的。值得注意的是，分析总评是结合平时分与期末考成绩（40%+60%），但是会有斩杀线（期末考分数不能太低），大约<span class="heti-skip"><span class="heti-spacing"> </span>40<span class="heti-spacing"> </span></span>分的卷面分就可以保证通过了。</p>
+<p>作为一门<span class="heti-skip"><span class="heti-spacing"> </span>5.5<span class="heti-spacing"> </span></span>学分的大课，无论从知识的重要性还是单纯对绩点的考量，这门课虽然难度在大一上所有课程中最大，但也不是松懈放弃的理由。如果你很后悔在秋学期的数分学习过于摆烂，在冬学期建议各位抓住计算题，并确保自己知道最常用的一些定理，可以在考场中默写出来。在考试前掌握了极限、泰勒公式、不定积分和定积分的简单计算，并至少知道柯西收敛定理、闭区间上的相关性质、求导链式法则、微分中值定理、黎曼积分、<span>A-D<span class="heti-spacing"> </span></span>判别法这些定理，相信通过考试考到<span class="heti-skip"><span class="heti-spacing"> </span>60<span class="heti-spacing"> </span></span>分以上是没问题的。值得注意的是，分析总评是结合平时分与期末考成绩（<span>20%<span class="heti-spacing"> </span></span>作业<span class="heti-skip"><span class="heti-spacing"> </span>+20%<span class="heti-spacing"> </span></span>小测<span class="heti-skip"><span class="heti-spacing"> </span>+60%<span class="heti-spacing"> </span></span>期末），但是会有斩杀线（期末考分数不能太低），大约<span class="heti-skip"><span class="heti-spacing"> </span>40<span class="heti-spacing"> </span></span>分的卷面分就可以保证通过了。</p>
 <div class="admonition note">
 <p class="admonition-title">注</p>
 <p>以下为正常的学习内容，一定注意参考书目虽然多，但是一共选择<span class="heti-skip"><span class="heti-spacing"> </span>1-2<span class="heti-spacing"> </span></span>本就足够了</p>
 </div>
 <h3 id="1-85">第<span class="heti-skip"><span class="heti-spacing"> </span>1<span class="heti-spacing"> </span></span>级【想要一个正常的成绩（达不到满绩，但至少可以<span class="heti-skip"><span class="heti-spacing"> </span>85<span class="heti-spacing"> </span></span>分以上）】<a class="headerlink" href="#1-85" title="Permanent link">¶</a></h3>
-<p>拿到一个正常的成绩，上课认真听课做笔记或者听别的老师的智云课堂是必不可少的，同时需要你可以按时完成作业并参加习题课，掌握作业的解答方法并完成助教给出的额外习题。在完成作业和习题课内容之外，建议大家把课本上的课后习题尽可能全部做一遍（做的时候不要看答案）。同学们的课本不出意外仍然是复旦大学<strong><em>陈纪修教授主编的《数学分析》</em></strong>，这本书对初学者还是很友好的，依托这本书就差不多了。当然，考前适度的复习（补天）依旧必不可少，做两套往年卷并复习一遍可能遗忘的知识就差不多啦！</p>
+<p>拿到一个正常的成绩，上课认真听课做笔记或者听别的老师的智云课堂是必不可少的，同时需要你可以按时完成作业并参加习题课，掌握作业的解答方法并完成助教给出的额外习题。在完成作业和习题课内容之外，建议大家把课本上的课后习题尽可能全部做一遍（做的时候不要看答案）。往年的数分教材是复旦大学<strong><em>陈纪修教授主编的《数学分析》</em></strong>，<span>24<span class="heti-spacing"> </span></span>级变成了华东师大出版社的<strong>数学分析</strong>，内容变得更简略了（但是笔者还是建议看一下陈纪修，对初学者还是很友好的）。当然，考前适度的复习（补天）依旧必不可少，做两套往年卷并复习一遍可能遗忘的知识就差不多啦！</p>
 <h3 id="2-48">第<span class="heti-skip"><span class="heti-spacing"> </span>2<span class="heti-spacing"> </span></span>级【想要<span class="heti-skip"><span class="heti-spacing"> </span>4.8+<span class="heti-spacing"> </span></span>的绩点（满绩可遇不可求）】<a class="headerlink" href="#2-48" title="Permanent link">¶</a></h3>
 <p>想要一个漂亮的成绩，如果不是考试简单或你把课后习题大量完成，或者你擅长考试，那么还是需要一些其他补充的。在第<span class="heti-skip"><span class="heti-spacing"> </span>1<span class="heti-spacing"> </span></span>级的基础上，补充的内容会是一些难度相对而言更大的教材以及对应的习题集，让你在学习中可以有高屋建瓴的感觉。以下是推荐的教材：</p>
 <h4 id="_5">苏联式教材推荐<a class="headerlink" href="#_5" title="Permanent link"><span><span class="heti-spacing"> </span>¶</span></a></h4>
@@ -1232,7 +1233,7 @@ <h3 id="3">第<span class="heti-skip"><span class="heti-spacing"> </span>3<span
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+<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M21 13.1c-.1 0-.3.1-.4.2l-1 1 2.1 2.1 1-1c.2-.2.2-.6 0-.8l-1.3-1.3c-.1-.1-.2-.2-.4-.2m-1.9 1.8-6.1 6V23h2.1l6.1-6.1-2.1-2M12.5 7v5.2l4 2.4-1 1L11 13V7h1.5M11 21.9c-5.1-.5-9-4.8-9-9.9C2 6.5 6.5 2 12 2c5.3 0 9.6 4.1 10 9.3-.3-.1-.6-.2-1-.2s-.7.1-1 .2C19.6 7.2 16.2 4 12 4c-4.4 0-8 3.6-8 8 0 4.1 3.1 7.5 7.1 7.9l-.1.2v1.8Z"></path></svg></span> 2025-02-09  <span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"></path></svg></span> Contributors <span class="contributors"><a href="https://github.com/TonyCrane" target="_blank" title="TonyCrane"><img alt="TonyCrane" src="https://avatars.githubusercontent.com/u/44120331"/></a><a href="https://github.com/45gfg9" target="_blank" title="45gfg9"><img alt="45gfg9" src="https://avatars.githubusercontent.com/u/37043529"/></a><a href="https://github.com/Fairicle" target="_blank" title="Fairicle"><img alt="Fairicle" src="https://avatars.githubusercontent.com/u/126493285"/></a><a href="https://github.com/jayi0908" target="_blank" title="jayi0908"><img alt="jayi0908" src="https://avatars.githubusercontent.com/u/180948899"/></a><a href="https://github.com/Xecades" target="_blank" title="Xecades"><img alt="Xecades" src="https://avatars.githubusercontent.com/u/33767256"/></a><a href="https://github.com/yhwu-is" target="_blank" title="yhwu-is"><img alt="yhwu-is" src="https://avatars.githubusercontent.com/u/80104150"/></a><a href="https://github.com/rzm0572" target="_blank" title="rzm0572"><img alt="rzm0572" src="https://avatars.githubusercontent.com/u/52785233"/></a><a href="https://github.com/V1CeVersaa" target="_blank" title="V1CeVersaa"><img alt="V1CeVersaa" src="https://avatars.githubusercontent.com/u/141535263"/></a></span></p>
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math_phys/math_analysis1/数学分析（甲）I（H）2024秋冬期末回忆卷.pdf

@@ -0,0 +1,57 @@
+\documentclass{ctexbook}
+\usepackage{amsmath, amsfonts, amssymb, geometry}
+\usepackage{enumitem} % 用于自定义列表格式
+
+\geometry{left=2.5cm,right=2.5cm,top=3cm,bottom=3cm}
+\AtBeginDocument{
+    \abovedisplayskip=3pt plus 3pt minus 3pt
+    \belowdisplayskip=3pt plus 3pt minus 3pt
+    \abovedisplayshortskip=0pt plus 3pt
+    \belowdisplayshortskip=3pt plus 3pt minus 3pt
+}
+
+\begin{document}
+
+\centering
+\subsection*{2024 - 2025学年数学分析I (H)期末试题}
+\centering
+\textbf{图灵回忆卷}
+
+\begin{enumerate}[leftmargin=*,labelwidth=!,labelsep=0pt]
+    \item[一、]计算题
+    \begin{enumerate}[leftmargin=*,labelwidth=!,labelsep=0pt]
+        \item[(1)] \(\lim\limits_{n\to\infty}\dfrac{1}{n}\displaystyle\sum\limits_{k=1}^{n}\ln\left(1+\dfrac{k}{n}\right)\).
+        \item[(2)] \(\lim\limits_{x\to0}\dfrac{\int_{0}^{x^{2}}\left(\sin{\sqrt{t}}\right)^{2} \mathrm{d}t}{x^{4}}\).
+        \item[(3)] \(f(x)=\int_{0}^{x}\left(1+t\right)\arctan t \mathrm{d}t\), 求\(f(x)\)的极值.
+        \item[(4)] 求由如下方程：
+            \(
+            \begin{cases}
+                e^{x}=\sin t+2t+1\\
+                t\sin y-y+\dfrac{\pi}{2}=0
+            \end{cases}
+            \)
+            确定的\(y,x\)所对应的\(\dfrac{\mathrm{d}y}{\mathrm{d}x}\vert_{x = 0}\).
+        \item[(5)] \(\int_{0}^{+\infty}\dfrac{xe^{x}}{\left(1+e^{x}\right)^{2}} \mathrm{d}x\).
+    \end{enumerate}
+
+    \item[二、]叙述确界原理，并用确界原理证明：定义在\((0,1)\)上的单增函数的间断点只能是跳跃间断点.
+    
+    \item[三、]数列\(\{x_n\}\)满足：\(0<x_{1}<\dfrac{1}{2},x_{n+1}=\dfrac{1}{4(1-x_{n})},\forall n \in \mathbb{N_+}\),
+    证明：\(\{x_n\}\)收敛，且\(\lim\limits_{n\to\infty}x_{n}=\dfrac{1}{2}\).
+    
+    \item[四、]\(f\in C[0,2025]\),且\(f(0)=f(2025)=0,f_{+}^{\prime}(0)>0,f_{-}^{\prime}(2025)>0\),
+    证明：至少存在一个\(\xi\)使得\(\xi\in(0,2025)\)且\(f(\xi)=0\).
+
+    \item[五、]叙述一致连续定义，并证明：\(f(x)=\sqrt{x}\ln x\)在\((0,+\infty)\)上一致连续.
+    
+    \item[六、]\(f(x)\)在\(\mathbb{R}\)上有连续二阶导数，且\(f''(x)<0\),证明：\(\int_{0}^{1}f(x^{2}) \mathrm{d}x\leq f(\dfrac{1}{3})\).
+    
+    \item[七、]\(f\in C[0,1]\),证明：
+    \begin{enumerate}[leftmargin=*,labelwidth=!,labelsep=0pt]
+        \item[(1)] \(\exists\xi\in[0,\dfrac{1}{2}]\),使得\(\dfrac{1}{2}\int_{0}^{1}f(x) \mathrm{d}x=\int_{0}^{\xi}f(x) \mathrm{d}x+\int_{1-\xi}^{1}f(x) \mathrm{d}x\).
+        \item[(2)] 将\(\xi\in[0,\dfrac{1}{2}]\)改为\(\xi\in(0,\dfrac{1}{2})\),结论是否成立？证明或否定.
+    \end{enumerate}
+
+\end{enumerate}
+
+\end{document}