---
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title: 高等数学II
breadcrumb: 高等数学II
description: 理工科基础必修课《高等数学II》教学大纲、章节课件与复习专题讲义。内容涵盖常微分方程、空间解析几何、多元微分学、多元积分学及无穷级数。
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      content: 高等数学II, 多元微分学, 多元积分学, 无穷级数, 空间解析几何, 常微分方程, 课件下载, 复习讲义
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# 高等数学II

《高等数学II》是理工科专业常见的基础课程。本页面提供章节课件与复习讲义下载。

<p class="mobile-desktop-hint">建议使用电脑桌面端访问，以获得更佳的课件浏览与下载体验。</p>

---

## 章节大纲与课件下载

### 第 7 章：常微分方程

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">7.1</td>
      <td class="chap-title">微分方程的基本概念</td>
      <td class="download-cell"><a :href="CDN_BASE + '/7/7-1_basic_concepts_of_differential_equations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">7.2</td>
      <td class="chap-title">一阶线性微分方程</td>
      <td class="download-cell"><a :href="CDN_BASE + '/7/7-2_first_order_linear_differential_equations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">7.3</td>
      <td class="chap-title">可降阶的高阶微分方程</td>
      <td class="download-cell"><a :href="CDN_BASE + '/7/7-3_higher_order_differential_equations_reducible_in_order.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">7.4</td>
      <td class="chap-title">二阶线性微分方程解的结构</td>
      <td class="download-cell"><a :href="CDN_BASE + '/7/7-4_structure_of_solutions_to_second_order_linear_differential_equations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">7.5</td>
      <td class="chap-title">二阶常系数齐次线性微分方程</td>
      <td class="download-cell"><a :href="CDN_BASE + '/7/7-5_second_order_homogeneous_linear_differential_equations_with_constant_coefficients.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">7.6</td>
      <td class="chap-title">二阶常系数非齐次线性微分方程</td>
      <td class="download-cell"><a :href="CDN_BASE + '/7/7-6_second_order_nonhomogeneous_linear_differential_equations_with_constant_coefficients.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与计算方法讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/7/Chapter_7_Differential_Equations_Student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

### 第 8 章：向量代数与空间解析几何

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">8.1</td>
      <td class="chap-title">向量代数及其几何意义</td>
      <td class="download-cell"><a :href="CDN_BASE + '/8/8-1_vector_algebra.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">8.2</td>
      <td class="chap-title">数量积与向量积的坐标运算</td>
      <td class="download-cell"><a :href="CDN_BASE + '/8/8-2_dot_product_and_cross_product.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">8.3</td>
      <td class="chap-title">空间曲面及其方程（二次曲面）</td>
      <td class="download-cell"><a :href="CDN_BASE + '/8/8-3_surfaces_in_space_and_their_equations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">8.4</td>
      <td class="chap-title">空间曲线及其方程与投影</td>
      <td class="download-cell"><a :href="CDN_BASE + '/8/8-4_space_curves_and_their_equations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">8.5</td>
      <td class="chap-title">平面及其方程计算</td>
      <td class="download-cell"><a :href="CDN_BASE + '/8/8-5_planes_and_their_equations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">8.6</td>
      <td class="chap-title">空间直线及其方程与夹角</td>
      <td class="download-cell"><a :href="CDN_BASE + '/8/8-6_lines_in_space_and_their_equations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与空间解析几何几何法讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/8/Chapter_8_Spatial_Analytic_Geometry_Student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

### 第 9 章：多元函数微分学

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">9.1</td>
      <td class="chap-title">多元函数的基本概念与极限</td>
      <td class="download-cell"><a :href="CDN_BASE + '/9/9-1_basic_concepts.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">9.2</td>
      <td class="chap-title">偏导数的定义与高阶偏导</td>
      <td class="download-cell"><a :href="CDN_BASE + '/9/9-2_partial_derivatives.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">9.3</td>
      <td class="chap-title">全微分的定义及其计算</td>
      <td class="download-cell"><a :href="CDN_BASE + '/9/9-3_total_differential.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">9.4</td>
      <td class="chap-title">多元复合函数求导法则</td>
      <td class="download-cell"><a :href="CDN_BASE + '/9/9-4_composite_functions.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">9.5</td>
      <td class="chap-title">隐函数的求导公式及求导法则</td>
      <td class="download-cell"><a :href="CDN_BASE + '/9/9-5_implicit_functions.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">9.6</td>
      <td class="chap-title">多元函数的极值及其求法</td>
      <td class="download-cell"><a :href="CDN_BASE + '/9/9-6_extrema.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">微积分期末“保命”公式定理速查与计算专题</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/9/Chapter_9_Multivariable_Differentiation_Student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

### 第 10 章：多元函数积分学

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">10.1</td>
      <td class="chap-title">二重积分的概念与性质</td>
      <td class="download-cell"><a :href="CDN_BASE + '/10/10-1_integral_concepts.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">10.2</td>
      <td class="chap-title">二重积分的计算（直角坐标、极坐标）</td>
      <td class="download-cell"><a :href="CDN_BASE + '/10/10-2_double_integral.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">10.3</td>
      <td class="chap-title">三重积分的计算（直角、柱面、球面坐标）</td>
      <td class="download-cell"><a :href="CDN_BASE + '/10/10-3_triple_integral.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">10.4</td>
      <td class="chap-title">重积分的几何与物理应用</td>
      <td class="download-cell"><a :href="CDN_BASE + '/10/10-4_integral_applications.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与重积分几何/物理计算讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/10/Chapter_10_Multiple_Integrals_Student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

### 第 12 章：无穷级数

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">12.1</td>
      <td class="chap-title">常数项级数的概念与基本性质</td>
      <td class="download-cell"><a :href="CDN_BASE + '/12/12-1_series_concepts.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">12.2</td>
      <td class="chap-title">正项级数与交错级数的收敛性审敛法</td>
      <td class="download-cell"><a :href="CDN_BASE + '/12/12-2_series_convergence.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">12.3</td>
      <td class="chap-title">幂级数及其收敛半径与收敛域</td>
      <td class="download-cell"><a :href="CDN_BASE + '/12/12-3_power_series.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">12.4</td>
      <td class="chap-title">函数展开成泰勒幂级数及其应用</td>
      <td class="download-cell"><a :href="CDN_BASE + '/12/12-4_function_expansion.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">12.5</td>
      <td class="chap-title">傅里叶级数展开及正交函数系</td>
      <td class="download-cell"><a :href="CDN_BASE + '/12/12-5_fourier_series_review.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与无穷级数收敛性判定/展开式大题讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/12/Chapter_12_Infinite_Series_Student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

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