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<!DOCTYPE html>
<html lang="zh-cn">
<head>
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<meta name="keywords" content="note, math, music, 笔记, 数学, 音乐">
<meta name="description" content="zmx0142857 的个人笔记，包括数学、计算机、物理、语言、音乐等学科">
<meta name="author" content="zmx0142857">
<title>zmx0142857 的数学笔记</title>
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<nav id="nav" hidden>
<header>
<a id="prev-article">❮</a>
<div id="book-wrapper">
<select name="book" id="book" title="book">
<!--⌄-->
</select>
</div>
<a id="next-article">❯</a>
</header>
<!-- Search Engine Optimize -->
<ul id="table-of-contents"><li>示例<ul><li><a href="math/example/editor">公式编辑器</a></li><li><a href="math/example/mathml">Mathml</a></li><li><a href="math/example/surface">曲面在线绘制</a></li></ul></li><li>未分类<ul><li><a href="math/misc/0">问题</a></li><li><a href="math/misc/2">三角函数</a></li><li><a href="math/misc/3">不等式</a></li><li><a href="math/misc/4">微积分不等式</a></li><li><a href="math/misc/5">因式分解</a></li><li><a href="math/misc/6">数学家</a></li><li><a href="math/misc/7">算术与进制</a></li></ul></li><li>高等代数<ul><li><a href="math/linalg/0">初等代数</a></li><li><a href="math/linalg/1">矩阵</a></li><li><a href="math/linalg/2">行列式</a></li><li><a href="math/linalg/3">向量的相关性与线性方程组</a></li><li><a href="math/linalg/4">线性空间</a></li><li><a href="math/linalg/5">线性映射与线性变换</a></li><li><a href="math/linalg/6">特征值与特征向量</a></li><li><a href="math/linalg/7">λ 矩阵与相似标准形</a></li><li><a href="math/linalg/8">线性空间中的度量与内积</a></li><li><a href="math/linalg/9">实二次型与正定矩阵</a></li><li><a href="math/linalg/10">张量初步</a></li></ul></li><li>数学分析<ul><li><a href="math/analysis/0">附录</a></li><li><a href="math/analysis/1">初等函数</a></li><li><a href="math/analysis/2">数列的极限</a></li><li><a href="math/analysis/3">函数的极限与连续性</a></li><li><a href="math/analysis/5">导数的应用</a></li><li><a href="math/analysis/6">不定积分</a></li><li><a href="math/analysis/7">定积分与广义积分</a></li><li><a href="math/analysis/8">特殊函数 (1): Gamma 函数, Euler 和, 指对数积分</a></li><li><a href="math/analysis/9">特殊函数 (2): 椭圆函数, 超几何函数</a></li><li><a href="math/analysis/10">特殊函数 (3): Bernoulli 数与 Riemann zeta 函数</a></li><li><a href="math/analysis/11">常数项级数</a></li><li><a href="math/analysis/12">函数列与函数项级数</a></li><li><a href="math/analysis/13">Fourier 级数</a></li><li><a href="math/analysis/14">多元函数的极限与连续性</a></li><li><a href="math/analysis/15">多元函数微分学</a></li><li><a href="math/analysis/17">多元函数的极值</a></li><li><a href="math/analysis/19">重积分</a></li><li><a href="math/analysis/22">场论初步</a></li><li><a href="math/analysis/23">分数阶微积分</a></li><li><a href="math/analysis/24">函数方程</a></li></ul></li><li>数论<ul><li><a href="math/number/0">整数, 有理数, 代数数, 连分数</a></li><li><a href="math/number/1">整除, 最大公约数, 素数</a></li><li><a href="math/number/2">同余</a></li><li><a href="math/number/3">阶与原根</a></li><li><a href="math/number/4">二次剩余</a></li><li><a href="math/number/5">不定方程</a></li><li><a href="math/number/6">积性数论函数</a></li><li><a href="math/number/7">素数分布</a></li><li><a href="math/number/11">代数数域和代数整数</a></li><li><a href="math/number/12">理想的分解</a></li></ul></li><li>集合论与点集拓扑<ul><li><a href="math/set/2">集合及其运算</a></li><li><a href="math/set/3">二元关系与映射</a></li><li><a href="math/set/4">自然数</a></li><li><a href="math/set/6">基数</a></li><li><a href="math/set/7">Lambda 表达式</a></li><li><a href="math/set/8">范畴论基础</a></li></ul></li><li>复变函数<ul><li><a href="math/complex/1">复数与复变函数</a></li><li><a href="math/complex/2">全纯函数</a></li><li><a href="math/complex/3">复变函数的展开</a></li><li><a href="math/complex/6">积分变换</a></li></ul></li><li>实变函数<ul><li><a href="math/real/1">预备知识</a></li><li><a href="math/real/2">Lebesgue 测度</a></li><li><a href="math/real/3">可测函数</a></li><li><a href="math/real/4">Lebesgue 积分</a></li></ul></li><li>概率论<ul><li><a href="math/prob/1">事件与概率</a></li><li><a href="math/prob/2">随机变量</a></li><li><a href="math/prob/4">极限定理</a></li><li><a href="math/prob/5">常用分布</a></li></ul></li><li>数理统计<ul><li><a href="math/stat/1">数理统计的基本概念</a></li><li><a href="math/stat/2">参数估计与假设检验</a></li></ul></li><li>数值分析<ul><li><a href="math/numeric/2">插值与样条</a></li><li><a href="math/numeric/5">线性方程组</a></li><li><a href="math/numeric/6">矩阵</a></li><li><a href="math/numeric/7">非线性方程数值解法</a></li><li><a href="math/numeric/8">常微分方程数值解法</a></li><li><a href="math/numeric/9">偏微分方程的 Ritz-Galerkin 方法</a></li></ul></li><li>泛函分析<ul><li><a href="math/functional/1">度量空间</a></li><li><a href="math/functional/2">线性赋范空间</a></li><li><a href="math/functional/3">有界线性算子</a></li><li><a href="math/functional/4">Hilbert 空间及其上的有界线性算子</a></li></ul></li><li>抽象代数<ul><li><a href="math/algebra/2">群 (上)</a></li><li><a href="math/algebra/3">群 (中)</a></li><li><a href="math/algebra/4">群 (下)</a></li><li><a href="math/algebra/5">环</a></li><li><a href="math/algebra/6">模</a></li><li><a href="math/algebra/7">域</a></li><li><a href="math/algebra/8">Galois 理论</a></li></ul></li><li>李群与李代数<ul><li><a href="math/lie/0">矩阵李群</a></li><li><a href="math/lie/1">李代数初步</a></li></ul></li><li>拓扑学<ul><li><a href="math/topology/1">拓扑空间与连续映射</a></li><li><a href="math/topology/2">分离性、可数性、紧致性、连通性</a></li></ul></li><li>常微分方程<ul><li><a href="math/ode/2">一阶微分方程的初等解法</a></li><li><a href="math/ode/4">高阶微分方程</a></li><li><a href="math/ode/5">线性微分方程组</a></li></ul></li><li>偏微分方程<ul><li><a href="math/pde/1">方程的导出</a></li><li><a href="math/pde/2">波动方程</a></li><li><a href="math/pde/3">热传导方程</a></li><li><a href="math/pde/4">位势方程</a></li><li><a href="math/pde/5">二阶线性偏微分方程的分类</a></li></ul></li><li>平面几何<ul><li><a 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href="exercise/analysis/5-3">利用导数判定两个函数相等</a></li><li><a href="exercise/analysis/5-4">函数的增减性与极值</a></li><li><a href="exercise/analysis/5-5">函数的凹凸性</a></li><li><a href="exercise/analysis/5-6">泰勒公式</a></li><li><a href="exercise/analysis/5-7">方程求根的牛顿迭代公式</a></li><li><a href="exercise/analysis/5-8">函数的作图</a></li><li><a href="exercise/analysis/6-1">原函数与不定积分</a></li><li><a href="exercise/analysis/6-2">换元积分法和分部积分法</a></li><li><a href="exercise/analysis/6-3">几类初等函数的积分</a></li><li><a href="exercise/analysis/7-1">定积分的概念和基本性质</a></li><li><a href="exercise/analysis/7-2">定积分的计算</a></li><li><a href="exercise/analysis/8-1">定积分在分析学中的应用</a></li><li><a href="exercise/analysis/8-2">定积分在几何学中的应用</a></li><li><a href="exercise/analysis/8-3">定积分在物理学中的应用</a></li><li><a href="exercise/analysis/9-1">无穷积分</a></li><li><a href="exercise/analysis/9-2">瑕积分</a></li><li><a href="exercise/analysis/9-3">一些定积分公式的推广</a></li><li><a href="exercise/analysis/14-1">`RR^m` 中的点列和点集</a></li><li><a href="exercise/analysis/final-1">综合习题一</a></li><li><a href="exercise/analysis/final-2">综合习题二</a></li><li><a href="exercise/analysis/final-3">综合习题三</a></li></ul></li><li>抽象代数<ul><li><a href="exercise/algebra/1">集合论的基本概念</a></li><li><a href="exercise/algebra/2">抽象代数的基本概念</a></li></ul></li><li>实变函数<ul><li><a href="exercise/real/1-2">集合的运算</a></li><li><a href="exercise/real/1-3">映射与基数</a></li><li><a href="exercise/real/1-4">`RR^n` 中的度量, 点集的极限点</a></li><li><a href="exercise/real/1-5">闭集, 开集, Borel 集, Cantor 集</a></li></ul></li><li>算法导论<ul><li><a href="exercise/algorithm/2">算法基础</a></li><li><a href="exercise/algorithm/4">分治策略</a></li></ul></li></ul>
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