From 09394f5725567c569c20c7e766b7207a46ef4b10 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BE=99=E6=89=93=E9=87=8E?= <18128966990@163.com> Date: Wed, 17 Jul 2024 10:23:58 +0800 Subject: [PATCH] math --- ...60\345\255\246\345\255\246\344\271\240.md" | 190 ++++++++++-------- .../image-20240717095836968.png" | Bin 0 -> 156110 bytes 2 files changed, 103 insertions(+), 87 deletions(-) create mode 100644 "_posts/img/2024-03-01-\346\225\260\345\255\246\345\255\246\344\271\240/image-20240717095836968.png" diff --git "a/_posts/2024-03-01-\346\225\260\345\255\246\345\255\246\344\271\240.md" "b/_posts/2024-03-01-\346\225\260\345\255\246\345\255\246\344\271\240.md" index 11cfbba..c4b9cb3 100644 --- "a/_posts/2024-03-01-\346\225\260\345\255\246\345\255\246\344\271\240.md" +++ "b/_posts/2024-03-01-\346\225\260\345\255\246\345\255\246\344\271\240.md" @@ -6,7 +6,7 @@ tags: [] img_path: /assets/ --- -一、微积分 +## 一、微积分 1. 函数与极限 • 函数的概念与性质 @@ -27,92 +27,6 @@ img_path: /assets/ • 曲线积分与曲面积分 • 格林公式、高斯公式与斯托克斯公式 -二、线性代数 - - 1. 行列式 - • 行列式的定义与性质 - 2. 矩阵 - • 矩阵的基本运算 - • 逆矩阵 - • 矩阵的秩 - 3. 向量空间 - • 向量的线性组合与线性相关性 - • 基与维数 - 4. 线性变换 - • 线性变换与矩阵的关系 - 5. 特征值与特征向量 - • 特征值的定义与性质 - • 矩阵的对角化 - 6. 二次型 - -三、常微分方程 - - 1. 一阶微分方程 - • 分离变量法 - • 齐次方程与非齐次方程 - • 一阶线性微分方程 - 2. 高阶微分方程 - • 常系数齐次线性微分方程 - • 常系数非齐次线性微分方程 - • 拉普拉斯变换 - 3. 微分方程的应用 - • 物理、工程中的微分方程模型 - -四、无穷级数 - - 1. 数项级数 - • 收敛与发散 - • 收敛判别法 - 2. 幂级数 - • 幂级数的收敛半径与收敛区间 - • 泰勒级数 - 3. 傅里叶级数 - • 傅里叶级数的基本理论 - -五、向量分析 - - 1. 向量代数与解析几何 - • 向量的运算 - • 空间解析几何 - 2. 向量函数 - • 向量函数的极限与连续性 - • 向量函数的导数与积分 - -六、复变函数 - - 1. 复数与复平面 - • 复数的基本运算 - • 复平面与复数的几何意义 - 2. 解析函数 - • 解析函数的定义与性质 - • 柯西-黎曼方程 - 3. 复积分 - • 复积分的基本概念 - • 柯西积分定理与积分公式 - 4. 级数展开 - • 复变函数的幂级数展开 - • 势级数与留数定理 - -七、概率与统计 - - 1. 概率论基础 - • 概率的基本概念 - • 随机变量与分布 - • 数学期望与方差 - 2. 数理统计 - • 抽样分布 - • 参数估计 - • 假设检验 - -八、数值分析 - - 1. 插值法 - • 拉格朗日插值 - • 牛顿插值 - 2. 数值积分与数值微分 - 3. 线性方程组的数值解法 - 4. 常微分方程的数值解法 - ### 数列极限 #### 定义: @@ -347,5 +261,107 @@ f''(x) = 2c, 1/2 f''(0) = c --- +![image-20240717095836968](img/2024-03-01-%E6%95%B0%E5%AD%A6%E5%AD%A6%E4%B9%A0/image-20240717095836968.png) + +已知加水速率dV/dt = 2 + +r/h = 4/10, V = 1/3 πr^2h + +what is dh/dt when h = 5? + +r = 2/5h, V = 1/3 π (2/5h)^2 h + +2 = dV/dt = π/3 (2/5)^2 3h^2 dh/dt +dh/dt = 1/2π (升/秒) + +--- + + + +## 二、线性代数 + + 1. 行列式 + • 行列式的定义与性质 + 2. 矩阵 + • 矩阵的基本运算 + • 逆矩阵 + • 矩阵的秩 + 3. 向量空间 + • 向量的线性组合与线性相关性 + • 基与维数 + 4. 线性变换 + • 线性变换与矩阵的关系 + 5. 特征值与特征向量 + • 特征值的定义与性质 + • 矩阵的对角化 + 6. 二次型 + +## 三、常微分方程 + + 1. 一阶微分方程 + • 分离变量法 + • 齐次方程与非齐次方程 + • 一阶线性微分方程 + 2. 高阶微分方程 + • 常系数齐次线性微分方程 + • 常系数非齐次线性微分方程 + • 拉普拉斯变换 + 3. 微分方程的应用 + • 物理、工程中的微分方程模型 + +## 四、无穷级数 + + 1. 数项级数 + • 收敛与发散 + • 收敛判别法 + 2. 幂级数 + • 幂级数的收敛半径与收敛区间 + • 泰勒级数 + 3. 傅里叶级数 + • 傅里叶级数的基本理论 + +## 五、向量分析 + + 1. 向量代数与解析几何 + • 向量的运算 + • 空间解析几何 + 2. 向量函数 + • 向量函数的极限与连续性 + • 向量函数的导数与积分 + +## 六、复变函数 + + 1. 复数与复平面 + • 复数的基本运算 + • 复平面与复数的几何意义 + 2. 解析函数 + • 解析函数的定义与性质 + • 柯西-黎曼方程 + 3. 复积分 + • 复积分的基本概念 + • 柯西积分定理与积分公式 + 4. 级数展开 + • 复变函数的幂级数展开 + • 势级数与留数定理 + +## 七、概率与统计 + + 1. 概率论基础 + • 概率的基本概念 + • 随机变量与分布 + • 数学期望与方差 + 2. 数理统计 + • 抽样分布 + • 参数估计 + • 假设检验 + +## 八、数值分析 + + 1. 插值法 + • 拉格朗日插值 + • 牛顿插值 + 2. 数值积分与数值微分 + 3. 线性方程组的数值解法 + 4. 常微分方程的数值解法 diff --git "a/_posts/img/2024-03-01-\346\225\260\345\255\246\345\255\246\344\271\240/image-20240717095836968.png" "b/_posts/img/2024-03-01-\346\225\260\345\255\246\345\255\246\344\271\240/image-20240717095836968.png" new file mode 100644 index 0000000000000000000000000000000000000000..07bb9c9110bf61e503c0fe81d10357a9f97a788f GIT binary patch literal 156110 zcmV)(K#RYLP)4Tx07!|ImIqLi*%rs|_oat~7J3c63DOB5C4?4wZ=w>C0HK5s2nse-7FS?J zQ4v99L6@rFsuWo(g4hSEDb;!KT8j_&R%mM&aj>L6VW(j8aB*Jn+q(OwQ&v4=#|2f0) zbNq2OCoF^k0Gb23Q}1)|L1l5Z%a!R&7YwUW(E*?hajGa+}Yif zbYC&^;{yWcna7#UpXDTxclbQBGZ``S%wf6viua}l_|0fp?H2`qVLX4>lK>t=H~?^N zh%FLk&&AL)KNzGdDIf=wfdfeYXYxDIZE2VfA4fEQpKd;n7r1mPeuM1hncO-K(i zfh-{!aae%7^cB=*cT3im%)i}2Am7$!&~8UxCTB1x54M&EAVZ25Pktqpa4n&rGU~x znWAVY1}YF0gGxXNQR`5Js4`Rysu|UZ>P6i|4WeG6KB2K_3Yv;GMLVLs(cx$|Is?59 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