微积分(下)
正版保障 假一赔十 可开发票
￥ 34.63 6.7折 ￥ 52 全新
库存63件
广东广州
认证卖家担保交易快速发货售后保障
作者尤超，尹逊波，靳水林编著
出版社电子工业出版社
ISBN9787121450051
出版时间2023-02
装帧平装
开本其他
定价52元
货号12214025
上书时间2024-10-27
商品详情
- 品相描述：全新
- 商品描述
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目录
第 7 章 多元函数微分学 ············································································································.1 7.1 多元函数的基本概念及其极限 ·····················································································.1 7.1.1 n 维欧式空间 ········································································································.1 7.1.2 多元函数 ···············································································································.2 7.1.3 多元函数的重极限与连续 ························································································.3 7.1.4 多元函数的累次极限 ·······························································································.7 习题 7.1 ···························································································································.8 7.2 偏导数与高阶偏导数 ····································································································.9 7.2.1 偏导数的定义 ·········································································································.9 7.2.2 高阶偏导数 ··········································································································.11 习题 7.2 ·························································································································.14 7.3 全微分 ··························································································································.14 习题 7.3 ·························································································································.18 7.4 复合函数求导法 ··········································································································.19 习题 7.4 ·························································································································.25 7.5 隐函数求导法 ··············································································································.26 习题 7.5 ·························································································································.30 7.6 偏导数的几何应用 ······································································································.31 7.6.1 空间曲线的切线与法平面 ······················································································.31 7.6.2 曲面的切平面与法线 ·····························································································.33 7.6.3 二元函数全微分的几何意义 ···················································································.35 习题 7.6 ·························································································································.35 7.7 多元函数的极值 ··········································································································.36 7.7.1 多元函数的无条件极值 ··························································································.36 7.7.2 条件极值与拉格朗日乘数法 ···················································································.42 习题 7.7 ·························································································································.46 7.8 方向导数与梯度 ··········································································································.46 7.8.1 场的基本概念 ·······································································································.46 7.8.2 方向导数 ·············································································································.46 7.8.3 梯度 ····················································································································.49 习题 7.8 ·························································································································.51 综合题 ··································································································································.52 第 8 章 多元数量值函数积分学 ······························································································.53 8.1 黎曼积分 ······················································································································.53 8.1.1 二重积分的概念 ···································································································.53 8.1.2 黎曼积分的概念 ···································································································.54 8.1.3 黎曼积分的分类 ···································································································.54 8.1.4 黎曼积分的性质 ···································································································.55 习题 8.1 ·························································································································.57 8.2 二重积分的计算 ··········································································································.58 8.2.1 直角坐标系下二重积分的计算 ················································································.58 8.2.2 极坐标系下二重积分的计算 ···················································································.62 8.2.3 二重积分的对换对称性 ··························································································.66 8.2.4 二重积分的变量代换 ·····························································································.67 习题 8.2 ·························································································································.70 8.3 三重积分的计算 ··········································································································.72 8.3.1 直角坐标系下三重积分的计算 ················································································.72 8.3.2 柱坐标系下三重积分的计算 ···················································································.75 8.3.3 球坐标系下三重积分的计算 ···················································································.77 8.3.4 三重积分一般的变量代换 ······················································································.79 习题 8.3 ·························································································································.81 8.4 第一型曲线积分 ··········································································································.83 习题 8.4 ·························································································································.86 8.5 第一型曲面积分的计算 ·······························································································.87 习题 8.5 ·························································································································.93 8.6 黎曼积分的应用实例 ··································································································.93 8.6.1 物体质心 ·············································································································.94 8.6.2 转动惯量 ·············································································································.96 习题 8.6 ·························································································································.98 8.7 含参变量的积分 ··········································································································.99 习题 8.7 ·······················································································································.101 综合题 ································································································································.101 第 9 章 多元向量值函数积分学 ····························································································.104 9.1 向量场 ························································································································.104 9.1.1 向量场与向量线 ·································································································.104 9.1.2 向径的导数 ········································································································.105 9.2 第二型曲线积分 ········································································································.106 9.2.1 第二型曲线积分的定义 ························································································.106 9.2.2 第二型曲线积分的计算 ························································································.108 9.2.3 两种类型曲线积分的关系 ····················································································.111 习题 9.2 ·······················································································································.112 9.3 格林公式及平面流速场的环量与旋度 ·····································································.113 9.3.1 格林公式 ···········································································································.113 9.3.2 平面流速场的环量与旋度 ····················································································.117 习题 9.3 ·······················································································································.117 9.4 平面曲线积分与路径无关的条件及保守场 ······························································.118 9.4.1 平面曲线积分与路径无关的条件 ··········································································.118 9.4.2 保守场、原函数、全微分方程 ··············································································.123 习题 9.4 ·······················································································································.126 9.5 第二型曲面积分 ········································································································.127 9.5.1 第二型曲面积分的定义 ························································································.127 9.5.2 第二型曲面积分的计算 ························································································.130 习题 9.5 ·······················································································································.135 9.6 高斯公式、通量与散度 ·················································
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