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Jingdong book

微积分与解析几何（影印版原书第2版）

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微积分与解析几何（影印版原书第2版）

Name: 微积分与解析几何（影印版 原书第2版）
Brand: Jingdong book
SKU: 3101003781
Price: 62.11 USD
Availability: OutOfStock
Rating: 4.0 (1 reviews)

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Content Description

《微积分与解析几何（影印版原书第2版）》除具有标准微积分教材的内容外，书中例子偏重实际，侧重于微积分的应用。同时补充了三角函数、极坐标等理论知识，使学生从高中到大学平稳过渡。文中穿插数学史与数学文化的相关内容，同时附录中提供了大量的补充内容以及严格的理论证明，适合不同层次的学生按需要学习。附加问题生动有趣，多是相关内容的经典结论

Author Description

乔治·西蒙斯(George F.Simmons) ，博士毕业于耶鲁大学。他通常能用简练精妙的语言表达深刻的数学思想，他在科罗拉多学院任教的日子，以其鲜明的个性以及引入入胜的教学方式，赢得学生的喜爱。

Catalogue

致教师
致学生
第一部分
第1章数、函数与图形
1.1 引言
1.2 数轴与坐标平面毕达哥拉斯
1.3 直线的斜率和方程
1.4 圆与抛物线笛卡儿和费马
1.5 函数的概念
1.6 函数的图形
1.7 三角函数的引入：函数sinθ和cosθ
复习小结：定义、概念及方法
附加问题
第2章函数的导数
2.1 什么是微积分切线问题
2.2 如何计算切线的斜率
2.3 导数的定义
2.4 速度与变化率牛顿和莱布尼茨
2.5 极限的概念两个三角函数的极限
2.6 连续函数中值定理和其他定理
复习小结：定义、概念及方法
附加问题
第3章导数的运算
3.1 多项式函数的导数
3.2 函数积、商的求导法则
3.3 复合函数求导和链式法则
3.4 一些三角函数的导数
3.5 隐函数和分数指数函数的求导
3.6 高阶导数
复习小结：概念、公式及方法
附加问题
第4章导数的应用
4.1 递增函数与递减函数最大值与最小值
4.2 凹性与拐点
4.3 最大值和最小值问题的应用
4.4 更多最大/最小值问题光的反射与折射
4.5 复合函数的变化率
4.6 牛顿法解方程
4.7 (选学)经济学上的应用边际分析法
复习小结：概念及方法
附加问题
第5章不定积分和微分方程
5.1 引言
5.2 微分与切线逼近
5.3 不定积分换元积分法
5.4 微分方程分离变量法
5.5 重力作用下的运动逃逸速度和黑洞
复习小结：概念及方法
附加问题
第6章定积分
6.1 引言
6.2 面积问题
6.3 “∑”符号与某些特殊求和
6.4 曲线下的面积定积分黎曼
6.5 极限思想下的面积计算
6.6 微积分基本定理
6.7 定积分的性质
复习小结：概念及方法
附加问题
附录：希波克拉底拱形
第7章定积分的应用
7.1 引言：定积分的直观含义
7.2 两条曲线之间的面积
7.3 体积计算1：圆盘法
7.4 体积计算2：圆柱壳法
7.5 弧长
7.6 旋转曲面的面积
7.7 功和能
7.8 流体静力学
复习小结：概念与方法
附加问题
附录：阿基米德与球体体积
第二部分
第8章指数函数与对数函数
8.1 引言
8.2 指数与对数的回顾
8.3 数e和函数y=e^x
8.4 自然对数和函数y=lnx 欧拉
8.5 应用人口增长和放射性衰变
8.6 更多应用--控制人口增长
复习小结：概念及公式
附加问题
第9章三角函数
9.1 三角函数的回顾
9.2 正弦和余弦函数的导数
9.3 正弦和余弦函数的积分蒲丰投针问题
9.4 其他四个三角函数的导数
9.5 反三角函数
9.6 简谐运动：钟摆问题
9.7 (选学) 双曲函数
复习小结：定义及公式
附加问题
第10章积分法
10.1 简介基本公式
10.2 换元法
10.3 三角函数的积分
10.4 三角换元法
10.5 完全平方法
10.6 部分分式法
10.7 分部积分法
10.8 综合法处理复杂类型的积分策略
10.9 数值积分辛普森法则
复习小结：公式及方法
附加问题
附录1：悬链线或悬挂链曲线
附录2：沃利斯乘积：pi/2=2/1*2/3*4/3*4/5*6/5*6/7...
附录3：莱布尼茨如何发现公式:pi/4=1-1/3+1/5-1/7+...
第11章积分的进一步应用
11.1 离散系统的质心
11.2 形心
11.3 帕普斯定理
11.4 惯性矩
复习小结：定义及概念
附加问题
第12章不定式和反常积分
12.1 简介中值定理的回顾
12.2 "0/0"不定式：洛必达法则
12.3 其他类型的不定式
12.4 反常积分
12.5 正态分布：高斯
复习小结：定义及概念
附加问题
第13章常数项无穷级数
13.1 什么是无穷级数
13.2 收敛数列
13.3 收敛和发散级数
13.4 收敛级数的一般性质
13.5 正项级数比较判别法
13.6 积分判别法欧拉常数
13.7 比值判别法和根值判别法
13.8 交错级数的判别
复习小结：定义、概念及判别方法
附加问题
附录1：欧拉发现公式∑1/n^2=pi^2/6
附录2：更多关于无理数的问题：证明pi为无理数
附录3：关于级数∑1/Pn,其中Pn为素数
第14章幂级数
14.1 引言
14.2 收敛区间
14.3 幂级数的微分与积分
14.4 泰勒级数和泰勒公式
14.5 应用泰勒公式的计算
14.6 微分方程的应用
14.7 (选学)幂级数的运算
14.8 (选学)复数和欧拉公式
复习小结：定义、公式及方法
附加问题
附录：伯努利数和欧拉的众多美妙的发现
第三部分
第15章圆锥曲线
15.1 引言圆锥截面
15.2 重新审视圆与抛物线
15.3 椭圆
15.4 双曲线
15.5 焦点－准线－偏心的定义
15.6 (可选)二次方程绕坐标轴旋转
复习小结：定义及性质
附加问题
第16章极坐标
16.1 极坐标系
16.2 极坐标方程的更多图像
16.3 圆、圆锥曲线和螺旋线的极坐标方程
16.4 弧长和切线
16.5 极坐标中的面积
复习小结：定义及公式
附加问题
第17章参数方程及平面内的向量
17.1 曲线的参数方程
17.2 摆线和其他类似曲线
17.3 向量代数单位向量i和j
17.4 向量函数的导数速度和加速度
17.5 曲率和单位法向量
17.6 加速度的切分量和法分量
17.7 开普勒定理和牛顿的万有引力定律
复习小结：定义及公式
附加问题
附录1：最速降线问题的伯努利解法
第18章三维空间的向量与曲面
18.1 三维空间的坐标和向量
18.2 两个向量的标量积
18.3 两个向量的向量积
18.4 直线和平面
18.5 圆柱坐标和旋转曲面
18.6 二次曲面
18.7 圆柱坐标和球面坐标
复习小结：定义及方程
第19章偏导数
19.1 多元函数
19.2 偏导数
19.3 曲面的切平面
19.4 增量和微分基本引理
19.5 方向导数和梯度
19.6 偏导数的链式法则
19.7 最大值和最小值问题
19.8 条件极值拉格朗日乘数法
19.9（选学）拉普拉斯方程、热传导方程和波动方程拉普拉斯和傅里叶
19.10 (选学)隐函数
复习小结：定义及方法
第20章重积分
20.1 累次积分－体积
20.2 二重积分和累次积分
20.3 二重积分的物理应用
20.4 极坐标下的二重积分
20.5 三重积分
20.6 圆柱坐标
20.7 球面坐标万有引力定律
20.8 曲面面积勒让德公式
复习小结：方法和公式
附录：欧拉公式∑1/n^2=pi^2/6的二重积分证明
第21章曲线积分和曲面积分格林公式高斯公式和斯托克斯公式
21.1平面上的曲线积分
21.2 与路径无关：保守场
21.3 格林公式
21.4 曲面积分和高斯公式
21.5 斯托克斯公式
21.6 麦克斯韦方程组终极思考
复习小结：概念及定理

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微积分与解析几何（影印版 原书第2版）

微积分与解析几何（影印版原书第2版）