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Jingdong book

微积分基础：引入Mathematica软件求解

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Jingdong book

微积分基础：引入Mathematica软件求解

Name: 微积分基础：引入Mathematica软件求解
Brand: Jingdong book
SKU: 3118081871
Price: 23.48 USD
Availability: OutOfStock

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Content Description

微积分是人类文明发展史上理性智慧的精华，它的出现，不仅彻底更新了数学的面貌，而且显著地促进了整个科学技术的发展。目前，微积分的理论与方法已广泛地应用于自然科学、工程技术乃至社会科学的各个领域。它提供给人们的不仅是一种高级的数学技术，而且是一种人类进步必需的文化素质和能力。
本书力求运用通俗的语言向读者介绍高等数学中最基础的知识，全书以微积分为核心，在高等数学学习中结合使用数学软件，通过参与 “演示与实验”帮助学生理解数学中的一些抽象概念和理论，并方便、简捷地用计算机来解复杂的实际运算问题。本书引入国外先进的教学模式和教学理念，注重知识的实用性、生动性和趣味性，削弱了过难过繁的运算技巧，将学生从枯燥的公式和大量的运算中解放出来。

Catalogue

第一章数学与计算机
第一节计算机与数学的关系
一、计算、计算方法和计算工具
二、计算机数学软件
三、．Mathematica的特点
第二节初等数学的计算机算法
一、Mathematica的启动和运行
二、用Mathematica作算术运算
三、用Mathematica作代数运算
四、用Mathematica作函数运算
五、用Mathematica解方程
六、用Mathematica作图
第二章极限与连续
第一节数列的极限
一、数列的概念
二、数列的极限
第二节函数的极限
一、函数极限的定义
二、函数极限的性质
三、函数极限的基本运算
第三节利用Mathematica计算极限
第四节函数的连续性
一、f(x)在点x0的连续
二、间断点的类型
三、f(x)在区间上的连续性
第三章一元函数微分学
第一节导数的概念
一、导数概念实例
二、函数的变化率——导数
三、求函数y=f(x)的变化率(导数)的方法
四、可导与连续的关系
五、导数的几何意义
第二节导数的运算
一、用导数的定义求导
二、导数基本运算法则和基本初等函数导数公式
三、反函数的导数
四、基本初等函数导数公式
五、复合函数的导数
六、利用Mathematica求导数
第三节隐函数和参数方程所确定的函数的导数
一、隐函数的导数
二、参数方程所确定的函数的导数
第四节高阶导数
一、高阶导数的概念
二、高阶导数的求导法则
三、利用Mathematica求高阶导数
第五节函数的微分
一、微分的定义
二、可导与微分的关系
三、微分的几何意义
四、微分的运算法则
五、微分在近似计算中的应用
六、利用Mathematica求微分
第四章导数的应用
第一节利用导数求极限
一、中值定理简介
二、罗父塔法则
第二节函数的单调性
第三节函数的极值与最值
一、函数的极值
二、函数的最大值与最小值
第四节导数在经济分析中的应用
一、经济学中几个常用函数
二、边际函数
第五节曲线的凹凸性
第六节导数应用的Mathematica求解
第五章不定积分和定积分
第一节不定积分
一、不定积分的概念
二、不定积分的基本公式
三、不定积分的性质
四、基本积分方法
五、利用Mathematica计算不定积分
第二节定积分
一、定积分的概念
二、定积分的性质
三、微积分的基本是理
四、利用Mathematica计算定积分
第三节广义积分
一、无穷区间上的广义积分
二、无界函数的广义积分
第六章定积分的应用
第一节定积分在几何上的应用
一、利用定积分求平面图形的面积
二、利用定积分求体积
三、利用定积分求平面曲线的弧长
第二节定积分在物理上的应用
一、变速直线运动的路程
二、变力沿直线所作的功
三、静止液体的压力
四、在电学上的应用
第三节定积分在经济上的应用
第七章常微分方程
第一节微分方程的基本概念
一、微分方程的发展
二、微分方程的基本概念
第二节如何建立微分方程
第三节微分方程的求解
一、可分离变量的微分方程
二、一阶线性微分方程
三、二阶常系数线性微分方程
四、可降阶的高阶微分方程
第四节利用Mathematica求解微分方程
一、可以准确求解的微分方程
二、微分方程(组)的数值解
第八章无穷级数
第一节无穷级数的概念
一、常数项无穷级数和函数项无穷级数
二、无穷级数的敛散性
三、利用：Mathematica软件来判断级数的敛散性
第二节无穷级数的性质与敛散性
第三节正项级数
第四节交错级数与任意项级数
一、交错级数
二、绝对收敛与条件收敛
第五节幂级数
一、幂级数的收敛区间
二、幂级数的性质
第六节幂级数在函数逼近中的应用
一、泰勒公式
二、泰勒级数
三、幂级数在近似计算中的应用
附录一 Mathematica软件常用操作命令
附录二微积分基本公式
附录三初等数学部分公式
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