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    大学数学实验是大学数学教学改革的内容。该课程的开设使得学生学会使用计算机中的数学软件去作计算和研究工作,而不再是花大量的时间去钻研计算技巧。掌握运用数学软件进行计算、编程、设计,已是一个大学生必备的技能。

      本书结合大学数学课程内容,以美国研制的数学软件MATLAB为计算工具,对如何运用该工具作微积分、空间解析几何、线性代数、概率统计等各种数学计算及绘图进行了详细的说明。并配有大量的例题和实验题目。

      完成本书内容的学习大约需30~50学时。1/4学时的多媒体教学,1/6学时的上机实验。本书分为这样几个部分:软件入门与编程篇、空间解析几何实验篇、线性代数实验篇、一元微积分实验篇、多元微积分实验篇、概率统计实验篇、数学模型实验篇、几何与代数实验课题篇、微积分实验课题篇、概率统计实验课题篇、数学模型实验课题篇。本书所介绍的数学实验内容可与大学数学课程同步开设。由于有详尽的方法介绍和例题演示及上机实验题,本书也适合大学生自学。

      本书已经过多届大学生的使用,在教学中不断改进、补充,随着MATLAB软件的升级,功能越来越强大,部分函数名称及使用方法也有所改变,故本次修订出版较原稿有较大地改动。本书中程序部分用加粗表示,语句后%是对程序语句的注释。另配套的数学实验讲座也随着教学实践会不断更新,仍放在我的主页《长虹雪苑》中的长虹数学实验室网页中,目前网页地址为:http://jwc.cuit.edu.cn/Yg/chxue/。希望各位读者在阅读本书的过程中,对书中的内容有疑问或发现有错误时,能通过E-mail或网页上留言与我联系,以便于我及时修正。E-mail地址是: chxue@cuit.edu.cnchxue180@sina.com

 

 

 

作者


 

第一章                         MATLAB 认识与编程

 

§1-1  MATLAB简介                                                              1

§1-2  MATLAB的发展史                                                       1

§1-3  MATLAB的主要功能和特性                                         2

§1-4  MATLAB主包和工具箱                                                2

§1-5  MATLAB的安装与启动                                                4

§1-6  MATLAB入门                                                              5

§1-7  工作空间命令行的编辑与运行                                     10

§1-8  工作空间命令行的热鍵操作                                         11

§1-9    常量与变量及常用函数                                                11

§1-10   注释和标点                                                                 12

§1-11   编程及运行方法                                                           13

§1-12   条件语句                                                                     13

§1-13   循环语句                                                                     15

§1-14    关系与逻辑运算                                                          16

 

第二章                         空间解析几何实验

 

§2-1      空间直角坐标系                                                            19

§2-2      向量分析                                                                      20

§2-3      图形绘制的基本知识                                                     23

§2-4      平面曲线的图形绘制                                                     25

§2-5      多元函数绘图                                                               30

§2-6      统计图形绘制                                                               33

§2-7      图像处理                                                                      36

§2-8      动态图形                                                                      37

 

第三章                         线性代数实验

 

§3-1  矩阵的创建                                                                 38

§3-2  行列式的计算与矩阵的操作                                         41

§3-3    多项式                                                                        45

§3-4  矩阵的运算                                                                 46

§3-5  向量的相关性                                                              47

§3-6  求解线性方程组                                                          47

§3-7    矩阵的特征值与特征向量                                            49

§3-8    二次型化标准形                                                          50

 

第四章                         一元微积分实验

 

§4-1      符号运算                                                                      52

§4-2        解代数方程                                                                   59

§4-3      函数的极限与连续性                                                     61

§4-4        求导数与微分                                                               62

§4-5        泰勒展开                                                                      64

§4-6        求一元函数的极小值                                                     65

§4-7       一元函数积分                                                               67

 

第五章                         多元微积分实验

 

§5-1        多元函数定义                                                               71

§5-2       多元函数偏导数及高阶偏导数                                       71

§5-3        多元函数的微分                                                            72

§5-4    多元函数的极值                                  73

§5-5       重积分                                          74

§5-6        曲线积分                                                                      75

§5-7       曲面积分                                                                      78

§5-8        无穷级数                                                                      81

§5-9       微分方程                                                                      86

§5-10      函数计数器                                                                   88

 

第六章                         概率统计实验

 

§6-1      古典概型                                                                      90

§6-2      随机数的产生                                                               92

§6-3      随机变量与概率分布密度                                              93

§6-4      随机变量与概率分布函数                                              96

§6-5      随机变量的数字特征                                                     98

§6-6      二维随机向量及其分布函数                                          100

§6-7      统计中的样本数字特征                                                 101

§6-8      参数估计                                                                      105

§6-9      假设检验                                                                      106

§6-10    方差分析与回归分析                                                     111

 

第七章                         数学模型实验

 

§7-1      线性规划模型          &nbsllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll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