微积分课程教学大纲.docx
微积分课程教学大纲
目录
一、课程概述...............................................3
1.1课程简介...............................................3
1.2课程目标...............................................4
1.3课程内容安排...........................................4
二、微积分基本概念.........................................5
2.1微积分的起源与发展.....................................6
2.2微积分的基本思想.......................................6
2.3微积分的基本术语.......................................7
三、极限与连续.............................................8
3.1极限的概念.............................................9
3.2极限的性质............................................10
3.3极限的计算方法........................................11
3.4连续的概念与性质......................................12
四、导数与微分............................................13
4.1导数的定义............................................14
4.2导数的几何意义........................................14
4.3导数的计算方法........................................16
4.4微分及其应用..........................................17
五、导数的应用............................................18
5.1函数的单调性..........................................19
5.2函数的极值与最值......................................19
5.3函数的凹凸性与拐点....................................20
5.4应用题解析............................................21
六、不定积分..............................................22
6.1不定积分的概念........................................23
6.2基本积分公式..........................................24
6.3积分的计算方法........................................25
6.4积分的应用............................................25
七、定积分................................................27
7.1定积分的概念..........................................27
7.2定积分的性质..........................................28
7.3定积分的计算方法......................................29
7.4定积分的应用..........................................30
八、级数..................................................30
8.1级数的基本概念........................................32
8.2收敛性判别法..........................................32
8.3级数的性质..............