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微积分课程教学大纲.docx

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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..............

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