高等數(shù)學同濟第四版筆記

1、目錄目錄第一章函數(shù)與極限.......................................................................................................................1一、函數(shù)....................................................................................

2、...............................................11.1、注意以前所學習的一些概念..................................................................................11.2、函數(shù)概念.................................................................

3、.................................................11.3、函數(shù)的幾種特性......................................................................................................11.4、反函數(shù).................................................

4、.....................................................................11.5、幾種特殊的函數(shù)......................................................................................................1二、初等函數(shù)..............................

5、.............................................................................................22.1、基本初等函數(shù)..........................................................................................................22.2、雙曲函數(shù).

6、.................................................................................................................2三、數(shù)列的極限...................................................................................................

7、....................33.1、數(shù)列極限的定義......................................................................................................33.2、收斂數(shù)列的特性..........................................................................

8、............................3四、函數(shù)的極限.......................................................................................................................44.1、定義..........................................................

9、................................................................44.2、函數(shù)極限的特性......................................................................................................5五、無窮小與無窮大................................

10、...............................................................................85.1、無窮小的定義..........................................................................................................85.2、無窮大的定義.............

11、.............................................................................................85.3、相關定理..................................................................................................................8六、極

12、限的運算法則...............................................................................................................9極限的疊代求法...............................................................................................

13、..............10七、極限存在準則：兩個重要極限.....................................................................................127.1、準則I：夾逼準則..........................................................................................

14、........127.2、準則II：單調(diào)有界數(shù)列必有極限.........................................................................127.3、兩個重要極限........................................................................................................12

15、八、無窮小的比較.................................................................................................................158.1、無窮小的階........................................................................................

16、....................158.2、等階無窮小的性質(zhì)................................................................................................158.3、一些常用的等階無窮小..........................................................................

17、..............15九、函數(shù)的連續(xù)性與間斷點.................................................................................................179.1、函數(shù)的連續(xù)性...................................................................................

18、.....................179.2、函數(shù)的間斷點........................................................................................................17十、連續(xù)函數(shù)的運算與初等函數(shù)的連續(xù)性...............................................................

19、..........1810.1、連續(xù)函數(shù)的和、積及商的連續(xù)性......................................................................1810.2、反函數(shù)與復合函數(shù)的連續(xù)性..............................................................................1810.3、初等函數(shù)的連續(xù)性.......

20、.......................................................................................20十一、閉區(qū)間上的連續(xù)函數(shù)的性質(zhì).....................................................................................2111.1、最大值和最小值定理...............

21、...........................................................................2111.2、介值定理..............................................................................................................2111.3、一致連續(xù)性............

22、..............................................................................................21第二章導數(shù)與微分....................................................................................................................

23、.231二、換元積分法.....................................................................................................................412.1、第一類換元法................................................................................

24、........................412.2、第二類換元法........................................................................................................41三、分部積分法.......................................................................

25、..............................................43四、幾種特殊類型函數(shù)的積分.............................................................................................434.1、有理函數(shù)的積分.....................................................

26、...............................................434.2、三角函數(shù)有理式的積分........................................................................................434.3、簡單無理函數(shù)的積分......................................................

27、......................................44五、積分表的使用.................................................................................................................44第五章定積分...................................................

28、..........................................................................45一、定積分的概念.................................................................................................................455.1、定積分問題舉例..........

29、..........................................................................................455.2、定積分定義............................................................................................................45二、定積分的性質(zhì).

30、................................................................................................................46三、微積分的基本公式................................................................................................

31、.........47四、定積分的換元法.............................................................................................................48五、定積分的分部積分法..............................................................................

32、.......................48六、定積分的近似計算.........................................................................................................48七、廣義積分........................................................................

33、.................................................497.1、無窮限的廣義積分................................................................................................497.2、無界函數(shù)的廣義積分..............................................

34、..............................................50八、廣義積分的審斂法函數(shù).....................................................................................51Γ?8.1、無窮限的廣義積分的審斂法.......................................................

35、.........................518.2、無界函數(shù)的廣義積分的審斂法............................................................................528.3、－函數(shù)...........................................................................................

36、....................52?？偭曨}.....................................................................................................................................53第六章定積分的應用..................................................

37、...............................................................57一、定積分的元素法.............................................................................................................57二、平面圖形的面積..........................

38、...................................................................................57三、體積.................................................................................................................................58

39、四、平面曲線的弧長.............................................................................................................58五、功水壓力和引力...........................................................................................

40、..............58六、平均值.............................................................................................................................59第七章空間解析幾何與向量代數(shù)..........................................................

41、...................................60一、空間直角坐標系.............................................................................................................60二、向量及其加減法向量與數(shù)的乘法...............................................

42、..............................602.1、向量的概念............................................................................................................602.2、向量的加減法...........................................................

43、.............................................602.3、向量與數(shù)的乘法....................................................................................................60三、向量在軸上投影...................................................

44、..........................................................613.1、向量在軸上的投影................................................................................................613.2、向量在坐標軸上的分向量與向量的坐標.............................

45、...............................613.3、向量的模與方向余弦的坐標表達式....................................................................61四、數(shù)量積向量積混合積.......................................................................................