曲线与曲面的积分.ppt

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1、重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛(1)(1)当当Riemann积积分分 中中或或上的函数上的函数时时,就是就是对对弧弧长长的曲的曲线积线

2、积分分,也称也称为为第第一一是是的弧的弧长长元素元素(弧微分弧微分).是定是定义义在在(平面曲平面曲线线段段)或或(空空间间曲曲线线段段),其中其中或或类曲曲线积分分,记为重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛 当当Riemann积积分分 中中 ,面面面面积积元素元素.是定是定义义在在上的函数上的函数时,就是就是对面面积的曲面的曲面积分分,也称也称为是是,其中其中第一第一类曲面曲面积分分

3、,记为的曲的曲重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more

4、 important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more import

5、ant than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学

6、院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagin

7、ation is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学

8、院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important t

9、han knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛xzy2.o重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛.重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important t

10、han knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imag

11、ination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination

12、 is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛从从 轴轴正向看去正向看去为为逆逆时针时针向向.重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than know

13、ledge.数学竞赛数学竞赛 重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛 重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imaginatio

14、n is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is mo

15、re important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文

16、理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowled

17、ge.Imagination is more important than knowledge.数学竞赛数学竞赛不能就不能就组合合积分整体使用，要分成分整体使用，要分成单个个积分分进行；行；与与Riemann积分的分的对称性的称性的结论刚好相反，例如好相反，例如重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more

18、 important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more import

19、ant than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学

20、院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagin

21、ation is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学

22、院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important t

23、han knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than kno

24、wledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination

25、 is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is mor

26、e important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理

27、学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledg

28、e.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数

29、学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more imp

30、ortant than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important

31、than knowledge.数学竞赛数学竞赛 重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Im

32、agination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imaginati

33、on is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学

34、与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛重庆文理学院数学与统计学院重庆文理学院数学与统计学院Imagination is more important than knowledge.Imagination is more important than knowledge.数学竞赛数学竞赛