Sections 13.2, 13.7,

1
Greens Theorem ??????????????
2
George Green

• July 14, 1793 - May 31, 1841
• British mathematician and physicist
• First person to try to explain a mathematical
  theory of electricity and magnetism
• Almost entirely self-taught!
• Published An Essay on the Application of
  Mathematical Analysis to the Theories of
  Electricity and Magnetism in 1828.
• Entered Cambridge University as an undergraduate
  in 1833 at age 40.

(No, he was not French)
3
?????

• ??????????????????????????? C ????? D
  ?????????????????????????????????

????????
4
???????
???????? P(x,y) ??? Q(x,y) ???????????????????????
?????????????????? R ??????
????? C ????????????????? R ????????
5
??? C C1 C2 C3 C4 ?????
C1 y c ??? a ? x ? b ?????? (a,c) ????????
(b,c)
C2 x b ??? c ? x ? d ?????? (b,c) ????????
(b,d)
C3 y d ??? a ? x ? b ?????? (b,d) ????????
(a,d)
C4 x a ??? c ? x ? d ?????? (a,d) ????????
(a,c)
6
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7
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8
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9
????????
?????????? ????? C ????????????????????
10
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11
(No Transcript)
12
????????
?????????? ????? C ????????????????????
13
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?????????????????
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14
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15
????????
?????????? ????? C ??????????????????????????????
(0,0), (2,0) ??? (0,3)
??? 12
16
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?????????? ????? C ?????????????????????
???
??? 1/3
17
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1. ?????????? ????? C ?????????????????????? 2.
?????????? ????? C ?????????????????
??? y 4