1 / 34

: Vector

???????? ?? ????? ???????? ??? ????? ?????? ??? ????? ??????? ????????? ????? ???????? ?? ????? ???????? ??? ????? ??? ???? ????? ??? ??????? ??????? ???????. ??????? ?? ???????? ?????? ???? ??????????.?????? ??????????????? ????? ??????? ???? ???????? ?????????? (x,y,z) ??????????? (r, f,z) ?????

louis
Télécharger la présentation

: Vector

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. ????? ?????: ???????? Vector ????? ???????? Vector Analysis: ??? ???????? (?????? ????????) ????? ??????? (??????? ????????) ???? ??????? ???????? ??????? ?????? ??????? ?????? (???????) ???????? ????? ????? ???? ??????? ??????? ???????? ??????? ??????? ???????? ?????? ??????? ???????? ???????? (????????) ?????????? ????????

    2. ???????? ?? ????? ???????? ??? ????? ?????? ??? ????? ??????? ????????? ????? ???????? ?? ????? ???????? ??? ????? ??? ???? ????? ??? ??????? ??????? ???????. ??????? ?? ???????? ?????? ???? ??????????. ?????? ??????????????? ????? ??????? ???? ???????? ?????????? (x,y,z) ??????????? (r, f,z) ???????? (r,?, f). ????? ???????? ??????? ?????????? (x,y,z) ???? ????? ?????? ?????? ?????? ?????? ?????? ??????? ??????? (ax, ay, az) & (I, j, k) ??????: ??? ax'=I' & ay'=j' & az'=k' ??????? ?????? ?????? ??? ?????? ??????? ?????? ???? ??? ???: ????? ???? ?????? aA ??? ??? ?????? A ?????:

    3. ????? ???????? (??? ????????): ???????? ???? ????? ??????? ????? ????? ?? ?????? ??????? ???????? ???????? A'+(B'+C') = (A'+B')+C' K(A'+B')= KA'+KB' (K1+K2)A' = K1A'+K2A' A'+B' = B'+A'

    4. ????? ??????? (??????) ???????: A'.B' = AB Cos C A' & B' ?? ??????? ??? ???????? ? ??? A'.B'= Ax Bx + Ay By + Az Bz ??? ?? cos 90 = 0 & cos 0 =1 ???? ????? ?????? ??????? ??????? ?????? ??????? A'.(B'+C') = A'.B' + A'.C' A'.KB = K(A'.B')

    5. ????? ??????? (???????) ???????: A' x B' = (AB sin ?) an' ??? an' ?? ???? ?????? ????????? ??? ????? ?????? ????????? ??? ?? ???? ?????? ????? ???? ?????? ?????? ???? ?????? ?????? A' x B' = - A' x B'

    6. ????? ????? ??????? ????? ??? ???????? ????? A' x B' = (Ax ax' +Ay ay' + Az az') x (Bx ax' +By ay' + Bz az') A' x B' = (AyBz AzBy) ax' + (AzBx - AxBz) ay' + ( AxBy AyBx) az' ????? ??? ????? ????? ??? ????? ?????? ?? ????? ????????? ??: i' x j' = - j' x i' & j' x k' = - k'x j' & k' x i' = - i' x k'

    7. ????: ??? ???? A' = ax' ay' & B' = 2 ax'+4ay' 3 az' ???? ???? A'.B' & A' x B' ?????? ????? ????? A'.B'= (2x1)+(4x-1)+(-3x0) = 2-4+0=-2 Cos? = A'.B'/ AB ?? A'xB' =(AyBz AzBy) ax' + (AzBx - AxBz) ay' + ( AxBy AyBx) az'= A'xB' = (9+9+36)0.5 = 11.6 Sin ? = A'xB' / AB

    8. ????? ?????????? ??? ??? ???? ???? P ??????? ????? ???? ???? ???? ???? ????? ???????? ???? ??? ??????????? ?????????? (x,y,z) ?????????? ???????? (r,f,z) ??????? (r,?,f)

    9. ??????? f ???? ??? ???????? ??? ?? ??????? ????????? ??????? ?? ?????? ??????? (????? ???? ??????????) ?????? ????? r ?????? ??????? ?????? ??????? ????????? ???? ??????? ?? ?????? z ?? ??????? ??????? ??? z? ??????? ?????? ???? ??????? ?? ???? ????? ?????? P.

    11. ????? ???? ???????? ?????? P ??? (x+dx, y+dy, z+dz) ?? (r+dr, f+df, z+dz) ??(r+dr,?+d?, f+df)

    12. ??? ????? ???????? ???? ?????? ????? dv ???: ??????? ??????? ???? dv=dx dy dz dv= r dr df dz dv = r2sin?drd?df ?????? ??????? ???????? ???? ???? ????? ???????? ??????? ??? ar ds = (rd?) (r sin?df) = r2 sin? d? df ?????? ????? ???????? dl ?? ????? ???? P ????? ??? dl2 = dx2 + dy2 + dz2 ??????? dl2 = dr2 + r2df2 + dz2 ??????? dl2 = dr2 +r2d?2 + r2 sin2? df2 ????

    13. ?????: ???????? ???? ???? ?????? A ???? ???? ?? ?????? (2,-4,1) ??? ?????? (0,-2,0) ??????????? ?????????? ???? ???? ???? ???? ?????? ??? ??? ?????? A? A'=(0-2)ax' + (-2+4) ay' + (0-1)az' =-2 ax' + 2 ay' -az' A=[(-2)2+(2)2+(-1)2]0.5= 3 aA'= A'/A= (-2/3)ax' + (2/3) ay' (1/3)az' aA=[(-2/3)2+(2/3)2+ (-1/3)2]0.5=1

    14. ???? ??????? ??? (5,3p/2, 0) & (5,p/2,10) ??????????? ?????????? A'= -5 ay' & B'= 5 ay' + 10 az' ??????? ???????? ??? ???????? ?? A'-B' = 10 ay'+ 10az' A-B= (102+102)0.5 ?? ???? ??????? ?????????? ?????????? ?????? ?????? ??? ???? ?????? ???? ??????? ??????? ?????????? ??????????

    15. ???? ?? ?? ?? ?????? A & B ???????? ???? A'=4 ax'-2 ay'-az & B'= ax'+ 4 ay' 4 az ?=90 Cos 90 = 0 A'.B'=0 ----------------------------------------------------------------------- ??? ??? A'=2ax' +4ay' & B'= 6ax'- 4AZ' ???? ???? ??????? ?????? ?????? ???????? ????? ??????? ?????? ???????? --------------------------------------------------------------------------- ??? ??? A'= ax'+ay' & B'=ax' + 2az' & C'=2ax'+az ???? ?????? (A'xB')xC * ??????? ????? A'x(B'xC') & A'.B'xC' ??????? ?? A'xB'.C'

    16. ?????? ?????????? ??????? ?????? ????? ?????? ?=?=?? ??? ?????? ??????? ???? ??? ????? a ????? ???? ????? ???? ??=p & ?=0? ???? ????? ???????? ?? ds=r2 sin? d? df ????? ????? ????? ?? A=2p a2 (cos? - cos??) ????? ?=0 [cos0=1] & ??=180 [cos 180= -1] ??? A=4pa2 ??? ????? ????? ???????

    17. ???????????????

    18. ???????? ??????? ???? ??????? ????????? ?????? ?????? ?????? Divergence and the divergence theorem *?????? Divergence ???? ??????? ??????? ???? ????? ??? ???? ???? ?? ???? ??? ???? ?? ????? ?????? ?????? ??? ????? ?????? ??????? ?? ???? ?????? ???????? ??? ???? ????. ????? ???? ???? ???? ?????? ???? ??? ????? (0 ? ) ???? ???? ??????? ???? ????? ??? ????? ?? ??? ???????. ??????? ?????? ????? ???? ?????? ????? ???? ????? ?????? ??????? ?? ???????? ???????? ???????? ????? ????????? ????? ???? ?????? ????? ???? ????? ?????? ??????? ?? ???????? ???????? ???????.

    19. ????? ????? ??????? ? ??? ?????? ??????? ???? ??? ??? ??????? ???? ????? ??? ????? ????? ????? ??? ????? ?? ? ?????? ???? ????? ????? ??????? D ????? ???? ???????. ???? ???? ????? ????? ??? ?????? ?????? ?? ?????????- ??????? ??????? ???? ???? ?????? ?????? A' ?? ?????? P ???????

    20. ?????? ??????????? ??????????: ???? ?????? A ?????? ??????? P? ??? ??? ?????? ??? ????? ?????? ?????????? x,y,z A=Ax ax + Ayay' + Azaz ??? ???? ?? ??????? ???? ??? ????? ?????? ????? ???? ???? ?????? ??? ??????? ???????.

    21. ???? ???? ??????? ????? ??????? ?? ?????? ?????? ????? ???? ???? ?????? ??? ??????? ??????? ??? ??????? ??? ?v=?x?y?z ????? ?v?0

    22. ???????? ???????? ?????

    23. ??????? ??? (?)? ???????

    24. ????: ???? ?????? ??? v(x,y,z) ? ?? ???? ??? dL'=dx i'+dy j' + dz k

    25. ????: ???? '.r' ? & '.z'? ??? ??? r'=xi' + yj'+ zk'

More Related