??????? ????????-
Download as doc, pdf2 likes4,559 views
?????? ??????? ????? ??????? ???????? ?? ????????? ??? ??? ??????? ???????? ???????? ???????? ???????? ???????? ???????? ???????? ???????????????. ???? ??????? ????? ?????? ??? ???????? ?????? ????? ??? ????????? ???????? ??? ????? ???????? ???????? ????????? ?????????. ????? ??????? ??? ????? ??????? ??????? ??????? ???????? ?? ??? ??????? ?????????? ????????????.
??????? ????????-
- 1. ????????? ??????? ???????? ????????)1(? ?????? ???? ?General introduction?? ?????????? ?????????? ??????????????? ?????????? ???????? ?????? ????? ????? ????????? ????? ?????????? ????????? ?????? ????????? ?????????? ??????????????? ???????? ??????? ??????? ??????? ?????????? ?????????????????? , ?????? ????? ???????? ?????? ????????? ?James Clerk?? ?? Maxwell????? ?????? ???? ??????? ????? ????????? ???????????? ???? ???? ?? ? ??????? ?????? ???? ????? ????? ??????? ???? ??? ??????? ??? ?????? ?????? ????????? ????????????????? ?????? ?????? ??? ????? ? c???????? ?????? ?????? ????? ?? ??????? ????? ?????? ????? ????? ?? ???? ?????? ????? ??????? ????? ??2.9979 10 8 m / s?? ???????? ??????? ?????? ??? ???? ??? ??????? ????????? ???? ??????? ??????? ??????? ??? ? ?????? ???? ???? ????? ?????????????? ????? ??????? ????????? ???????? ????????? ?????????? ???????? ??????? ??? ?????? ??? ????? ? ??????? ?????????? ?????? ??????? ????????? ???? ? v?????? ??????? ?? ? ?????? ? ??????? ???? ?? ? ???? ??????? ??????? ??v = ˦?? ????? ?? ??????? ?????????????????? ??????? ?????? ???? ????????? ?????????? )?????? ?????????????? (? ?1(??????? ???????? ?Vector Analysis?? ????? ?????? ??????? ?????????? ??? ????? :? ?1( ????? ?????? ?scalars?? ?1?
- 2. ?2( ????? ????? ?vectors?? ?1( ????????? ?????????? ?????????? ????? ???? ??????? ? Magnitude???????? ?????? ??????? ? direction???? ?????? ?????? ??????? ???????? ?????? ?? ???????? ??????? ???? ????? ?????????? ???????? ????? ????? ??????? ??????????? ?2(? ???? ?????? ? displacement????????? ?velocity????????? ?accelerat?? ????? ??A, A?? ?? ion?????????? ? force?????????? ???????? ????????? ????????? ????????? ????????? ???? ???? ?????? ??? ?????? ?? ????? ?????? ??????? ??????? ??????? ??????? ????????? ??A?? ??????? ????? ? ? A???????? ????? ??? ????????? ?? modulus????? ????? ? modA???????? ?????? ?? ???????? ???? ????????? ??????? ????????? ????????? ??? ????????? ??????????? ???? ????????? ??? ? ????????????????????? ????????????????????? ?????????????????? ?????????????????????? ???? ?????????? ?????????? ?? ??A = A 1 i + A 2 j + A 3k?? ??or?? ??A = A 1 e x + A 2 e y + A 3 ez?? ??????? ??????? ?????????? ????? ???????? ????????? ??????????? ?} 3 ?A = {A 1 , A 2 , A?? ??A?? ?,??????? ?= ?eA?? ??A?? ???? ????? ????? ??????? ?= ?A = mod A?? ?2 ?A1 + A 2 + A?? ?2? ?2? ?3? ?????????? ??????????? ???? ????? ?????? ?? ???????? ?????????? ? ?i,j,k?? ?3? or e1,e2,e?????? ???? ???????? ????????? ???????? ????????? ????? ?????? ????????? ????????? ???????? ???????? ????? ???? ???????? ?, Null Vector?? ???????? ??? ?????? ???? ???????? ????????? ??????? ?????????? ?????? ???????? ??????? ? (P(x,y,z????? ??????????? )? (x,y,z??????? ???????? ?????? ???????? ???? ??r = xi + y j + z k?? ?= ?r?? ?2 ?x2 + y 2 +z?? ?2?
- 3. ???? ??????? ??? ???????? :? ?1. ??? ? ?? ???????? ????????? ??? ??? ???? ??? ????????? ??????????? ??????? ?????? ?? ???? ???? ??????? ??? ????? .? ?2. ???????? ? A????? ?????? ??????? ????????? ????????? ???????? ????????? ???????? ?, A?? ?????????? ??? ?????? ?????? ?. A?? ?3. ????? ?????? ?? ???? ???? ????? ?????? ???? ? ???????? ??????? ????????? ???????.? ????? ???? .? ??A?A?? ???????? ?4.? ?5. ??? ??? ???? ????? ? p??? ???? ? A????? ????? ?????? ???? ?????? ???????? ?? pA???????? ???? ?? ???? ??????? ? p????? ???????? ???? ???????? ??????? ??????? ???? ??????? ????? ????? ?? C? p????? ???? ??????? ????? ??????? ???? ?????? ????? ??? ?????? ?????? .? ???? ?????? ??? ???????? :? ??A+B = B+A?? ?????? ?????? ? ?commutation law?? ?1.? ???????? ???????? ?( A + B ) + C = A + ( B + C ) Associative law?? ?2.? ??p (qA ) = ( pq ) A = ( qp ) A?? ??????? ?????? ?3.? ??( p + q ) A = pA + qA?? ???????? ?????? ?distribution law?? ?4.? ?3?
- 4. ??p ( A + B ) = pA + p B?? ??????? ?????? ?5.? ???????? :? ???? ????? ????? ??????? ??????? ??????? ??????? ?????? ????? ?????? ??? ????????? ???? ????? ??? ??? ???? ...???? ???? ?????? ???? ????????? ?????? ???? ????? ?????????? ?????? ???? ???????? ??????? ??? ????? ?????? ??????? :? ?1. ????? ? ??????? ? : scalar field??????? ???? ????? ?????? ??? ??? ????? ?? ?????? ??????? ??? ???? ?????? ??? ?????? ??????? ????????? ???????? ???????????? ?????? ? ???????? ? : vector field??????? ???? ?????? ??????? ????? ?2.? ??? ???? ?? ?????? ??????? ????????? ???????????? ????? ???????? ?????????? ??????? ?? ??? ?????? ??????? ??????? ??? ????? ???? ? ????????? ??????? ????????? ????????? ? R???????? ? ??????? ???????? ???????? ??????? ??????????? ??F( x, y , z ) = x 2 y i + 3xyzj + 4zk?? ???? ???????? ?Multiplication of Vectors?? ??????? ????? ?? ??? ???????? :? ???????? ???? ? : ??????? ????????? ? Dot of Scalar Product????????? ?????????? ??? ? ??????? ????????? ???????? ?????? ?????? ??A ?B = A B cos ?? ?????????? ?????????? ??????? ??????? ?????? ???? ? ?? ?????? ??????? ?????? ?????? ?? ??? ??????? ??????????? ??????? , ???? ????? ??? ????? ?? ????? :? ?4?
- 5. ?1. ?? ????? ????? ???? ???? ?????? ??? ????? ??? .? ?2. ????? ????? ?????? ???? ??? ??? ?????? ?????? ??? ???? .? ?3. ??? ??? ????? ????? ?????? ???? ???? ???? ????? ?? ???????? ??????? ?????? ????? ??? ?? ?????? ?????? ???? .? ?4. ???? ??? ????? ????? ??????? ????? :? ??A ?B = B ?A?? ??A ? (B + C) = A ? B + A ? C?? ??p ( A ? B ) = ( p A ) ? B = A ? ( p B ) = ( A ? B )p?? ?1 = ?i ? i = j ? j = k ?k?? ?0 = ?i ? j = j ?k = i ?k?? ?2?B2 = B2 + B2 + B?? ??x?? ??y?? ??z?? ??A ? B = A xBx + A yBy + A zBz?? ?????? ???????? :??????? ?????????? ?Cross Product of Vector Product?? ??????????? ??????? ?????? ??A B = AB sin n?? ??,0 < < ?? ??????? ????????? ????????? ????????? ?????? ?????? ????? ???? ????? ?????????? ? A,B???????? ??????????? , ??????????? ?????? ??????? ???? ??? ?????? ??????? ??? ???? ?????????? ???? ????? ??????????? ??????? ?? ???? ?????? ??????? ??? ??????? ????? ????? ????? ????????? . ?????? ?????? ????? ???????? :? ??A B = ?B A?? ??A (B + C) = A B + A C?? ??p( A B ) = (pA ) B = A (p B ) = ( A B )p?? ?0 = ?i i = j j = k k?? ?,?i j = k?? ??j k = i?? ??,k i = j?? ??i?? ??j?? ??k?? ??A B = Ax?? ??Ay?? ??Az?? ??Bx?? ??By?? ??Bz?? ?5?
- 6. ????????? ??????? ?????? ????????? ??????? ????? ?????????? ?????? ??????? ????????? ????????? ? Multiple Products of Vectors??????? ??????? ???? ??? ?????? ?????? :? ?????? ?????? ???????? :?????? ?????? ??????? ??( A ? B )C = m C?? ??where?? ??m = A?B?? ???????????? ?? ????????? ????????? ?????????? ????????????? ??????????? ?????????? ???????????? ??( A B ) C = ( C ? A)B ? ( C ? B )A?? ?????? ?????? ??????? ?????? ???????? ??Ax?? ??Ay?? ??Az?? ??A ? ( B C) = Bx?? ??By?? ??Bz?? ??Cx?? ??Cy?? ??Cz?? ????????? ????? ???????? ????? ???????? ???????? ?????? ????? ? A??? ? B??? ? C??? ? ??????? ????????? ????? ?? ???? ??? ???????? ????? ? cross????? ???? ? dot????????? ??????? ?????? ?? ??? ?????? ?????? ???? ?????? ?. Triple scalar product?? ??????? ???? :? ????? ??????? ?vector of area?? ?????? ??????? ????? ???? ?? ???????? ??????? ????? ????????? ???????? ???????? ????? ?? , dsy=dxdz??????? ?????? ???? ???????? ??? ?dsz=dxdy , dsx=dzdy?? ???? ? n??? ???? ?????? ??????? ??? ??????? .? ??ds =dsn?? ??????? ??????? :? ?6?
- 7. ???? ?????? ?flux of vectors?? ?????? ??????? ? normal flux??? ???? ?? ?? ? ???? ????? ? ds????? ????? ????? ????? ??????? ??? ?????? ?????? ???? ??????? . ???? ??? ????? ????????? ?? A??????? ????? ?????? ? ????????? ? E????? ??????? ????????? ????????? ??????? ?? ?? ??dE n = E ? ds = E ? n ds =E n ds?? ????? ??????? ? ds????? ???? ??????? :? ???? ?En?????? ??? ?????? ? ???????? ???? ???????? ????????? ???? ??????? ???????? ??????? ????? ????? ??????? ???????? ?? A ? ds?? ??= ҡ Ax dydz + ҡ Ay dxdz + ҡ Az dydx?? ????? ???? ??????? ????? ?????? ??????? ????? ???????? ?????? ???????? ?????? ????? ??????? ?????? ?????? , ?? ?? ??????? ??????? ?????? ????? ? ???????? ???????? ???????? ??????? ?????? ????? ?????? ????? ??????? .? ?????? :? ?????? ? ???? ? :? ?????? ?? ????????? ??A = cos +sin ?? ??i?? ??j?? ??B = cos +sin ?? ??i?? ??j?? ???? ????? ????? ?? ??????? ? xy???? ???? ? ?????? ???????????? ???????? ????????? ?????? ????? ? x????????? ?A,B?? ??A?? ??B?? ?= ?eA?? ??A?? ?,? ?= ?eB?? ??B?? ????? :???? ????? ???? ?????? ?? ?????? ???????? ?7?
- 8. ?1 = ?A = cos 2 + sin 2 ?? ?1 = ?B = cos 2 + sin 2 ?? ??e A = cos i + sin j?? ??e B = cos i + sin j?? ?????? ? ?????? :? ??????? ???????? ??? ????????? ??A =i ?3 j +2k?? ??B = ? i +4 j ?k?? ?2? ?????? ??A ? B = AB cos ?? ?=?A?? ?2 ) 2 ( + 3 )3 ? ( + 2 )1(? ?41 =? ?=?B?? ?)3 ? (? ?2? ?62 = )1? ( + ) 4 ( +? ?3? ?2? ??A ? B = ?3 ?12 ? 2 = ?17 = AB cos ?? ??A ?B?? ?71?? ?= ?cos ?? ?=? ?98.0? =? ??AB?? ?463? ?00.351 = ??? ?????? ? ?????? :? ??????? ???? ?????? ??????? ??? ??????? ???? ???? ???????? ? A,B????? ??A = 2a r + a + a z?? ?3? ?+ ?B = ?a r?? ??a ? 2a z?? ?2? ????? :? ??A B?? ?= ?en?? ??A B?? ?8?
- 9. ??ar?? ??a?? ??az?? ????? ?7? ?2 = ?A?? ??B?? ???? ?1? ?=? ??a r + a + z?? ?3? ??4 a?? ??3?? ?2? ????1? ????2? ?2? ? ?A???569. = ?B = 12.25 + + ?? ?2? ?9? ?2 61? ?61? ??n = 0.65a r + .18a + .7 a z?? ??a?? ??? ?0? ?0? ??????? :? ?1. ?????? ???? ???????? ????????? ????? ????????? ?????? ?????? ?? ??????????? ????????? :? ???? ?? ?A = 2ar + a?? ??az?? ?2? ?1? ??B = ar ? a?? ?3? ?2. ?????? ???????? ??? ????????? ??A =2i ?7 j +4k?? ??B =5i +4 j ?3k?? ?9?