作业四参考答案-资料文档

1、作业四参考答案一、选择题 d2dd xa yb z c222( , , ) ( , , ) 0 0 x y z E x y z 2 222( , , ) 0 x y z 其他( , , ) ( ( , ) x y z x 设 x y z0 xa,0 yb,0 z c在 ( ( , ) ( ) x y z x( , )dd222( ( , ) y z E x y z222d( , )y zd2222 ( ( , ) ( ) ( , ) x y z x E y z 22 22( )1 ( , )y z E ,xdd2222( , )E y z 2 (x) (y,z)2 22xE x( )2dx0

2、xa2( )x(1)(2) E x2 dx2dd ( , ) 0 0y z EE y z yb zc222( , ),02 dy dz 22xy,z( , ) ( ( )y z y z 2( ( ) ( ( )y z y z EE( ( ) 0 0y z yb z c2x22 ( ( ) ( )y z y( )z EE( ) 0 yb,0 z cz22x( )1 y 022(z) EE( ) yb,0 zc ，z E2 (y) (z) 2xyE y第1 9 页2220yb0zc( )( )yy E y ( )( ) ( )z E zz EE2xy令 E E E E 及k2 E , i x,y,

3、zzxyii( ) ( )0 0 x k x az2x yb( ) ( ) 0 0ky y2y zc( ) ( ) 0 0 z kz 2zn xx2n2x2 ( )x 2 sinE a2aa22nnxxn xyn2 ( )y 2 n 1,2,yEby2bbnyny2n x2n2z2 ( )y 2 sinn 1,2,zE cz2bc2nnzz nn2n2222E E E E n1,2,yx2z22 a b cn ,n ,nnnn2x,y,zxyzxyzn xyxan xn x 8 abcsinsinsin, 0 xa,0 y,0 z cz( , , ) ( ( ( )x y z x y z bc

4、，其他区域22bc当a EEEEn n n n2n2n2nz22222a2n ,n ,nnnnxyzxyxyzxyz22E n22a2n n nnxyz , ,n n n xyz , ,n n n 6xyz第2 9 页n x2 asin0 xa ( ) 。x anx0,xa02x12x aaa ( )xsin1 cosx xxdxdxx dx22aaa a n000a 12n xa1a xd sinn x2 aa xcosdx 2 aa2 a 2a0012n xn x2 aaa xsin sindx2 2aa001 2n x1n x2 aaa aaa sindx cos2 2a2 2 2a20

5、02x12x aaa ( )sin21 cosx xxdxx2dxx dx2222aaaa n000a 12n xa1n x2 a 2a2a 3 ax cos2dx x d sin2a3 a 2a00a12n xa2 n x2a x sin22 xsindx3 2aa001 2n x1n x2 aaa cos2a2a xsindx 3 a3 2a00aa2xa2x2a xcos cosdx3 2n aa22200aaa2xaaa222sin 3 nacos2n 2a3 n2220 a2a2a2xx x 2xx x x x 222223 n422aa2a 6 22 112 n 12 n2222

6、a2当n x x21(0,a) xxdx内dxa第3 9 页1aax x dxa2 a2 xx 201 a2ax x dx22a30 n a22 asinxx a 2n22 ( )1,2,x a 和 En2a2nn0 x a 2 x ( )2 cos2x axa1a1eipx( )( )得x dxp12xa 2e( )p cosdxaaa 2112a 2expi a p xexpi a p x dxaa 2xi aexp pxa 2expi a pa 21i a p 2ai a pa 2a 2 cos2cos2 1papa a pa paa 2 a cos pa 21a p2222 4 a c

7、os pa 2122( )2pa 222a p22 ( ) 1 x dx2ax a5aa5a2A x (xa) A x x4 3 A 1 A222225 23a500a( ) ( ) ( ( ) 得及xcxxx dxnnnmmnn10第4 9 页n x2 15n xaaa( ( )2()sin() cosc xx A a x xadx xx ax d2n a2aa nn0002 15x2 15aa(x ax)coscosd(x ax)22n an aaa22004 15x2 15x4 15x 2 15x aaaaxcosdxcosdxxd sinsinn an an a( )a n( )2aa

8、a2200004 15xxaaxsin sindx() aaa2004 15x4 154 15acoscos 1 (1) n()3a()3()30 P c 1( 。2n(n )6nnA d )a22 a2 ( ) ( )x H x dx()(H x xax xa dx*2mdx200A A 11a302a5222 a223x(xa)dxx ax 32mm 32a 6m ma5 2002 A2a a 4ax H2a244 ( ) ( )( )2H x H x a m2 m a2*2m5200 1 142得(2n (2n842n0n052 1( 12n224H PE (2n 2424n42442n

9、nn0n0n0 1( 144n44H PE 22(2n m a 4 2m an2m am a2 4nn24224222n0n0n0 2ak x1 sin a(0 x2a)k222(n1,2, ) ( )2a、 x 82kk0(x0,x2a)( ,0) ( )xx 1第5 9 页x1 asin(0 x2a)222 ( ) Ek x a22210(x0,x2a)2a及 ( ) ( ) ( ( ) 得由xcxxx dxnnnmmnn102x2aa2aa( ,0) ( ) ( ,0) ( ) ( ,0) ( )sin21c xx xx xx dx2222aa00a012x1a2xaa1cosdx1si

10、na2aa 2a 22001( )2P Ec2。E121 n2E 22nn x xa2 0aan(x,t 0)( , 0)( )x x t CnnnA 2 xx Axx A ax x( , 0)x t sincossinsin ( ) ( )2aa 4aa4 231aA2 ( , 0) x t1得1 A 42dxa161( , ) ( ) ( )t t。x tex ex t312311W21121222 EE1E223第6 9 页da ( , ) ( , )pix tx t *0ixxxxa aeeee tt tt3131a2aa a0第6 9 页3x 1xx xxxasinsin sine

11、cossine cos sindxi E E ti E E t3131a 2a2aaaaa 203x 131xxxdxa a 1e e sin e sin e sini E E ti E E ti E E ti E E t31313131a 2a2a2a2200da ( , ) ( , )p 2x tx t 2*0 xxxxa 22 aeeee tt tt3131a3aa a0 ( ) 922 a ( )x e ( ) ( )x 1exex e tt tt2a331331310222 91 2a3a3 pp2e ( )x E 及2mp(x 1A A 1( ,0)x 1 cos2cos1kxkx

12、 e e e ei2i22222Aei k)xei(2 k)xei( k)xei( k)x 1222 A2 ( )x x ( ) (x) ( ) x x( )222p0p2 kp2 kp kp k1A 21 22 A, 即422 122( ,0)x ( )x x ( ) (x) ( ) x x( )244p0p2 kp2 kp kp k第7 9 页122222222222p 00 k( k) k)5 k(2 k)024444122k224 k22222E 22242m42m8mt0122( , )x t ( )x x ( ) ( ) ( ) x x( )ei2k2 t mx eik2 t (2

13、m)244p0p2 kp2 kp kp k1222222222p 00e 2 k( k) k)(2 k)0 t m)244441222k224 k5 k222222E 22。242m42m8m 1n xsinnnx a正偶数正奇数2aa1n xn 222cosn1,2,x ax aE ,2a2nna0(x1 ( ) ( ) ( ) | |A axx xx a( ,0)x 41630|xa14 2 11A1 A aat0 4 1 ( )x e ( ) ( ) | |e tx e txx at( , )x t 164333。1630|xa第8 9 页n x ( )2 x a ann22E n1,2,22n4 x1x10将t( x5a5a55124etx1ex 。( , ) ( ) ( )t x t t2 051 05001241220t EE1E；555224122在 t t EE1E。5552020 xa 2 t t 02Wt ,0 xa 2)( , )x t dx00014e1a 2 ( )x e ( ) ( ) ( )2 04exx ex dx*1*2 tt tt51 052 051 05120