第七章静电场与积分计算

1、0022001( )(,)4()aaxv xydxxxyaa00( ,)x yxy( )1,14xa-2-1.5-1-0.500.511.5-2-1.5-1-0.500.511.52( ),14xxa-2-1.5-1-0.500.511.5-2-1.5-1-0.500.511.5( )( )( )bavf x dxf bf a2( )f xaxbxc22( ),sinxf xex-1-0.8-0.6-0.4-0.200.20.40.60.810.50.550.60.650.70.750.80.850.90.951f(x)x ( )bavf x dx1baxn xi xi+1( )iisf xx

2、1,2,.,1in11( )niivf xxxi xi+1 11 ( )()2iiisf xf xx1111 ( )()2niiivf xf xx12111()() ,.,()()22nnvf xf xf xf xx11211()()( )22nniivf xf xf xxxi-1 xi xi+1 111111111()()()()( )()( )()()()()iiiiiiiiiiiiiixxxxxxxxy xf xf xxxxxxxxx11111()()()()()iiiiiiixxxxf xxxxx111122()()()()( )()( )2()()iiiiiixxxxxxxxy xf

3、 xf xxx 112()()()2()iiixxxxf xxbxbaxaxiii11,2,)()(xfxybabadxxydxxf)()(xabhthxxi2,12011)(2) 1()()2()(2)2)(1()(hdtxfttxfttxfttdxxyiiiba)()(4)(311iiixfxfxfh11111( )()4 ( )()3iixiiiixsy x dxf xf xf xx12341 ()4 ()2 ()4 () ,.,()3nvf xf xf xf xf xx(1)/2(3)/21221111 ()4()2()()3nnijnijvf xf xf xf xx nnijjinn

4、idtjtininc00)()!( !) 1(1111( )()22iiivf xf xx11141()( )() 2666iiiivf xf xf xxniiniihxfcv0)(nic11111, | 1 , | 1iiiiiiisssdssss (相对误差)(1)/2(3)/211221111 ()4()2()()32nnikknkkhsf xf xf xf x211kxxkh211112111()()2()4()62iikiknhhsff xf xf xhkxhk212khxxkh2111()2iikhrcf xkh211111 ()()2()iinkrpf xf xf xkh1114, ( h i )6iiihsrprc是第 步时的步长121111 ()()2(2)iinkrpf xf xf xkh1211(2)iikrcf xkhh12iiirprprc12iii