计算机数学基础下第编数值分析PPT学习教案

1、会计学1计算机数学基础下第编数值分析计算机数学基础下第编数值分析第1页/共39页)(xf,baxxfxxfxfx)()(lim)(0000niiibanxfdxxf1)(lim)(第2页/共39页), 2 , 1 , 0(nkxk,baknkkbaxxfdxxf1)()(kAkx1kkkxxxnkkkbaxfAdxxf0)()(kAkx01,kk变为了从求和下限注意第3页/共39页nkkkbaxfAdxxf0)()()1 ()0(2) 1(21)(11fffdxxf)(xf1)(xf1121dx2 121 21第4页/共39页)(xfxxf)()(xf2)(xxf110 xdx0 101211

2、1232dxx1 101 21), 2 , 1 , 0()(kxxfk第5页/共39页)(3)(2) 1(31)(11fffdxxf1)(xf112dx2321 31xxf)(321311322)(xxf32321 3122132221321322215623,561016152第6页/共39页)(xf,ba,banabh), 2 , 1 , 0(nkkhaxk)(xf)(xPnnkkknxfxlxPxf0)()()()( nkkkbankkkbabankkkxfAxfdxxldxxfxldxxf000)()()()()()(dxxxxxxxxxxxxxdxxlAbabankkknkk)()(

3、)()()(1010可见第7页/共39页kkxx kxxdxxxxxxxxxxxxxdxxlAbabankkknkk)()()()()(1010thaxhdtdx hntxxhthaxxxthaxxxn)() 1()(,10hnkxxhkxxkhxxnkkk)() 1(,10hdtnkkkntttAnk0)() 1()() 1(kt kk )!() 1( !)()2)(1(1)2)(1(knkknkkkkn第8页/共39页 nnkjjknkdtjtnabknkA00)()!( !) 1( nnkjjknnkdtjtknknC00)()()!( !) 1()()(nkkCabA则bankknkx

4、fCabdxxf0)()()()()(nkC应当记住本公式之一是数值积分的基科茨公式牛顿,第9页/共39页10)(nknkC)()(nknnkCC21,21)1(1)1(0CC61,64,61)2(2)2(1)2(0CCC81,83,83,81)3(3)3(2)3(1)3(0CCCC)(nkC第10页/共39页)83,81,81,83()82,82,82,82()BAC)3(3)3(2)3(1)3(0,CCCC)84,82,81,81()81,83,83,81()DC第11页/共39页9012,9032,907)4(2)4(3)4(1)4(4)4(0CCCCC,babxxxxxa43210ba

5、dxxf)()()()(40)4(kkkbaxfCabdxxf)(7)(32)(12)(32)(790)(43210 xfxfxfxfxfab第12页/共39页21,21)1(1)1(0CC)()(2)(21)()(10bfafabxfabdxxfkkba)(af)(bf)(xfab第13页/共39页,ba)(af)(bf)(xfab,1kkxx)()(2)()(2)(1111kkkkkkxxxfxfhxfxfxxdxxfkk)()(2)(2)(2)(2)(1210nnbaxfxfxfxfxfhdxxf第14页/共39页dxx21242)2(, 11) 1 (, 112)( :22ffab解2

6、541 21)2() 1 (2212ffabdxx第15页/共39页dxxf10)()(xf2484. 12113. 11442. 10727. 10195. 11)(18 . 06 . 04 . 02 . 00 xfx1143. 1)2484. 12113. 121442. 120727. 120195. 121 (22 . 0)1 () 8 . 0(2) 6 . 0(2) 4 . 0(2) 2 . 0(2) 0(2)(10ffffffhdxxf第16页/共39页bbaa,2,)()2(4)(6)(bfbafafabdxxfba第17页/共39页)(xf,ba,ba,222kkxx)()(4

7、)(62)(22122222kkkxxxfxfxfhdxxfkk)()(4)(2)(4)(2)(4)(3)(21243210mmbaxfxfxfxfxfxfxfhdxxf第18页/共39页badxxf)(4abh)()(4)(2)(4)(12)()(4)(2)(4)(3)(4321043210 xfxfxfxfxfabxfxfxfxfxfhdxxfba第19页/共39页907,9032,9012,9032,907)4(4)4(3)4(2)4(1)4(0CCCCC)(907)(9032)(9012)(9032)(907)()(43210 xfxfxfxfxfabdxxfba第20页/共39页)(

8、12)(3bafabfRT)(12)(2,bafhabfRnT| )(|f2312)(| |MabfRT223,12)(| |MnabfRnT第21页/共39页)()2(180)4(4bafababfRS)(180)()4(4,bafhabfRnS| )(|)4(f452880)(| |MabfRS445,180)(| |MnabfRnS)()4(945)(2)6(6fababfRC第22页/共39页111100)()()(xfAxfAdxxf)()(0kbankkxfAdxxf11) 1 () 1()(ffdxxf11)31()31()(ffdxxf第23页/共39页)()(0kbankkx

9、fAdxxfnxxxx,210), 2 , 1 , 0(nkAk第24页/共39页2ab 22batabxbadtbatabfabdxxf)22(2)(11)()(110knkkxfAdxxf22batab第25页/共39页nnnnndxxdnxP) 1(!21)(20, 0) 1(212xdxxd即0)12(81, 0) 1(2212422222xxdxxd即31, 0) 13(21, 0)(2123xxxx求导并解方程0)133(481, 0) 1(62124633233xxxdxxd即第26页/共39页)0(2)(11fdxxf1551, 0, 0353 , 213xxxx求三阶导数后得

10、)31()31()(11ffdxxf)515(95)0(98)515(95)(11fffdxxf第27页/共39页dxx115 . 15774.0315 . 15774. 05 . 15774. 05 . 111dxx4018. 24413. 19605. 0)31()31()(11ffdxxf第28页/共39页dxx11cos7147. 05556. 08889. 07147. 05556. 0cos11dxx6831. 13971. 08889. 03971. 07147.0)515cos()515cos(,8889.098,5556.095)515(95)0(98)515(95)(11f

11、ffdxxf第29页/共39页)(kkxfy 101001011)(yxxxxyxxxxxp1,kkxxkkxxh1111)(kkkkyhxxyhxxxp)(1)( 111kkkkyyhhyhyxp第30页/共39页2120210121012002010212)()()()()()()(yxxxxxxxxyxxxxxxxxyxxxxxxxxxp11,kkkxxxkkkkxxxxh11kkkkkkkkkkyhhxxxxxxxyhhxxxxxxxxp)()()2)()()(111121112211122)(kkkkkyhhxxxxxxx121211121222222)( kkkkkkkkkyhxx

12、xyhxxxyhxxxxp)(1)( )(1)( 111kkkkkkyyhxfyyhxf第31页/共39页11,kkkxxxx)34(21( )(21)( )43(21)( 11)111111kkkkkkkkkkkyyyhxfyyhxfyyyhxf, 0)( , 3)( 11的系数为中的系数为中kkkkyxfyxf. 0, 3)( 11每个括号中系数和都为的系数为中kkyxf中的系数号后颠倒是第三个括号第一个括号中的系数变第32页/共39页)101( f14889.100995.1004988.10)(103102101iixfx1,103,102,101, 1210hxxxk14889.10

13、,0995.10,04988.10210yyy)43(21)( )101( 2100yyyhxff)14889.100995.10404988.103(21049735.0有误课本上的结果048735. 0第33页/共39页)2(),1 (ff) 1 () 2() 2() 1 ()ffBffAB2 , 1x) 1 ( f)1 () 2(21)2() 1 (21)ffDffC) 1 ()2() 1 ( )2(),1 (, 2, 1, 1),(1)(xf,:111kffffyfyxxhyyhkkkkkk注意到由两点求导公式解第34页/共39页1741.184446.168797.144637.131285.12)(9 . 28 . 27 . 26 . 25 . 2xfyx)( , 9 . 2, 7 . 2, 5 . 211kkkkxfxxx求)(21)( 11kkkyyhxf)1741.181285.12(4 . 01114.1