Bài giảng môn học Phương pháp tính

 TR :             17201 TRÌNH  DÙNG CHO SV NGÀNH :  - 2009 Bài gi      2      CNTT  : 3       60 45 15 0 0 0      n cho các bài toán         TS LT TH/Xemina BT KT  10 8 2 0  1  2  2 1  2 1 1.5. Sai  1 1  15 10 4 1  1  1  2 1  2 1  2 1  2 1  12 9 3 0  2  2 1  2 1  3 1  12 8 3 1  4 1  4 2  11 7 3 1 Bài gi    TS LT TH/Xemina BT KT phân  1  3 2 Runger-Kutta 3 1  60 42 15 3     - Anh,  -  -   -  - Sinh     ,   / /2010  Bài gi  1   Trang  1  2 1. 1.   2 1.  3 1. 3. và sai  4 1.  5 1.  7  10  12   14  14 2. 2 14 2. 3.  17 2. 4.  20 2.  26 2. (Newton) 28  33 3:  34  34  34 3. 3.  Newton 35 3. 4.  36  37 4TÍCH PHÂN  38 4.  38 4.  38  40 5:   41 5. 1.  41 5.  41 5. Runge-Kutta 42  43 : 6  44 6.  44 6.  46 6.  54   60  60  62  64  65 Bài gi  2    1.1.   1.                                   . Cho nên    , .  a.         .  Aa     (           ).  , nên không . Do           a         Aa  : Aa    a (1.1)  a          .  a              a  .               a     (1.1)                a     A = a   a (1.2)    ( 1.1)     : a -  a  A   a (1.3) 2.     :  a Aa   A Aa  (  ).            .     :  a = a a  ( 1.4) .  a = a  a ( 1.5)  (1.4) (1.5)          .  a ( 1.4)    a ,  a ( 1.5)      a . Do ( 1.5) nên ( 1.2) : A= a ( 1   a ) (1.6)      a  a . Bài gi  3 3.                ,             .   :        = 10    a = 0,05    = 2   b = 0,05m.    .              ,  i:  a 10 05,0 = 0,5% <  b = 2 05,0 = 2,5% 1.2.  1.                       ,                  .        2,74 3       , 0,0207 . 2.        : A =  10 s s a  (1.7)   : a s 0 9,     65,807 : 65,807 = 6.10 1 + 5.10 0 + 8.10 -1 + 0.10 -2 + 7.10 -3       ( 1.7)   :  1 = 6,  o = 5, -1 = 8, -2 = 0, -3 = 7  a .         s              .  a  0,5 .10 s  s      ,  a > 0,5 .10 s  s     .                     . : Cho a = 65,827    a  6, 5, 8, 2 ,  7, 4 ghi.  a = 0,0067  6, 5, 8,  2, 7, 4 .  s   s  nghi. 3.                       a .    .           (1.2)   ( 1.6) .  Bài gi  4       :  .           không               .  , v v           . 1.3. S     1.               .                                 ,               .                       . . T   :                               ,     5          ,  ,       5  ,       tiên < 5   . : 62,8274            (                        a) 62,827;           h 62,83;  (                 ) 62,8. 2.           . Gi a .   aa '      .    a : aa '    ( 1.8) , .   .   : - - a + a - A   : Aa '  aa ' + Aa      a         a  a +   (1.9)     a                 . 3.          :  = ( 2 - 1 ) 10 .  (Newton)       : ( 2 - 1) 10 = 3363 - 2378 2 ( 1.10) Bài gi  5   : 2 = 1,41421356       (1.10)    2     c   (  1.1): Bng 1.1 2       1,4 0,0001048576 33,8 1,41 0,00013422659 10,02 1,414 0,00014791200 0,508 1,41421 0,00014866399 0,00862 1,414213563 0,00014867678 0,0001472                                                   .          (1.10)  ,  (1.10)  . 1.4.  1.     . : u = f( x,y) (1.11)   , .   : , ,       , y, u Dx, dy,       , y, u  x  y  u , y, u.     (1.1)   : x   x ; y   y (1.12) Ta  u    u   u 2.       = x + y    Ta suy ra: u  x + y   ( 1.12)   : u   x  y   :  x+y  x  y (1.13)   : u   u . Bài gi  6     :   (    )  (    )  . . = x -       . :  u = u u  = yx yx    yx             .              . 3.       = xy    du = ydx + xdy   u  y x + x y  y  x + x  y  u = y  x + x  y   :  u = u u  = xy xy yx   =   x x y y        :  xy =  x +  y ( 1.14)      :  (    )  (  )   . :  (x n ) = n x ;  (1.15) 4.     /y ()           :                  :  x/y =  x + y ( 1.16) 5.       : Cho : u = f( x 1 , x 2 , ,x n )      u = x i n n f    1  i ( 1.17)  u     (1.4) : (    ) (    ) : V= 6 1  3     = 3,7  0,05   = 3,14. Bài gi  7  .         , theo (1.14) (1.15)   :  v =   + 3 d   d = 0,05/3,7 =0,0135 Suy ra:  V = 0,0005 + 3.0,0135 = 0,04     : V= 6 1  3 = 26,5 cm 3      V = 26,5 .0,04 = 1,06  1,1cm 3 V= 26,5  1,1 cm 3 1.5. S      1.                                                         .                           .             .                          , ta luôn          .               .     . 2.  a) T: A = 3 1 1 - 3 2 1 + 3 3 1 - 3 4 1 + 3 5 1 - 3 6 1 .       6 .                       .  .            : 3 1 1 = 1 1 = 1,000    1  = 0 3 2 1 = 8 1 = 0,125    2  = 0 3 3 1 = 27 1 = 0,037    3  = 4. 4 10  3 4 1 = 64 1 = 0,016    4  = 4. 4 10  [...]... 2 1 n3 Bài toán tính Bn đơn giản hơn bài toán tính B Lúc đó B  Bn là sai số phƣơng pháp, và số n phải đƣợc chọn sao cho sai số phƣơng pháp ấy cộng với sai số tính toá n vẫn còn nhỏ hơn 5.10-3 Ta có : B  Bn = 1 n  1 3  1 n  2 3   1 n  13 (theo lí thuyế t về chuỗi số đan dấ u ), với n = 6 ta thấ y : B  B6  1 1   3.10 3 3 334 7 8 Bài giảng môn học Phƣơng pháp tính Ta... 5) Sơ đồ thuật toán Tính: x1  x0  f x0  f ' x0  Tính e = x1  x0 S e .  DÙNG CHO SV NGÀNH :  - 2009 Bài gi     .  n cho các bài toán     .  4 2  11 7 3 1 Bài gi    TS LT TH/Xemina BT