Введение в лабораторный практикум по курсу общей физики

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  • 1999

  • 2

    22 1998

    -

    : . . , ..-.., ,

    . . , , . . , ..-..,

  • 3

    . : 1.

    . 2. . 3.

    . I

    . II .

    I

    I.

    1.

    . , , . .

    , , : , , . .

  • 4

    , , , : , . .

    , . . : xi = xi X, , i i- , xi i- .

    .

    (x) (), :

    i = xi / X.

    . ,

    , . , , .

    3 : , , .

  • 5

    2. 1. ,

    ( , . .).

    (xi) () , xi , 1.

    X x1 = x2 == xn

    = i - = const

    . 1.

    ,

    : , , , , , . . .

    . : 1. . 2. (,

    , , ).

  • 6

    3. .

    2. ,

    . : , , . . - . , , , : , , , . , , (i) (. 2).

    . 2.

    .

  • 7

    , x1, x2, x3xn ,

    x1 = x1 X x2 = x2 X x3 = x3 X (1.1) xn = xn X

    xn, n . (1.1), :

    = =

    =n

    i

    n

    iii nXxx

    1 1,

    = =

    =n

    i

    n

    iii xn

    xn

    X1 1

    11 (1.2)

    =

    =n

    ii xxn 1

    1

    . x

    , , Xx . n, , .. x

  • 8

    II.

    ,

    . n , x . x ? , .

    1.

    . , . , , , , , - , . , ( , ), .

    nA , (, ), n . = lim nA/n

    n . n: nA/n.

    , , : nA = n .

    . = 1,

  • 9

    , = 0, ( , ).

    , , . , , , .

    , , , , , , , . 1/3, .

    2.

    ,

    . 1, 2n . ,

    n , ,

    =

    ==n

    iixn

    xX1

    ,1 (2.1)

    .xxx ii = xi, .

    xi , . k nk ,

    Pk nk/n. (2.2)

  • 10

    , , 3. .

    . 3. ,

    ,

    =

    =

    nnP

    y kk ,

    . , y = Pk =1. , , . y (i ) , (i ) (. 3).

  • 11

    .4. n (n )

    , 0 , . , , . , y xi :

    ( ) 2

    1= ixy

    ( )2

    2

    2ix

    l , (2.3)

    l ; 2 , ( ).

  • 12

    , , 4.

    , .

    =

    nn

    y k , P(xk)

    , xk xk + , :

    P(xk) = y(xk).

    (. 4). , , 2 xk (. 4).

    5 , . , , . , , . , 2, .

    , y(xi) - , . . .

  • 13

    . 5.

    3.

    1, 2n n ,

    . , . . :

    =

    =n

    iixn

    x1

    .1

    Sn, :

  • 14

    ( )

    11

    2

    =

    =

    n

    xxS

    n

    ii

    n . (2.4)

    Sn . ,

    Sn , ,

    ( ) ( ).

    11

    2

    1

    2

    22

    n

    xx

    n

    xxS

    n

    ii

    n

    ini

    n

    ==

    = (2.5)

    ,

    , n. (n ) (2.5) . , , : , .

    4. , n

    , 1, 2,n.

    =

    =n

    iixn

    x1

    ,1 c

    . n m , m x , . Xxx kk = , xi = xi , ,

  • 15

    2x < 2 . 2x ,

    , x , n . ,

    .22

    nx = (2.6a)

    , x , , :

    nx

    = . (2.6)

    , n n1/2 . (2.5) (2.6) , n

    ( ))1(

    1

    2

    =

    =

    nn

    xx

    nS

    n

    ii

    nx

    .

    ( ))1(

    1

    2

    =

    =

    nn

    xxS

    n

    ii

    x (2.7)

    .

    5. , x .

    x , , x .

  • 16

    x , , , . . . x , .

    , , , , 2x .

    (. II, 2), , 2 (. 6).

    . 6.

  • 17

    =2x 2/n, ,

    , .

    ,

    = x

    X

    . = F(k) 7.

    . 7. =

    x

    XF

    , k .

    , = 0,68 k = 1, = 0,95 k = 2, = 0,997 k = 3. F k (. 1, 2).

    n (n < 30), xx S , . , ( ).

  • 18

    ,xx SXx

    SXt ==

    ( xS (2.7)).

    n n .

    . 8.

    8 y(t) n.

    xS X, t , n. , , t,n X = t,n xS n.

  • 19

    t,n n (. ).

    X . , . , R . R (n>>30), y (R) 2R .

    2R ,

    . R, 2R , , , Xx , . R , . , , R ( x X).

    , , , .

    = 0,997 (X = 3 x ). = 0,90; 0,95.

    : 1.

    x : =

    =n

    iixn

    x1

    .1

    2. i : xi = xi x .

  • 20

    3. :

    ( ))1(

    1

    2

    =

    =

    nn

    xxS

    n

    ii

    x .

    4. X n : X = .,nx tS

    5. : = x X x X xi +X.

    : xi xi = xi - x xi2 xS ,n X 1 2 .

    . xi2=

    i . 6. .

    ( ), , . , , , * :

    ( )2

    2

    3*

    +=

    kXX , (2.8)

    k = t() n = .

  • 21

    III.

    1.

    . x, y, z , W = f (x, y, z) , , . W.

    I . , Wi , .

    II . .

    2. ,

    zyx ,, , , , . , WW = ( zyx ,, ), , . , , , , W W W. , .

    , W , W = W(x). W(x) = (

  • 22

    ). , , ,

    ).()()( Xxdx

    dWXWxWXx

    +=

    =

    ).()()( Xxdx

    dWXWxWXx

    =

    =

    (3.1)

    (3.1) ,

    ,xxx

    W SdxdWS

    =

    =

    (3.2)

    xS WS

    x W . W, ,

    Xdx

    dWWWWxx

    =

    =

    , (3.3)

    W , .

    W , W = W(x, y, z), (3.3) Wx, Wy, Wz, . :

    Zz

    WW

    YyWW

    Xx

    WW

    zzz

    yyy

    xxx

    =

    =

    =

    =

    =

    =

    ,

    ,

    (3.4)

    .

  • 23

    (3.4) z

    WyW

    xW

    ,,

    , .

    (. 4):

    222zyx WWWW ++=

    22

    22

    22

    Zz

    WYyWX

    xWW

    +

    +

    = . (3.5)

    3.

    .WdW

    W =

    dlnu = du/u . , W = W(x) .

    WdWdW

    W ln== , (3.6)

    W W(x), .

    , , , :

  • 24

    ,ln xWxx

    =

    .ln

    ,ln

    zWz

    yWy

    z

    y

    =

    =

    (3.7)

    K222 zyxW ++= . (3.8) (3.7) (3.8)

    , () . , ,

    yxAW 4= ,

    . (3.7), : ,lnln4lnln 21 yxAW +=

    ,21 ,4 y y

    yx

    xx

    =

    =

    .4

    116 22

    22 yy

    xx

    +=

    . (3.8), , (3.7). , . (3.8) .

    W, () :

    W = WW . (3.9)

  • 25

    IV.

    y ,

    , y , . y: y1, y2yn, 1, 2 n.

    y . , , y = f(x).

    y = ax + b. (4.1)

    . , , , . , y = Ae/x ln y = ln A + /x, :

    ln y = f(1/x).

    ( (4.1)), .

    1.

    , .

    , 8 , . .

  • 26

    1 8 (. 9). 1 5; . a .

    y *8 *7 *6 *5 *3 *4 *2

    * 1 0

    . 9.

    , a , y ( ).

    , (x5 x1), (x6 x2), (x7 x3), (x8 x4) .

    2. () .

    . , n (x1, y1), (x2, y2)(xn, yn). , y.

  • 27

    ( ). .

    , , , ( y (. 10)) ,

    . 10.

    (4.1) ,

    ( ) = =

    ==n

    i

    n

    iiii baxydS

    1 1

    22 (4.2)

    . ,

    ( )=

    =+= n

    iiii xybaxa

    S1

    02 ,

    ( )=

    =+= n

    iii ybaxb

    S1

    02 . (4.3)

  • 28

    ,

    :

    = = =

    =+n

    i

    n