Уравнения математической физики. Уравнение колебаний струны. Хуснутдинов Н.Р. - 22 стр.

UptoLike

ВУЗ: 

КФУ | Казань

Составители: 

Рубрика: 

f(x) = 0 , F (x) =
x(x−l)
h
cos
πx
2l
.
F (x) = 0 , f(x) =
−2l(1 − cos
πx
l
) , 0 ≤ x ≤ 2l/3
−
27
l
(x − l)
2
, 2l/3 ≤ x ≤ l
.
G = g
x
2l
+ e
2x/l
, f(x) = 0 , F (x) = (x − l) sin
2πx
l
.
G = ge
−
2x
l
sin
2πvt
l
, F (x) = 0, f (x) =
(
4l(1 − cos
πx
l
), 0 ≤ x ≤ 3l/4
64(x−l)
2
l
(1 +
√
2
2
),3l/4 ≤ x ≤ l
ψ = g
e
πvt/l
− e
−πvt/2l
φ = 0
, f(x) = 0 , F (x) =
(x−l)
2
h
sin
πx
2l
.
F (x) = 0 , f(x) =
0 , 0 ≤ x ≤ 3l/8
(x−l)(x−3l/8)
h
, 3l/8 ≤ x ≤ l
.
f(x) = 0 , F (x) =
4l(1 − cos
πx
l
) , 0 ≤ x ≤ 2l/3
54
l
(x − l)
2
, 2l/3 ≤ x ≤ l
.
G = g
e
x
2l
−
3x
2
4l
, F (x) = 0, f (x) =
(
x(
l
4
−x)
h
, 0 ≤ x ≤ l/4
0, l/4 ≤ x ≤ l
G = ge
x
4l
sin
3πvt
l
, f(x) = 0, F (x) =
(
3x
2
l
, 0 ≤ x ≤ l/4
(x−l)
2
3l
, l/4 ≤ x ≤ l
φ = g
e
−
4πvt
l
− e
πvt
2l
ψ = 0
, F (x) = 0, f (x) =
(
x(
l
4
−x)
h
,0 ≤ x ≤ l/4
0, l/4 ≤ x ≤ l
                                   ÂÀÈÀÍÒ 24                                          Ñïèñîê ëèòåðàòóðû
1. f (x) = 0 , F (x) =
                              x(x−l)
                                 cos πx                                                 [1℄ Òèõîíîâ À.Í., Ñàìàðñêèé À.À. Óðàâíåíèÿ ìàòåìàòè÷åñêîé è-
                                h     2l .
                           −2l(1 − cos πx
                                                                                           çèêè. Ì., Íàóêà, 1973
2. F (x) = 0 , f (x) =                        l ) ,   0 ≤ x ≤ 2l/3
                                                                          .
                           − 27l  (x −  l) 2
                                             ,        2l/3  ≤x≤l                        [2℄ Âëàäèìèðîâ Â.Ñ. Óðàâíåíèÿ ìàòåìàòè÷åñêîé èçèêè. Ì. Íàóêà,
           x
              + e2x/l , f (x) = 0 , F (x) (      = (x − l) sin 2πx
                     
3. G = g 2l                                                        l .                      1971
                                                                πx
            2x                                      4l(1  − cos   l ),   0 ≤ x ≤ 3l/4
4. G = ge− l sin 2πvt
                    l , F (x) = 0, f (x) =          64(x−l)2
                                                                     √
                                                                       2                [3℄ Àðàìàíîâè÷ È. ., Ëåâèí Â.È. Óðàâíåíèÿ ìàòåìàòè÷åñêîé èçè-
                                                             (1 + 2 ),3l/4 ≤ x ≤ l
                                                        l                                   êè. Ì. Íàóêà, 1969
            πvt/l    −πvt/2l
                             
   ψ=g e          −e                                                2
5.                                , f (x) = 0 , F (x) = (x−l)         sin πx2l .
   φ=0                                                          h                       [4℄ Î÷àí Þ.Ñ. Ìåòîäû ìàòåìàòè÷åñêîé èçèêè. Ì. Âûñøàÿ øêîëà,
                                                                                            1965
                                   ÂÀÈÀÍÒ 25
                                                                                        [5℄ Êîøëÿêîâ Í.Ñ. è äð. Óðàâíåíèÿ â ÷àñòíûõ ïðîèçâîäíûõ ìàòåìà-
                                                                                            òè÷åñêîé èçèêè. Ì. Íàóêà, 1970
                              
                                  0,                  0 ≤ x ≤ 3l/8
1. F (x) = 0 , f (x) =            (x−l)(x−3l/8)                     .
                                        h       ,     3l/8 ≤ x ≤ l                      [6℄   îäóíîâ Ñ.Ê. Óðàâíåíèÿ ìàòåìàòè÷åñêîé èçèêè. Ì. Íàóêà, 1971
                                  4l(1 − cos πx
                              
                                                )   , 0 ≤ x ≤ 2l/3
2. f (x) = 0 , F (x) =            54        2
                                              l                       .
                                   l (x − l) ,       ( 2l/3 ≤ x ≤ l
                                                        x( 4l −x)
                                                                  ,    0 ≤ x ≤ l/4
                         
               x    3x2
3. G = g e 2l −      4l       , F (x) = 0, f (x) =           h
                                                       0,              l/4 ≤ x ≤ l
                                                 (
                                                      3x2
           x
4. G = ge 4l sin   3πvt                                l ,           0 ≤ x ≤ l/4
                     l , f (x)    = 0, F (x) =        (x−l)2
         4πvt                                         3l( ,        l/4 ≤ x ≤ l
                 πvt                                            x( 4l −x)
   φ = g e− l − e 2l                                                      ,0≤ x ≤ l/4
5.                     , F (x) = 0, f (x) =                          h
   ψ=0                                                          0,        l/4 ≤ x ≤ l




                                          43                                                                        44 

Страницы