wavelet / есептер
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1. :
f(x) = exp(−bx)
2.:
f(x) = exp(−ax2 )
3.:
f(x) = ax exp(−ax2 )
4.:
a, |
x [−1,1] |
f (x) = |
x [−1,1] |
0, |
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5. : |
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0, |
x [−∞,0] |
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x [0,1] |
f (x) = kx, |
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x [1,+∞] |
k, |
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6. f g :
0, |
x [−∞,0] |
0, |
x [−∞,0] |
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x [0,1] |
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x [0,1] |
f (x) = kx, |
g(x) = 1, |
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x [1,+∞] |
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x [1,+∞] |
k, |
0, |
7.f g :
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a, |
x [−1,1] |
0, |
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x [−∞,0] |
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x [0,1] |
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f (x) = |
x [−1,1] |
g(x) = 1, |
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0, |
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x [1,+∞] |
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0, |
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8. |
f g |
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1, |
x [−1,1] |
g(x) |
= exp(−ax2 ) |
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f (x) = |
x [−1,1] |
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0, |
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9. |
f g |
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1, |
x [−1,1] |
g(x) |
= exp(−ax2 ) |
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f (x) = |
x [−1,1] |
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0, |
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10. f g |
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1, |
x [−1,1] |
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g(x) |
= exp(−x2 ) / π |
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f (x) = |
x [−1,1] |
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0, |
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11.f g :
0, x [−∞,0]
g(x) = exp(−x2 ) / π
kx, x [0,1]
k, x [1,+∞]
12.[0,1] ! " ! #
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0, x {−∞,0] [1,+∞) |
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1, |
x (0,1/ 2] |
f (x) = |
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−1, |
x [1/ 2,1) |
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13. :
0, x {−∞,0] [1,+∞) |
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1, |
x (0,1/ 2] |
f (x) = |
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−1, |
x [1/ 2,1) |
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14. $ ! $ ?
f(x) = exp(−ax2 )
15.$ ! $ ?
f(x) = 2x exp(−x2 )
16.[0,1] ! " ! #
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0, x {−∞,0]
f(x) = 1− x, x (0,1]
0, x [1,+∞)
17.[0,2] ! " ! #
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0, x {−∞,0] [2,+∞) |
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x, x (0,1] |
f (x) = |
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1− x, x [2,+∞) |
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18. # $ # #%": ut = uxx , ux x=0 = 0, u x=1 = 0, u(x,0) = u0 (x)
19. # $ # #%": ut = uxx , u x=0 = 0, ux x=1 = 0, u(x,0) = u0 (x)
20.# $ # " % #%
! & ':
ut = uxx , ux − u x=0 = 0, ux x=1 = 0, u(x,0) = u0 (x)
21.# $ # " % #%
! & ':
ut = uxx , ux x=0 = 0, ux + u x=1 = 0, u(x,0) = u0 (x)
22.$ ! $ ? f (x) = exp(−a x ) ?
23.[-(,(] ! " ! #
:
f(x) = sin10x + 7 cos 3x
24.$ ! $ ? f (x) = x exp(− x )
25.$ ! $ ? f (x) = x exp(−x2 / 2)
26. [-1,1] " ! ! " ! #
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x +1, x (−1,0] f (x) = 1 − x, x (0,1
27. |
[-1,1] " |
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! " ! # |
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f (x) = x + sin πx |
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28. |
[-1,1] " |
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! " ! # |
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f(x) = x2 + cosπx
29.[-1,1] " $ ! $
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f(x) = x2 + sin πx
30.[-1,1] " $ ! $
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f (x) = x + 10 sin πx
31.[0,l] ' L2[0,l] % C[0,l]
$ :
f(x) = x2 + cosπx
32.! :
fˆ (ξ ) = exp(−ξ 2 / 2) + sin(πξ )/ ξ
33. :
f(x) = exp(−bx)
34.:
f(x) = exp(−ax2 )
35.:
f(x) = ax exp(−ax2 )
36.:
a, |
x [−1,1] |
f (x) = |
x [−1,1] |
0, |
37. :
0, |
x [−∞,0] |
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x [0,1] |
f (x) = kx, |
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x [1,+∞] |
k, |
38.
0, |
x [−∞,0] |
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x [0,1] |
f (x) = kx, |
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x [1,+∞] |
k, |
39.
f g :
0, |
x [−∞,0] |
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x [0,1] |
g(x) = 1, |
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x [1,+∞] |
0, |
f g :
a, |
x [−1,1] |
0, |
x [−∞,0] |
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x [0,1] |
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f (x) = |
x [−1,1] |
g(x) = 1, |
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0, |
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x [1,+∞] |
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0, |
40. f g :
1, x [−1,1]
f (x) = g(x) = exp(−ax2 )0, x [−1,1]
41. f g :
1, |
x [−1,1] |
g(x) = exp(−ax2 ) |
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f (x) = |
x [−1,1] |
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0, |
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42. f g |
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1, |
x [−1,1] |
g(x) = exp(−x2 ) / |
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f (x) = |
x [−1,1] |
π |
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0, |
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43. f g |
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0, |
x [−∞,0] |
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g(x) = exp(−x2 ) / |
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π |
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f (x) = kx, x [0,1] |
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x [1,+∞] |
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k, |
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44.[0,1] ! " ! #
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0, x {−∞,0] [1,+∞) |
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1, |
x (0,1/ 2] |
f (x) = |
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−1, |
x [1/ 2,1) |
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45. :
0, x {−∞,0] [1,+∞) |
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1, |
x (0,1/ 2] |
f (x) = |
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−1, |
x [1/ 2,1) |
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46. $ ! $ ? f (x) = exp(−ax2 )
47. $ ! $ ?
f(x) = 2x exp(−x2 )
48.[0,1] ! " ! #
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0, x {−∞,0]
f(x) = 1− x, x (0,1]
0, x [1,+∞)
49.[0,2] ! " ! #
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0, x {−∞,0] [2,+∞) |
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x, x (0,1] |
f (x) = |
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1− x, x [2,+∞) |
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50.# $ # " % #%
! & ':
ut = uxx , ux x=0 = 0, ux + u x=1 = 0, u(x,0) = u0 (x)
51.$ ! $ ? f (x) = exp(−a x )
52.[-(,(] ! " ! #
:
f (x) = sin10x + 7 cos 3x
53.$ ! $ ?
f (x) = x exp(− x )
54. $ ! $ ? f (x) = x exp(−x2 / 2)
55. [-1,1] ! " ! #
:
x +1, x (−1,0] f (x) =
1 − x, x (0,1