Учебное пособие 800365
.pdfA\(B C) = (A\C)\B.
G = [{x1 , x2 , x3 }, {(x3 , x2 ), (x2 , x1 ), (x1 , x2 ),
(x1 , x3 ), (x1 , x1 ), (x3 , x3 )}].
A = |
0 |
1 |
1 |
1 |
. |
|
1 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
1 |
|
|
1 |
1 |
0 |
0 |
|
|
|
|
|
|
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , X, {b, c}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = sin t + 1, a = −π/2, b = 0.
. / # # f (x, y) + # * F (x, y) = 0
|
|
f (x, y) = xy, |
F (x, y) = − |
x |
|
y |
||
|
|
|
+ |
|
|
. |
||
|
|
4 |
5 |
|||||
0 / * # * |
|
|
|
|
|
|
||
0 |
2 |
(2y + (y )2)dx, |
y(0) = 0, |
y(2) = 4. |
(A\C)\B = (A\B) ∩ (A\C).
G = [{a, b, c, d, e}, {(a, d), (a, b), (e, c), (a, e), (e, c),
(c, d), (d, a), (b, d), (a, a)}].
A = |
1 |
0 |
1 |
. |
|
1 |
1 |
0 |
|
|
1 |
1 |
0 |
|
! "# X = {a, b, c} $ % &' ( a% b c *& & * τ = { , X, {a, b}, {b, c}, {a, c}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = −t2 + 4, a = −1, b = 2.
. / # # f (x, y) + # * F (x, y) = 0
f (x, y) = x2 + y2, F (x, y) = |
3x |
+ |
|
5y |
− 1. |
|||
|
|
|
|
|||||
5 |
|
4 |
||||||
0 / * # * |
|
|
|
|
|
|
||
0 |
3 |
(3(y )2 − 4y + 1)dx, y(0) = 1, |
|
y(3) = 6. |
(A\B)\C = (A\C)\B.
G= [{a, b, c, d}, {(a, c), (d, b), (a, a), (a, b), (c, c), (c, b), (d, a)}].
A = |
1 |
1 |
1 |
. |
|
0 |
1 |
0 |
|
|
1 |
1 |
1 |
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , X, {a, b}, {b, c}, {a, c}, {a}, {c}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = −2t2 − 3, a = −1, b = 1.
. / # # f (x, y) + # * F (x, y) = 0
f (x, y) = xy, |
F (x, y) = |
3x |
+ |
|
5y |
. |
||
5 |
4 |
|||||||
|
|
|
|
|
||||
0 / * # * |
|
|
|
|
|
|
||
0 |
1 x1/5(y )2dx, |
y(0) = 0, |
y(1) = 1. |
A\(B C) = (A\B) ∩ (A\C).
G= [{d, e, f }, {(e, f ), (e, e), (f , e), (d, f ), (d, e), (f , f ), (f , d)}].
A = |
0 |
0 |
1 |
1 |
. |
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
|
|
1 |
1 |
0 |
1 |
|
|
|
|
|
|
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , X, {b}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = −t3 + t2, a = 0, b = 1.
. / # # f (x, y) + # * F (x, y) = 0
f (x, y) = x2 + y2, F (x, y) = |
3x |
+ |
5y |
− 1. |
||
|
|
|||||
7 |
3 |
|||||
0 / * # * |
|
|
|
|
||
0 |
1 |
(2(y )2 − y)dx, y(0) = 0, |
y(1) = 1. |
(A\B)\C = (A\B) ∩ (A\C).
G= [{e, f , g}, {(e, f ), (e, e), (f , f ), (g, f ), (g, e), (f , e), (f , g)}].
A = |
1 |
1 |
1 |
0 |
. |
|
1 |
0 |
1 |
0 |
|
|
1 |
1 |
0 |
1 |
|
|
0 |
1 |
1 |
0 |
|
|
|
|
|
|
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , X, {c}, {b}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = −3t2 − 4, a = −1, b = 1.
. / # # f (x, y) + # * F (x, y) = 0
f (x, y) = xy, |
F (x, y) = |
3x |
− |
5y |
|
|
|
. |
|||
7 |
3 |
||||
0 / * # * |
|
|
|
|
|
1 e(xey − y)dx, |
y(1) = 0, |
y(e) = 1. |
A (B\C) (A B)\C.
G = [{x1 , x2 , x3 , x4 }, {(x1 , x2 ), (x3 , x3 ), (x2 , x4 ), (x1 , x3 ), (x4 , x3 ),
(x4, x1), (x2, x2)}].
A = |
1 |
1 |
1 |
. |
|
0 |
1 |
0 |
|
|
0 |
1 |
0 |
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , X, {a, c}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = cos t + 2, a = −π/2, b = π/2.
f (x, y) + # * F (x, y) = 0
F (x, y) = 2x − 9y − 1.
2x3(y )2dx, y(1/2) = 1, y(1) = 2.
(A\B) C (A C)\B.
G= [{a, b, c, d}, {(b, d), (a, b), (a, d), (b, b), (d, c), (c, a), (d, a)}].
A = |
1 |
1 |
1 |
. |
|
0 |
1 |
1 |
|
|
1 |
1 |
0 |
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , {c}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = − cos2 x, a = 0, b = π.
. / # # f (x, y) + # * F (x, y) = 0
|
|
f (x, y) = xy, F (x, y) = 2x + 9y. |
0 / * # * |
||
0 |
1 |
(x1/3(y )2 + Y )dx, y(0) = 0, y(1) = 1. |
A\B = A ∩ B.
G = [{x1 , x2 , x3 }, {(x2 , x1 ), (x1 , x3 ), (x1 , x2 ),
(x1, x3), (x3, x1), (x3, x2)}].
A = |
1 |
0 |
1 |
1 |
. |
|
1 |
1 |
1 |
0 |
|
|
1 |
1 |
0 |
1 |
|
|
0 |
1 |
0 |
1 |
|
|
|
|
|
|
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , X, {a}, {c}, {a, c}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = sin2 t, a = 0, b = π.
. / # # f (x, y) + # * F (x, y) = 0
f (x, y) = x2 + y2, F (x, y) = 11x + 4y − 1.
0 / * # *
1
(x1/6(y )2 + 4y )dx, y(0) = 0, y(1) = 1.
0
A\B = A (A ∩ B).
G= [{a, b, c}, {(c, b), (a, b), (c, a), (c, c), (b, c), (c, b), (b, a)}].
A = |
1 |
0 |
1 |
1 |
. |
|
0 |
1 |
1 |
1 |
|
|
0 |
1 |
1 |
1 |
|
|
1 |
1 |
0 |
1 |
|
|
|
|
|
|
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = {X, {a}, {a, b}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = −t4 + 1, a = −1, b = 1.
. / # # f (x, y) + # * F (x, y) = 0
|
|
f (x, y) = xy, F (x, y) = 11x − 4y. |
0 / * # * |
||
0 |
1 |
(2(y )2 + 2y )dx, y(0) = 0, y(1) = 1. |
A B C = A ∩ B ∩ A ∩ C.
G = [{a, b, c, d, e}, {(d, d), (c, b), (c, e), (d, a), (e, c), (c, d),
(a, b), (b, d), (d, a)}].
A = |
1 |
1 |
1 |
. |
|
0 |
1 |
0 |
|
|
1 |
0 |
1 |
|
! "# X = {a, b, c} $ % &' ( a, b c. *& & * τ = { , X, {c}} + * ,
- " # + ( C[a, b] L2[a, b]
x(t) = −t3 + 3t, a = 0, b = 2.
. / # # f (x, y) + # * F (x, y) = 0
|
|
f (x, y) = xy, F (x, y) = 11x − 4y. |
0 / * # * |
||
0 |
1 |
((y )2 + y2 + 2xy)dx, y(0) = 0, y(1) = 1. |