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Учебное пособие 800365

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A\(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.

1/2 0
f (x, y) = x2 + y2,
0 / * # *
. / # #

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.