18.06 Strang a0 a1 a2 a3 3
2000 a4 12 a5 6 a6
a7a9a8a9a10
a11a9a12a9a13a9a14a9a15
a10
1) M2 2-131 Holm 2-181 3-3665 tsh@math
2) M2 2-132 Dumitriu 2-333 3-7826 dumitriu@math
3) M3 2-131 Holm 2-181 3-3665 tsh@math
4) T10 2-132 Ardila 2-333 3-7826 fardila@math
5) T10 2-131 Czyz 2-342 3-7578 czcy@math
6) T11 2-131 Bauer 2-229 3-1589 bauer@math
7) T11 2-132 Ardila 2-333 3-7826 fardila@math
8) T12 2-132 Czyz 2-342 3-7578 czcy@math
9) T12 2-131 Bauer 2-229 3-1589 bauer@math
10) T1 2-132 Ingerman 2-372 3-4344 ingerman@math
11) T1 2-131 Nave 2-251 3-4097 nave@math
12) T2 2-132 Ingerman 2-372 3-4344 ingerman@math
13) T2 1-150 Nave 2-251 3-4097 nave@math
1
1.(30 a16 )
(a) a17 A =
2
64 0:5 3 40 1 0
0 0 1
3
75
a18a20a19a22a21a9a23a9a24 A = S S
1 a25
(b) a26
lim
k!1
Ak
(c) a27a20a28 k !1a29a9a30 Bk ! I(2 a31a9a32a9a33a20a34 ) a25a36a35a9a37a9a38a9a39a9a40 Jordan a41 J ="
1 1
0 1
# a42a20a43
B = I a25
2
2.(40 a16 )
(a) a27 A a44 a18a20a19a22a21 A = S S 1 a45a9a46a9a47 A a44a9a48a9a49
a39
a16a9a50 A = U V T a51a20a52
(a53a22a54 S = U = V; = ) a25 A a55a9a56a9a57a20a58a22a59a9a60a62a61a64a63a9a65a9a48a9a49a9a44a9a66a62a61
(b) a26a9a67a9a68 2 a44 3 3 Markov a69a9a70a9a71a20a34a22a44
a37a9a38a9a39a9a25
(c) a71a72a34 A =
2
64 3 04 0
0 7
3
75
a30a36a73a75a74a72a76a78a77
a51a75a79a75a80a75a81
a30a36a26a82a63a75a44a82a48a82a49
a39
a16a82a50 A =
U V T a25
(d) a27 3 3 a71a20a34 B a44
a37a9a38a9a39
a68 1 a30 1 a30 2 a25 a71a20a34 A a51a9a83a9a84 B a25
a85a22a86 A
a44a20a87
a84a9a88a9a89a9a90a9a91a9a92a20a93
a44a20a94a22a95
a10
1)A a44
a37a9a38a9a39a9a25
2)A a65a9a96a9a97a20a98 a18a20a19a22a21 a61
3)A a44 a18a9a99 a59
a25
4)A a44
a80a9a100
a59
a25
a101 2)
a30 3) a30 4) a102a22a103a9a104 A a65a9a96a9a105a9a97a9a106a9a107a9a97a9a106a9a107a9a108
a100
a55a9a56a9a109a9a110a9a59a9a60
a25
3
3.(30 a16 )
(a) a111 A =
2
64 0 1 01 0 1
0 1 0
3
75
a30a36a26 A a44
a37a9a38a9a39 (
a112a9a113a20a114 ) a25
a37a9a38a9a39
a65 a53a22a68a9a71a20a34 A a65
a25
(b) a27 A a44
a37a9a38
a76a22a77a9a68 x1; x2; x3(a105a9a108a9a115a9a116a9a109a9a110
a37a9a38
a76a22a77 ) a30a118a117a20a119
a92a9a120 du
dt =
Au a44a9a121a9a50
a25
(c) a101 a57a20a58a22a29a20a122 T a30
a92a9a120
a44a9a50 u(T) a123
a84
a73a9a124
a39 u(0)
a61
4