Численные методы. Мирошниченко Г.П - 98 стр.

UptoLike

ВУЗ: 

Университет ИТМО | Санкт-Петербург

Составители: 

Рубрика: 

98
()()()() ()( )
00
11
5. , 6. ,
10 11 12 13 1 2
nn
kk
kkkkkkk
==
+⋅ +⋅ +⋅ + ⋅+⋅+
∑∑
()( )() ()()( )
()()( )( ) ()()()
()()()() ()()()
00
00
00
11
7. , 8. ,
123 8910
11
9. , 10. ,
891011 345
11
11. , 12. ,
3456 234
nn
kk
nn
kk
nn
kk
kk k k k k k
kk k k kkk
kkkk kkk
==
==
==
⋅+⋅+⋅+ +⋅+⋅ +
+⋅+⋅ +⋅ + +⋅+⋅+
+⋅+⋅+⋅+ +⋅+⋅+
∑∑
∑∑
∑∑
()()()() ()()()
()()()() ()()()
()()()() ()( )()
()( )()( ) ()()()
()()()()
0
00
00
00
11
13. , 14. ,
2345 678
11
15. , 16. ,
6789 456
11
17. , 18. ,
4567 123
11
19. , 20. ,
1234 567
1
21.
5678
n
k
nn
kk
nn
kk
nn
kk
k
kkkk kkk
kkkk kkk
kkkk kkk
kkkk kkk
kkkk
=
==
==
==
=
+⋅+⋅+⋅+ +⋅+⋅+
+⋅+⋅+⋅+ +⋅+⋅+
+⋅+⋅+⋅+ +⋅+⋅+
+⋅+⋅+⋅+ +⋅+⋅+
+⋅+⋅+⋅+
∑
∑∑
∑∑
∑∑
()( )( )
()()()() ()()()
00
00
1
,22. ,
91011
11
23. , 24. .
9101112 111213
nn
k
nn
kk
kkk
kkkk kkk
=
==
+⋅ +⋅ +
+⋅ +⋅ +⋅ + +⋅ +⋅ +
∑∑
∑∑
6. С помощью формулы суммирования по частям (11.23) вычислить
суммы (результаты проверить численно):
()
()
()
()
()
()
()
()
()
()
()
()
()
()
()
()
()
22
11
22
11
22
11
22
11
2
1. 8 6 4 cos , 2. 1 sin ,
3. 8 5 3 cos , 4. 7 2 9 sin ,
5. 8 6 2 cos , 6. 2 4 6 sin ,
7. 8 7 cos , 8. 5 sin ,
9. 5 9 4
nn
kk
nn
kk
nn
kk
nn
kk
kk ak kk ak
k k ak k k ak
kk ak kk ak
kk ak k ak
kk
==
==
==
==
−⋅+⋅ ⋅ ⋅ −+ ⋅ ⋅
−⋅−⋅ ⋅ ⋅ −⋅+⋅ ⋅ ⋅
+⋅−⋅ ⋅ ⋅ +⋅+⋅ ⋅ ⋅
+−⋅ ⋅ ⋅ + ⋅ ⋅
−⋅+⋅
∑∑
∑∑
∑∑
∑∑
()
()
()
()
()
()
()
2
11
22
11
cos , 10. 7 7 3 sin ,
11. 8 8 2 cos , 12. 1 3 8 sin ,
nn
kk
nn
kk
ak k k ak
k k ak k k ak
==
==
⋅⋅ +⋅+⋅⋅⋅
−⋅−⋅ ⋅ ⋅ −⋅−⋅ ⋅ ⋅
∑∑
∑∑

Страницы