Books
in black and white
Main menu
Share a book About us Home
Books
Biology Business Chemistry Computers Culture Economics Fiction Games Guide History Management Mathematical Medicine Mental Fitnes Physics Psychology Scince Sport Technics
Ads

Elementary Differential Equations and Boundary Value Problems - Boyce W.E.

Boyce W.E. Elementary Differential Equations and Boundary Value Problems - John Wiley & Sons, 2001. - 1310 p.
Download (direct link): elementarydifferentialequations2001.pdf
Previous << 1 .. 392 393 394 395 396 397 < 398 > 399 400 401 402 403 404 .. 609 >> Next

max|e| = 1.6025 at x = n max|e| = 1.5867 at x = n max|e| = 1.5788 at x = n
(c) Not possible
8. (a)
(b)
1 OO
1 2 1 cos nn
f (x) = - +------------T ----------------~------------cos nn x
2 n2
2
(c) 9. (a)
(b)
(c)
n = 10 n = 20 n = 40 n = 21
max|e| = 0.02020 at x = 0, 1 max|e| = 0.01012 at x = 0, 1 max|e| = 0.005065 at x = 0, 1
2 ^ (-1)n+1 f (x) = > --------------sin nn x
ҥ '
n=1
n = 10, 20, 40; max|e| = 1 at x 1
Not possible
33
n
2
44 n
22 n
n even
a
0
n
726
Answers to Problems
See SSM for detailed solutions to 12a
12b, 14
15, 16, 18a 18b
3, 6
7, 10, 13, 14 15, 18
1
10. (a) f(x) = 2 +
2 n=1
6(1 cos nn) nnx 2cos nn . nnx
22 n n
cos--------1-
2
sin -nn 2
(b) n = 10 n = 20 n 40
lub|e| = 1.0606 as x ^ 2 lub|e| = 1.0304 as x ^ 2 lub|e| = 1.0152 as x ^ 2
(c) Not possible
1
11. (a) f(x) = - + J2
2 cos nn
2 2 cos nn + n2n2 cos nn
cos nnx
(b) n = 10 n = 20 n 40
lub|e| = 0.5193 as x ^ 1 lub|e| = 0.5099 as x ^ 1 lub|e| = 0.5050 as x ^ 1 (c) Not possible
12 ft \ 12 (1)n
12. (a) (x) =---------3 > 3 sin nn x
n n=1 n
(b) n = 10 n = 20 n = 40
(c) n = 4
max|e| = 0.0013 45 at x = 0.973 5 max|e| = 0.0003534 at x = 0.9864 max|e| = 0.00009058 at x = 0.9931
13. = (a sin nt n sin at)/a(a2 n2), a2 = n2 = (sin nt nt cos nt)/2n2, a>2 = n2

14. = bn (a sin nt n sin at)/a(a2 n2), a = 1, 2, 3,...
n=1

7= E bn(m sin nt n sin mt)/m(m2 n2) + bm (sin mt mt cos mt)/2m2, a
n= 1
n=m
15. =
a2 (2n 1)2
11
---sin(2n 1)t-sin at
2n 1 a
16. 7 = cos a
cos(2n 1)n t cos at n2 (2n 1)2[a2 (2n 1)2]
Section 10.4, page 570
1. Odd
4. Even
2. Neither 5. Even
3. Odd 6. Neither
14 - 1 - cos(nn/2) nnx
14. f (x) = 7 + ^----------------------------2-cos-
4
n=1
2
4 (nn/2) sin(nn/2) nn x
f (x) = "1 > -----------------2----------sin -
n 2 n=1 n2
2
1 2 -
15 f(x) = 2 + -L
(-1)n
(2n 1)n x
2 ^ , 2n 1
n= 1
2 / 2 n^ \ nn x
16. f (x) = cos nn +------------------------sin ) sin -
< J ҥ \ 11 TJ "
n=1
17. f (x) = 1
xv
18. f (x) = -Y]
77" -4
4 ^ sin(2n 1)x
n=1
2n 1
n=1
2 / nn 2nn
19. f (x) = ^ ( cos-----------------+ cos-----------2
cos nn sin
22 n
33
n
1
cos
nx
3
=m
Answers to Problems
727
See SSM for detailed solutions to 20
25abc, 28b
28cd, 31,32
34, 35, 37ab 38, 39
3, 5
8
1 1 sin2nn x
20. f (x) = 2 - -J2-----------------
7 z4 n
n=1
L 4L TO cos[(2n - 1)-x/L]
Previous << 1 .. 392 393 394 395 396 397 < 398 > 399 400 401 402 403 404 .. 609 >> Next