MATH 251
Name:
Examination II
April 4, 2011
Student Number:
FORM A
Section:
This exam has 12 questions for a total of 100 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
deduc
MATH 251
Final Exam
December 14, 2011
ANSWER KEY (Form A)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
B
C
D
A
A
D
B
D
A
C
C
D
C
A
(a) T
16.
1
(a) Eigenvalues are ! = ,
4
(b) F
(c) F
(d) F
(e) T
9 25
(2 n ! 1)2
;
n = 1, 2, 3,
,
, . ,
4
4
4
(2 n ! 1
MATH 251
Exam II
July 25, 2011
ANSWER KEY
1.
y = C1 + C2 t + C3 t 2 + C4 e! t cos 2t + C5 e! t sin 2t
2.
#
!
x2
% x1 =
%
x3
$ x! =
2
%
!
% x3 = "4 x1 + 2 x2 " 3x3 + sin 2t
&
3.
(a) The integral represents the Laplace transform of f (t) = e4t cos 3t. There
MATH 251
Exam I
September 26, 2011
ANSWER KEY (Form A)
1.
(a) No
(b) Yes
(c) No (also acceptable: Yes, it can be rewritten
into an exact equation because the equation is separable.)
(d) No
2.
D
3.
A
4.
D
5.
A
6.
D
7.
B
8.
A
9.
B
10.
D
11.
y = ! 4et + 12
1
MATH 251
Name:
Final Examination
August 10, 2011
Student Number:
FORM A
Section:
This exam has 10 questions for a total of 150 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
MATH 251
Name:
Final Examination
April 30, 2012
Student Number:
FORM A
Section:
This exam has 15 questions for a total of 150 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
d
MATH 251
Final Examination
Name:
December 14, 2011
Student Number:
FORM A
Section:
This exam has 18 questions for a total of 150 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might b
MATH 251
Name:
Examination II
July 25, 2011
Student Number:
FORM A
Section:
This exam has 10 questions for a total of 100 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
deduc
MATH 251
Name:
Examination II
April 3, 2012
Student Number:
FORM A
Section:
This exam has 12 questions for a total of 100 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
deduc
MATH 251
Name:
Examination II
November 8, 2011
Student Number:
FORM A
Section:
This exam has 12 questions for a total of 100 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
de
MATH 251
Name:
Examination I
July 5, 2011
Student Number:
FORM A
Section:
This exam has 12 questions for a total of 100 points. Show all you your work! In order to obtain
full credit for partial credit problems, all work must be shown. Credit will not be
MATH 251
Name:
Examination I
February 16, 2012
Student Number:
FORM A
Section:
This exam has 12 questions for a total of 100 points. Show all you your work! In order to obtain
full credit for partial credit problems, all work must be shown. Credit will no
MATH 251
Name:
Examination I
September 26, 2011
Student Number:
FORM A
Section:
This exam has 14 questions for a total of 100 points. Show all you your work! In order to obtain
full credit for partial credit problems, all work must be shown. Credit will n
MATH 251
Exam II
April 4, 2011
ANSWER KEY (Form A)
1.
(a) k = 20
(b) = 20
(d) True the system is underdamped.
2,
B
3.
C
4.
A
5.
B
6.
A
7.
D
8.
(a) T
9.
(a) f (t ) =
10.
y (t ) = 2 sin 2t + u 3 (t )(2 cos(2t 6) 2 ) + u 5 (t ) sin( 2t 10)
11.
(a) x(t ) =
(