HKUST
MATH 152
Applied Linear Algebra and Differential Equations
MidTerm Examination
Name:
22nd October 2005
Student ID:
10:00–12:30
Tutorial Section:
Directions:
•
Do NOT open the exam until instructed to do so.
•
All mobile phones and pagers should be switched off during the examination.
•
Please write your Name, ID number, and Section in the space provided above.
•
Answer ALL questions. You are advised to try the problems you feel more comfortable with first.
•
This is a closed book examination.
•
No graphical calculators are allowed.
•
You may write on both sides of the examination papers.
•
Once you are allowed to open the exam, please check that you have 10 pages
in addition to this
cover page.
•
For answering Part II, you must show all your working steps in order to receive full marks.
•
Cheating is a serious offense.
Students who commit this offense may receive zero mark in the
examination. However, more serious penalty may be imposed.
Question No.
Marks
Out of
Q. 115
30
Q. 16
6
Q. 17
8
Q. 18
8
Q. 19
8
Q. 20
8
Q. 21
8
Q. 22
8
Q. 23
8
Q. 24
8
Total Marks
100
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1
Part I: Answer each of the following 15 multiple choice questions.
Each correct answer is worth 2 marks.
Question
1
2
3
4
5
6
7
8
9
10
Answer
Question
11
12
13
14
15
Total
Answer
1.
Which one of the following equations is solvable by the method of integrating factor?
(a)
dy
dt
+
ty
=
y
2
(b)
dy
dt
=
2
ty
t
2
+ 2
y
(c)
y
0
=
t
2
+
1
y
(d)
dy
dt

2
y
+ 1
2
t
=
2
t
+ 1
2
y
(e)
y
00
+ 4
y
0

5
y
= 0
2.
Consider the initial value problem
y
00

y
0
+
1
4
y
= 0
,
y
(0) = 1
,
y
0
(0) =
b.
Find the critical value of
b
that distinguishes
y
(
t
) grows positively and negatively, as
t
→ ∞
.
(a)
1
4
(b)
1
2
(c)
1
(d)
2
(e)
4
3.
The velocity
v
(
t
) of a falling object satisfies the initial value problem
dv
dt
+ 0
.
2
v
= 9
.
8
,
v
(0) = 0
.
Find the time that must elapse for the object to reach
98%
of its limiting velocity.
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 Spring '10
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 Math, Linear Algebra, Algebra, Equations, Laplace

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