MA1506 TUTORIAL 1
1.
Solve the following dierential equations:
(a) x(x + 1)y = 1
(b) (sec(x)y = cos(5x)
(d) (1 + y )y + (1 2x)y 2 = 0
(c) y = e(x3y)
Use www.graphmatica.com to sketch the functions you found as solutions of [a]-[d], if y =
1/2 at x = 1. Gr
2006/2007 SEMESTER 2 MID-TERM TEST
MA1506
MATHEMATICS II
February 26, 2007
SESSION
2:
7:30 - 8:30pm
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
1. This test paper consists of TEN (10) multiple choice questions and comprises
Twelve (12) printed pages
2006/2007 SEMESTER 2 MID-TERM TEST
MA1506
MATHEMATICS II
February 26, 2007
SESSION
1:
6:00 - 7:00pm
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
1. This test paper consists of TEN (10) multiple choice questions and comprises
Twelve (12) printed pages
2007/2008 SEMESTER 2 MID-TERM TEST
MA1506
MATHEMATICS II
March 4, 2008
8:00pm - 9:00pm
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
1. This test paper consists of TEN (10) multiple choice questions and comprises
Twelve (12) printed pages.
2. Answer a
2012/2013 SEMESTER 2 MID-TERM TEST
MA1506
MATHEMATICS II
March 2013
8:30pm - 9:30pm
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
1. This test paper consists of TEN (10) multiple choice questions and comprises Thirteen (13) printed pages.
2. Answer al
MA1506 Mid Term Test
_
General Information
1. Date: Tuesday, 5 March 2013.
2. Time: From 8:30pm to 9:30pm in the evening.
3. Venue: Please check module website on IVLE.
4. Format: 10 Multiple choice questions based on
Chapter 1.
5. This is a close book te
I
T "cfw_-onio +
GI
(q)Rucoff A n
:
c
o
$ r u en
" tullib'un
ODE
fs
p o;"cfw_(sol+;.?
"
a. s olrtion
L)
r"rhi. rs c oh-sIoncfw_.
h
etuill 5 ni m P +
u
IJ
rE
fhen
i = j(x),
rE = J f xu)
ls
oh
fi
ll
o
(l
ca
J6
(rE) = o
J
etuilibni u ln l 'o;rl r i
Jindty
ro
s olrtrl.rq 7 3
S.lplor.t.3
2Ld) So lve
^
. z = J _Cl -foSzr)
_\
z
Qinx)
=+a t c oi z *
u+43=
ll
:
5o1",
CunsiI t r
* OJ:
D
tl
ona
I\I
4
<rJ
l"
z
= -)
t 4\
Cufr)C.
ll
A p o$."[., t oln f r
ts
b
+ +)s
Jl.
t
8
Ne*l
tr
c,noider
t
Ft.r . o |e + t'J
il
q + 4.'
cr5
Pf:.1 Flo.
R e .|or
o
o ^d O tJte'
bdrogen
Hro
H2
:
ll t r omQ A t ot " f 6 * l i a.
r.
rt
V elocitT
tr
b d r o5en p ,rt ? .1
Cfots-
S ?ct;r"
t'r. o *t
t^
vQl"c\b
l.-p
Pu-p.f
P \r*pl^t
o rcr
A(r)= A re-d"
At
t =o ) x =o
At
t i-e t
A(x):
r -ut
A o e -t
MA1506
1.
Tutorial 11
Solutions
Let S (t) be the number of Spartans, P (t) the number of Persians. We have
dS
= P
dt
dP
= 11, 111, 111.1S
dt
so
dS
dt
dP
dt
[
0
1
=
11, 111, 111.1 0
][
S
P
]
Eigenvalues 2 11, 111, 111.1 = 0 = 3333.3333
[
Eigenvectors
3333.
MA1506
Tutorial 9
SOLUTIONS
Question 1. The thing to remember here is that there are six possible states in which
the cunning Miss Tan can nd herself: she can have $0, $1, $2.up to $5. She can never
have more than that because Ah Huat wont allow it. If at
MA1506 TUTORIAL 8 SOLUTIONS
Question 1
From the given hint, we see that we have to solve
d4 y
Mg
(x A),
=
dx4
EI
subject to the given boundary conditions. [Note that y (0) = y (0) = 0 since the pole is
horizontal at the point where it joins the wall.] Ta
ANSWERS TO MA1506 TUTORIAL 7
Question 1.
(a) We shall use the following s-Shifting property:
L(f (t) = F (s) L(ect f (t) = F (s c)
2
n!
2
n
L(t ) = 3 use L(t ) = n+1
s
s
2
2 3t
) = L(e3t t2 ) =
L(t e
(s + 3)3
(b) Here u denotes the Unit Step Function gi
ANSWERS TO MA1506 TUTORIAL 6
Question1.
B2
.
4s
1. 5
From Tutorial 5 we know B = 1.5 and and N = 376, so N = B/s s = 376
B2
4s = 141. This is the maximum number we can kill without causing extinction.
First compare 80 with
Setting E = 80,
B
1
=
2
B 2 4Es
ANSWERS TO MA1506 TUTORIAL 5
Question 1
Following the standard equations for the Malthus Model [Chapter 3]:
N = N ekt ; N (0) = 10000 = N
N (2.5) = 10000e2.5k = 11000
1
e2.5k = 1.1 k =
n(1.1)
2.5
= 0.0381
N (10) = 10000e10k = 10000e10(0.0381) 14600
1
200
2008/2009 SEMESTER 2 MID-TERM TEST
MA1506
MATHEMATICS II
March 4, 2009
8:30pm - 9:30pm
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
1. This test paper consists of TEN (10) multiple choice questions and comprises Fifteen (15) printed pages.
2. Answer
2007/2008 SEMESTER 2 MID-TERM TEST
MA1506
MATHEMATICS II
March 4, 2008
8:00pm - 9:00pm
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
1. This test paper consists of TEN (10) multiple choice questions and comprises
Twelve (12) printed pages.
2. Answer a
Name:
Ng Yee Sian
Matric No.:
A0073120Y
Lecture Grp:
B
I certify that the work submitted here represents solely my own effort. I am aware of the Universitys
regulations about, and penalties for, plagiarism.
Signature:
MA1506 Lab Assignment 2010/2011 (Sem2
National University of Singapore
Department of Mathematics
Semester II,
2008/2009
MA1506 Mathematics II
Assignment
Instructions
(i) This assignment is due on 27th March 2009 5:00pm.
(ii) This assignment counts towards 5% of your nal grade.
(iii) Assignmen
Name:
Ng Yee Sian
Matric No.: A0073120Y
Lecture Grp: B
I certify that the work submitted here represents solely my own effort. I am aware of the
Universitys regulations about, and penalties for, plagiarism.
Signature:
Q1)
MA1506 Lab Assignment 2010/2011 (
National University of Singapore
Department of Mathematics
Semester II,
2008/2009
MA1506 Mathematics II
Assignment
Instructions
(i) This assignment is due on 27th March 2009 5:00pm.
(ii) This assignment counts towards 5% of your nal grade.
(iii) Assignmen
MA1506 Mathematics II
2010/2011 Semester 2
Instructions for Lab Component/Assignment
The lab component for the module will consist of three self-study sessions and
one assignment which will count towards 5% of your final grade.
Aim:
Students are expected
National University of Singapore
Department of Mathematics
Semester II,
2010/2011
MA1506 Mathematics II
Assignment
Instructions
(i) This assignment is due on 22nd March 2011 1:00pm.
(ii) This assignment counts towards 5% of your nal grade.
(iii) Assignmen
MA1506 Mathematics II
2008/2009 Semester 2
Instructions for Lab Component/Assignment
The lab component for the module will consist of three self-study sessions and
one assignment which will count towards 5% of your final grade.
Aim:
Students are expected