MA1506 TUTORIAL 10
Question 1
Wherever possible, diagonalize the matrices in questions 4/5 of Tutorial 9. [That is, write
them in the form PDP1 , after finding P and D, where D is diagonal.] Using this, work
out their 4th powers.
[Answers: The first one c
Recall
where
As an illustration, let us assume that K=3.
Example of a standing wave
More Examples
Examples from past exam papers
2015 Q8a
2013 Q8b
Recall that
MA1506 Mathematics II
Instructions for Lab Component
The lab component for the module consists of three selfstudy Notes. It is not
counted towards the final grade.
Aim:
Students are expected to learn basic skills in the scientific computation software
MA
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1506 Laboratory 2 (MATLAB)
The aim of lab 2 is to demonstrate some tools available in MATLAB that help us to better
understand solutions of differential equations. In Part A, we will graph direc
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1506 Laboratory 1 (MATLAB)
In this course, we use a highly acclaimed numerical computing software called MATLAB.
MATLAB stands for matrix laboratory. The aim of lab 1 is to introduce the basic f
To help us guess the shape of the solution curve
(i.e. the graph of N against t), we try to get the
following information from the differential
equation without solving it:
1. Increasing or decreasing property of N.
2. Concavity of the solution curve.
3.
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1506 Laboratory 3 (MATLAB)
Part A: Working With Matrices
MATLAB actually stands for matrix laboratory, and as the name suggests, it was designed
for working with matrices.
We can input an m n ma
Matriculation Nurnl5er:
NATIONAL UNIVERSITY OF SINGAPORE
EI\CULTY OF SCIENCE
SEl'viESTER 2 EXAl'viiNATION 201:32014
1\!1Al50f$
1\!IATIIEl\!IATICS II
April 2014
Time allowed: 2 hours
Examiners: Brett l\l[clnnes, Chew Tua.n Seng, Leung Pui Fai, Quek Tong S
[
'
Examination
MA1506
Question 3 (b)
[5 rnarks]
(i) Let :r: (t) be the solution of the initial value problern
cl.r
= x 2  :30x
1
ct

+ 200, and x (/0) =
18.
Find t he exact value of lirn ~r (t) .
tt c>O
(ii) Let x (t) be the solut ion of t he init ial
Matriculation Number:
MA1506
A
NATIONAL UNIVERSITY OF SINGAPORE
FACULTY OF SCIENCE
SEMESTER 2 EXAMINATION 20142015
MA1506
MATHEMATICS II
April 2015
Time allowed: 2 hours
INSTRUCTIONS TO STUDENTS
1. Write down your matriculation number neatly in the space
2013/2014 SEMESTER 2 MIDTERM TEST
MA1506
MATHEMATICS II
March 2014
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
2014/2015 SEMESTER 2 MIDTERM TEST
MA1506
MATHEMATICS II
March 2015
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
2007/2008 SEMESTER 2 MIDTERM 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
MA1506 TUTORIAL 2
1.
Solve the following differential equations:
(a) xy 0 + (1 + x)y = ex ,
(b) y 0 (1 + x3 )y = x + 2,
(c) y 0 + y +
x
y
=0
x>0
y(1) = e 1,
x>0
(d) 2xyy 0 + (x 1)y 2 = x2 ex ,
x>0
2. If a cable is held up at two ends at the same height, t
MA1506 TUTORIAL 6
Question 1
In question 6 of Tutorial 5, let us assume that you are keeping the bugs not as a hobby,
but because you are developing a new insecticide. Suppose that you remove 80 bugs per
day from the bottle, and that all of these bugs die
MA1506 TUTORIAL 8
Question 1
Despite her vast wealth, Tan Ah Lian continues to live with her mother. The latter does
TALs laundry [of course], including a large heavy jacket. TALs mother hangs the jacket
out to dry on a bamboo pole inserted into a socket
MA1506 TUTORIAL 7
1. Find the Laplace transforms of the following functions [where u denotes
the unit step function and the answers are given in brackets]:
2
]
(a) t2 e3t .
[
(s + 3)3
2
1
(b) tu(t 2).
[e2s cfw_ 2 + ]
s
s
2. Find the inverse Laplace transf
MA1506 TUTORIAL 5
Question 1
Close examination of a can of MiloTM shows that, in fact, the bottom of the can is not
welded to the vertical part of the can; it is part of the same piece of metal. [If you dont
know what I mean, or even if you do, look at a
MA1506 TUTORIAL 4
Question 1
Find the equilibrium points for the following equations. Determine whether these equilibrium points are stable, and, if so, find the approximate angular frequency of oscillation
around those equilibria.
(i) x
= cosh(x)
(ii) x
CHAPTER 3
MATHEMATICAL MODELLING
3.1. MALTHUS MODEL OF
POPULATION
The total population of a country is clearly a
function of time, N(t) [NOTE: N may be measured in millions, so values of N less than 1 are
meaningful!]. Given the population now, can
we pre
MA1506
These notes contain suggested solutions to examination
questions in AY2009/2010 Semester 2.
In the upcoming examination, the examination paper layout
will be different: for each question, there will not be a box
that students are required to write
MA1506
These notes contain suggested solutions to examination
questions in AY2011/2012 Semester 2.
In the upcoming examination, the examination paper layout
will be different: for each question, there will not be a box
that students are required to write
MA1506
These notes contain suggested solutions to examination
questions in AY2007/2008 Semester 2.
In the upcoming examination, the examination paper layout
will be different: for each question, there will not be a box
that students are required to write