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 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,
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
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
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
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
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
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
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
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
MA1506
Examination
Question 1(a)(i)
1
d
ln(ln x) =
dx
ln x
d
ln x
dx
=
1
.
x ln x
Question 1(a)(ii)
1
x
dy
+
y=
.
dx x ln x
ln x
1
Integrating factor = e x ln x = eln ln x = ln x. Hence,
x2
x
ln x =
+C
y ln x =
ln x
2
e2
e2
= y (e) ln e = 0 =
+ C = C = .
2009/2010 SEMESTER 2 MID-TERM TEST
MA1506
MATHEMATICS II
March 1, 2010
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
NATIONAL UNIVERSITY OF SINGAPORE
DEPARTMENT OF MATHEMATICS
SEMESTER 1 EXAMINATION 2008-2009
MA1506
Mathematics II
December 2008 Time allowed : 2 hours
INSTRUCTIONS TO CANDIDATES
1. This examination paper consists of a total of SIX (6) questions and compri
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
Chapter 3
Mathematical Modelling
Chew T S MA1506 Chapter 3
1
Introduction
mathematical model uses mathematical
language to describe a system.
In this module, we use ODE to describe some
systems.
In the last two chapters, we have stud
MA1506
Mathematics II
Chapter 4
Laplace Transforms
Chew TS MA1506 SEM 1 Chapter 4
1
4.0 Introduction
4.0 Introduction
In Chapter one, we have learnt how to solve
nonhomogeneous 2nd order linear ODE (with
or without initial conditions) by
Method of undete
NATIONAL UNIVERSITY OF SINGAPORE
FACULTY OF SCIENCE
SEMESTER 2 EXAMINATION 2006-2007
MA1506
April 2007
MATHEMATICS II
Time allowed: 2 hours
Matriculation Number:
INSTRUCTIONS TO CANDIDATES
1. Write down your matriculation number neatly in
the space provid
Math Refresher Course
July 2015
Refresher 5: Sequences and Series
Department of Electrical and Computer Engineering
5.1
National University of Singapore
Infinite Sequence
A sequence is a list of numbers written in a specific order. Each term of the sequen
Math Refresher Course
July 2016
Solution 1: Function
Department of Electrical and Computer Engineering
1.1
National University of Singapore
Exercise
1
3
2
D
f1 (x ) = 2x
4
6
2
R
2
2
3
D
f2 (x ) = x 2
(a)
9
1
4
R
4
D
g(x)= x
(b)
1
4
4
D
h(x)= x
2
(c)
2
2
Matriculation Number:
NATIONAL UNIVERSITY OF SINGAPORE
FACULTY OF SCIENCE
SEMESTER 2 EXAMINATION 2011-2012
MA1506
April 2012
MATHEMATICS II
Time allowed: 2 hours
INSTRUCTIONS TO CANDIDATES
1. Write down your matriculation number neatly in
the space provid
Matriculation Number:
NATIONAL UNIVERSITY OF SINGAPORE
FACULTY OF SCIENCE
SEMESTER 2 EXAMINATION 2008-2009
MA1506
April 2009
MATHEMATICS II
Time allowed: 2 hours
INSTRUCTIONS TO CANDIDATES
1.
Write down your matriculation number neatly in
the space provid
MA1506
Mathematics II
Chapter 4
Laplace Transforms
Chew TS MA1506 SEM 1 Chapter 4
1
4.0 Introduction
4.0 Introduction
In Chapter one, we have learnt how to solve
nonhomogeneous 2nd order linear ODE (with
or without initial conditions) by
Method of undete
MA1506
Mathematics II
Chapter 7
Systems of First Order ODEs
1
7.1 Solving Linear System of ODEs
How to solve
dx
= ax + by
dt
i.e,
dy
= cx + dy
dt
a,b,c,d constants
d x a b x
=
y
c
d
y
dt
We shall look at an old problem,
which is related to our new pro
MA1506
Mathematics II
Chapter 8
Partial Differential equations
PDEs
Chew T S MA1506 Chapter 8
1
In this Chapter, we will study
(1) Method of separation of variables (MSV)
(2) Wave equation (Two versions)
(a)by MSV (b) by dAlemberts method
(3) Heat equatio