Solution :
Trigonometric identity
Q2: Find the Fourier transform of the following
functions:
Solution : (2a)
Trigonometric identity
Solution : (2b)
g(t)
Gate function:
1
-k
0
k
t
Q3: Find the inverse of the following Fourier
transforms.
Solution : (3a)

BEZOOGIIMZOO Engineering Mathematics I PDES by EK Teohi'Jan 2016
EE2006/IM2006 Engineering Mathematics I
Tutorial 5
Partial Differential Equations [1!
1. To each of the differential eguations gDE below, determine (i) the order of the DE,
(ii) if the DE 13

EE2006/IM2006
UIZ ON EE2006/IM2006 ENGINEERING MATHEMATICS I
AY2014/15- SEMESTER 1!
(832293-14 SOIWS.)
11 October 2014 Time Allowed: 1 hour
NANYANG TECHNOLOGICAL UNIVERSITY
INSTRUCTIONS
1. This paper contains FOUR (4) questions and comprises SEVEN (7) p

EE2006/IM2006 Engineering Mathematics I Fourier Analysis by EK Teoh/Jan 2016
EE2006/IM2006 Engineering Mathematics I
Tutorial 2
Fourier Transform
_1_._ 1m!) has a Fourier transform F (0) , nd the Fourier transform of the signal
g0) = f(t) cos wcr.
2.

EE2006KIM2006 Engineering Mathematics I Laplace Transform by EK Teoth an 2016
EE2006/IM2006 Engineering Mathematics I
Tutorial 4
Laplace Transform Applications
1. (a) Solve y(t) for the first order ODE using the method of Laplace Transform :
y 2y = 14(1)

EE2006HM2006 Engineering Mathematics I PDEs by BK Teothan 2016
EE2006/IM2006 Engineering Mathematics I
Tutorial 6
Partial Differential Equations (II)
1. Show that the solution obtained by the Method of Separation of Variables to the PDE
_-I -_'-.-. III
11

EE2006IIM2006 Engineering Mathematics 1 Laplace Transform by EK Teohan 2016
EE2006/IM2006 Engineering Mathematics I
Tutorial 3
Laplace Transform Basics
_l._ Com ute the Laplace Transforms of the followin based on the definition of the
Zaplace Transform :

PJY Wong
1. What is Least Squares Approximation?
2. Normal Equations
D. Least Squares Approximation
1. Lagrange Interpolation
2. Newtons Divided Dierence Interpolation
C. Polynomial Interpolation
4. Speed of Convergence
PJY Wong
Oce: S1-B1b-58, Tel: 67904

EE2006/IM2006 Engineering Mathematics I Fourier Analysis by EK Teoh/Jan 2016
EE2006 / IM2006
ENGINEERING MATHEMATICS I
[AY2015/16 Semester 2 (Week 1 to 2)]
FOURIER ANALYSIS
Dr Teoh Eam Khwang
Associate Professor
School of EEE, NTU
Office: S2-B2b-64
Tel: 6

EE2006/IM2006 Engineering Mathematics I Laplace Transform by EK Teoh/Jan 2016
EE2006 / IM2006
ENGINEERING MATHEMATICS I
[AY2015/16 Semester 2 (Week 3 to 4)]
LAPLACE TRANSFORM
Dr Teoh Eam Khwang
Associate Professor
School of EEE, NTU
Office: S2-B2b-64, Tel

EE2006/IM2006
Laplace Transform Table
f(t)
F(s)
1. Unit impulse
(t)
1
2. Unit step
u(t)
1
s
3. Unit ramp
r(t) = tu(t)
1
s2
4. Unit parabola
1
p (t ) = t 2 u (t )
2
1
s3
5. Exponential
e at
1
s+a
6. t-Multiplication
exponential
te at
1
(s + a) 2
7. Sine
si

(a)
Define
Since
,
hence, there is at least one root
in
.
1). Apply Theorem 2.1 to show the iterative converge
2). Use Fixed-Point Iteration to solve equation
Stopping criterion (Thm 1.1):
2). Use Fixed-Point Iteration to solve equation
Stopping criteri

Q1: Compute the Laplace Transform of the following
based on the definition of the Laplace Transform
Solution : (1a)
(1b)
Eulers formula
(1c)
(1d)
Q2: Sketch the function given by
Solution : (2a)
u(t-3)
(2b)
Shift/Exponential Property
Q3: With the aid o

EE2006 Engineering Mathematics I
Assignment 2
For both Full-time and Part-time students, the assignment should be submitted to your
tutor during the tutorial class in Week 12 of the semester, i.e. 3 7 November. The solution
of the assignment will be uploa

EE2006 Engineering Mathematics I
Assignment 2
For both Full-time and Part-time students, the assignment should be submitted to your
tutor during the tutorial class in Week 12 of the semester, i.e. 3 7 November. The solution
of the assignment will be uploa

EE2006/IM2006 Engineering Mathematics I Assignment 1 by EK Teoh/Feb 2014
Nanyang Technological University
School of Electrical & Electronic Engineering
EE2006/IM2006 - Engineering Mathematics
(AY2013/14 Semester 2)
Assignment 1
For both Full-time and Par

EE2006/IM2006 Engineering Mathematics I Assignment 1 by EK Teoh/Sep 2014
Nanyang Technological University
School of Electrical & Electronic Engineering
EE2006/IM2006 Engineering Mathematics
(AY2014/15 Semester 1)
Assignment 1
For both Full-time and Part-

Q1: For the following DE, determine
I.
II.
III.
IV.
The order of DE
If the DE is homogeneous
ODE or PDE
Variant or invariant
Order of DE: the highest derivative in the DE
Homogeneous: put all the terms containing u and its derivatives to the left and all

Q1: Show that the solution obtained by the Method of Separation of
Variables to the PDE
Solution : (1)
Put all terms containing x to the left, and
all terms containing t to the right.
Let both the left and the right equal to a
constant.
1st ODE with va

Q1: Find the Fourier expansions of the periodic
function whose definition on one period is
Review: Steps to get the Fourier Expansion of the periodic function f(t)
1. From period T, find p=T/2;
2. Calculate
3. Calculate
4. Calculate
5.
6.Find f(t) at the

Solution : (1a)
Differentiation Property:
partial fractions
Briefly speaking, y(t) is stable means y(t) can converge to a constant value.
Solution : (1b)
Differentiation Property:
Partial Fractions
Q2: Find the time function of i(t) after the switch S is

Tutorial 7 Q3.
(a) Consider the family with 3 children, all possible
composition are listed as follows:
No boy: GGG;
2 boys: BBG, BGB, GBB;
1 boy: BGG, GBG, GGB
3 boys: BBB
(b) Let = cfw_a family with exactly 2 girls;
= cfw_a family with at least 1 girl.

Let = error of depth perception
(a) =
2
=
= 1.43,
1
1
=
2
=0.1467,
2 = 0.383
(b) Since is unknown, n = 14 < 30,
we need to assume is normally distributed.
Then is also normally distributed.
1). Find critical value
= 0.9,
Find
= 1 = 0.1
2
= 0.05 o

EE2006/IM2006 Engineering Mathematics I Partial Differential Equations by EK Teoh/Jan 2016
EE2006 / IM2006
ENGINEERING MATHEMATICS I
[AY2015/16 Semester 2 (Week 5 to 6)]
PARTIAL DIFFERENTIAL EQUATIONS
Dr Teoh Eam Khwang
Associate Professor
School of EEE,