Engineering Mathematics 1
Part 1 Algebra
Dr Tang Wee Kee
Division of Mathematical Sciences,
School of Physical and Mathematical Sciences,
Nanyang Technological University,
Singapore
Semester 1 2016/17
2
Contents
Contents
-1
1 Complex Numbers
1
1.1 The set

PH1104/CY1305/SM2-18: Mechanics
Semester 1 2014
Mid-Term Exam I
Answer ALL TWO (2) questions. Take g = 9.8 m/s2.
1.
Another zookeeper is trying to catch a runaway monkey found hanging on a tree h = 12
m from the ground (see figure below). This zookeeper i

PH1104/SM2-B19: Mechanics
Homework 2
Due date: Thursday 8th October 2015
Homework solutions should be submitted during the first 10 minutes of Thursday
lecture on 8th October 2015 at the respective LTs according to Theta/Phi group.
Marks will be deducted

PH1104/SM2-B19: Mechanics
Homework 1
Due date: Thursday 17th September 2015
Homework solutions should be submitted during the first 10 minutes of Thursday
lecture on 17th September 2015 at the respective LTs according to Theta/Phi
group.
Please write the

PH1104/SM2-B19: Mechanics
Homework 3
Due date: Monday 26th October 2015
Homework solutions should be submitted during the first 10 minutes of Monday
lecture on 26th October 2015 at the respective LTs according to Theta/Phi
group. Marks will be deducted fo

PH1104: Mechanics
Tutorial 4
Qualitative questions
Quantitative questions
1
2
3
Challenging question
Extra question for thought:
As a cart is sliding down a frictionless incline, it ejects a ball upward into
the air in a direction that is normal to the in

PH1104: Mechanics
Tutorial 7
Qualitative questions
1
Quantitative questions
Note: mass of electron is 9.10938215(45) 1031 kg
2
Challenging question
3
Extra question - Falling rope
A rope of length L lies in a straight line on a frictionless table, except

PH1104/CY1305/SM2: Mechanics
Semester 1 2014
Mid-Term Exam 2
Nov 4, 2014
Answer ALL THREE (3) questions. Take g = 9.8 m/s2.
1.
A 5.00-g bullet moving with an initial speed of = 400 m/s is fired into and passes
through a 1.00-kg block as shown in the figur

MH1100/MTH112: Calculus I.
Problem list for Week #1.
This weeks topics:
The basic theory of functions. Chapters 1.1 through 1.3 in Stewart.
Your tutor will aim to discuss: Problem 1, 3, 5, 7(b), 11, 12, 14, 16, 17.
Problem 1: (Problem 1.1.35 from [St].)

Outline
1
Continuous Functions
Tang Wee Kee (Division of Mathematical Sciences School
MH1810
of Physical
Mathematics
and Mathematical
1 Part 2
Sciences Nanyang
Semester
Technological
1 2013/14
University)
1/1
Continuous Functions
Very often, we are intere

PH1104: Mechanics
Tutorial 9
Qualitative questions
Quantitative questions
1
2
Numerical Answers
8.82
8.95
8.104
8.106
8.110
29.5 cm
(a) 9.35 m/s (b) 3.29 m/s to the left
0.105 m/s to the right
1.29 m to the left
8.63 km from launch point; 5.33 105 J
3

PH1104/CY1305/SM2: Mechanics
Semester 1 2013
Mid-Term Exam 2
Nov 7, 2012
Answer ALL THREE (3) questions. Take g = 9.8 m/s2.
1.
A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass
until the spring is compressed a distance (see

MH1100/MTH112: Calculus I.
Problem list for Week #3.
This weeks topics:
Some basic properties of the absolute value function. (Appendix A
from [Stewart].)
The precise definition of limit. (Section 1.7 from [Stewart].)
Proving limits using the precise d

MH1100/MTH112: Calculus I.
Tutorial in the final week.
This weeks topics:
LHospitals rule.
Limits to positive and negative infinity.
Basics of antiderivatives and indefinite integrals.
Substitution method.
Integration by parts.
The problems that will

PH1104: Mechanics
Tutorial 11
Qualitative questions
1
Quantitative questions
2
3
Extra question
A uniform solid sphere with mass = 2.0 kg and radius = 0.10 m is
set into motion with angular speed o = 70 rad/s. At = 0 the sphere is
dropped a short distance

MH1100/MTH112: Calculus I.
Problem list for Week #2.
Tutorial in the week beginning 26th of August.
This weeks topics:
Some motivations for limits: tangents and velocities. (Section 1.4).
The basic concept of a limit. (Section 1.5).
Using the limit law

MH1100/MTH112: Calculus I.
Tutorial problems for Week #9.
This weeks topics:
Types of extreme values.
The Closed Interval Method.
Rolles Theorem and The Mean Value Theorem.
The tutor will aim to discuss problems: 3, 5, 9, 11, 15, 16, 18, 21, 22, 23,
an

Nanyang Technological University
Division of Mathematical Sciences, SPMS
AY 2015/2016 Semester 2
MH1810 Mathematics 1
Tutorial 8
Question 1
Let u = i + j 5k and v = 2i + j k. Find kuk, kvk, u v, u v, v u, and projv u.
Note that we have the formula:
) v
=

MH1810 Mathematics 1
Lecture 12
Rafael M. Siejakowski
NTU
Last time
Last week, we talked about complex numbers numbers of the
form x + yi with x, y R and i 2 = 1.
We defined algebraic operations +, , , on complex
numbers.
We also discussed different ways

Nanyang Technological University
MH1810 (FE1006) Mathematics 1
Tutorial 4
Announcement There is a 15-minutes Quiz 1 (10%) during tutorial class (TIME: XX:05 XX:20). The rst quiz contains 2-3 problems on topics discussed in Tutorials 1, 2 and 3.
Section A:

Nanyang Technological University
MH1810 (FE1006) Mathematics 1
Tutorial 6 (Solutions to Discussion Questions)
Discussion Questions
1. Evaluate the limit, if it exists.
(a)
lim
t 4
cos 2t
cos2 t sin2 t
(cos t sin t) (cos t + sin t)
= lim
= lim
cos t sin t

Nanyang Technological University
MH1810 (FE1006) Mathematics 1
Tutorial 4 Solutions to Discussion Questions
Basic Mastery
5. Use appropriate trigonometric identities to show that
p
p
(a) cos 12 = 14
2+ 6
p
p
2+ 6
(b) sin 512 = 14
Solution
(a)
cos
12
= cos

Nanyang Technological University
MH1810 (FE1006) Mathematics 1
Tutorial 2
Basic Mastery Question
1. For each of the following, nd jjujj, jjvjj ; u v,u
and projv u:
(a) v = i + j; u = 2i + j
(b) v = i + j + 2k; u =
(c) v = 2i + j
v, v
u; the angle
between

Nanyang Technological University
MH1810 (FE1006) Mathematics 1
Tutorial 1
Section A. Basic Mastery Questions.
This section comprises questions which are computational and basic to the topics discussed.
These problems will not be discussed during tutorial

MH1810 Mathematics 1
Lecture 10
Rafael M. Siejakowski
NTU
Last time
Last week, we discussed the fundamental concepts of analytic
geometry, describing points via coordinates and studying
differences of points, i.e. vectors, and their properties.
In particu

MH1810 Mathematics 1
Lecture 7
Rafael M. Siejakowski
NTU
Last time
In the previous lecture, we studied the notion of definite and
indefinite integrals and their relationship with antiderivatives.
We learnt the geometric interpretation of the definite inte

MH1810 Mathematics 1
Lecture 9
Rafael M. Siejakowski
NTU
Analytic geometry
In this lecture, we are going to revise basic methods of analytic
geometry. This is material from Chapter 12.
What distinguishes analytic geometry from synthetic geometry is
that a

MH1810 Mathematics 1
Lecture 11
Rafael M. Siejakowski
NTU
Last time
Last week, we discussed matrix algebra.
More specifically, we defined the operations of addition and
multiplication of matrices, whenever they can be performed.
We also defined the invers

MH1810 Mathematics 1
Lecture 8
Rafael M. Siejakowski
NTU
Last time
Last week, we talked about properties of integrals and methods
of integration:
Integration by substitution
Integration by parts
Integration of rational functions via partial fraction
decom