Faculty of Engineering
The University of Hong Kong
Dr. Kaimin Shih
2nd Semester, 2015-2016
ENGG1201: Engineering for Sustainable Development
Topic 4: Resource and Waste Management
[Office Hours: Feb.1
Determinants
Recall the 22 matrix inverse equation A 1 =
1 d b
ad bc c a
Is it possible to extend the result to matrix of dimension nn ?
We first look at the concept of determinant
a11 a12
For 2
Q1. In a lottery 10,000 tickets are sold for $1
each. There are five prizes: $5,000 (once),
$700 (once), $100 (three times). What is the
expected value of a ticket?
Answer. Let X denotes the value of
Q1. Let z = 1 i. Find |z| and Arg(z).
Answer.
|z| =
q
12 + (1)2 =
2 .
and
1
1
Arg(z) = tan
= .
1
4
1
Q2. Verify that each of the two numbers
z = 1 3i
satisfies the equation
z 2 2z + 4 = 0 .
Answer.
Matrices
As seen in the previous chapter, a matrix consists of vectors as
columns: A=[a1 a2 an]
For an mn matrix, its structure is
Two matrices are equal iff they have the same size and their
corre
Suggested solution for MATH 1853 homework 1
1. Determine the values of k so that the following system in unknowns x, y , z has:
(i) a unique solution, (ii) no solution, (iii) an infinite number of sol
MATH1853 (13/14 Semester 2) Assignment 3 (0%)
(Due date: 25 Apr 2014 5pm)
17-04-2014
Please submit your solution to the assignment box located on the 4th floor
of Run Run Shaw building. DO NOT COPY. L
MATH1853 (13/14 Semester 2) Assignment 4 (0%)
(Due date: NOT to be handed in)
30-04-2014
We will explain the solution to this assignment set on 08-05-2014(Thursday)
10:30am, Knowles Bldg 223.
1. Each
Eigenvalues and Eigenvectors
For an nn matirx A, if there is a nonzero vector x such that Ax=x
for some scalar , then is an eigenvalue of A, and x is the
eigenvector corresponding to
If we view A a
Q1. Let 3 = 1 and 6= 1.
Find the value of 2011 + 1997 + 1.
Answer. Since 3 = 1 we have
2011 + 1997 + 1
= 3670+1 + 3665+2 + 1
= + 2 + 1 .
Now we also have
0 = 3 1 = ( 1)( 2 + + 1) .
Since 6= 1, 2 + +
Inner Product
For two vectors u, v in Rn, the inner product is defined as
v1
v
uT v = [u1 u2 . un ] 2 = u1v1 + u2 v2 + . + un vn
#
vn
It is obvious that uTv= vTu
From inner product, we can d
Vectors
A real number is a point on the real line R
To describe a point on a plane R2, we use two numbers, e.g., (3,-1)
In fact, this is just an expression of a point using rectangular
coordinate s
The solid waste generation, transportation and disposal costs for two sources (1 & 2 ) and two disposal
sites (A & B) are:
Source
Generation (tons/wk)
Transportation Cost ($/ton)
1
100
5 (Site A)
12 (
MATH1853 (13/14 Semester 2) Assignment 2 (0%)
(Due date: 11 Apr 2014 5pm)
04-04-2014
Please submit your solution to the assignment box located on the 4th floor
of Run Run Shaw building. DO NOT COPY. L
Q1. Let A = cfw_1, 2, 3 and B = cfw_1, 3, 5, 6, 7.
(a) What are |A| and |B|?
(b) Find A B.
(c) Find A B.
(d) Write down all the subsets of A.
Answer. (a) |A| = 3 and |B| = 5.
(b)
A B = cfw_1, 3 .
(c)
Faculty of Engineering
The University of Hong Kong
Dr. Kaimin Shih
2nd Semester, 2015-2016
ENGG1201: Engineering for Sustainable Development
Topic 2: Atmosphere and Air Pollution
[Office Hours: Jan. 2
ENGG1201:
Engineering for
Sustainable Development
ENGG1201: Engineering for Sustainable Development
Course Coordinator
Dr. Kaimin SHIH
(Weeks 1, 2, 3, 4)
Professor Albert K.H. KWAN
Professor S.C. WONG
ENGG 1201 Engineering for Sustainable Development
Assessment Task 5
1.
Describe a completed engineering project (such as a water supply system, a
new town, an airport, a mass transit railway system, a
THE UNIVERSITY OF HONG KONG
FACULTY OF ENGINEERING
ENGG1201 Engineering for Sustainable Development
Study Topic: Sustainable Building Design and Construction
Date: Oct 6, 2016 TIME: 3:30PM
Student Name:
Faculty of Engineering
The University of Hong Kong
University ID#:
Dr. Kaimin Shih
1st Semester, 2016-2017
ENGG1201: Engineering for Sustainable Development
Topics 1-4 Homework Question
Engineering for Sustainable Development
ATMOSPHERE AND AIR POLLUTION
PROGRESS & OUTCOMES
Atmospheric Environment
Protect us from hostile environment
Absorbs cosmic rays & (some)
meteorites
Allow sun
ENGG1201:
Engineering for Sustainable Development
Sanghoon Lee, Ph.D.
Department of Civil Engineering
The University of Hong Kong
[email protected]
Study Topics
First Week:
Sustainability in Lifec
MATH1853 (13/14 Semester 2) Assignment 1 (0%)
(Due date: 28 Mar 2014 5pm)
21-03-2014
Please submit your solution to the assignment box located on the 4th floor
of Run Run Shaw building. DO NOT COPY. L
MATH1853 (13/14 Semester 2) Assignment 3 (0%)
(Due date: 25 Apr 2014 5pm)
17-04-2014
Please submit your solution to the assignment box located on the 4th floor
of Run Run Shaw building. DO NOT COPY. L
MATH1853 (13/14 Semester 2) Assignment 2 (0%)
(Due date: 11 Apr 2014 5pm)
04-04-2014
Please submit your solution to the assignment box located on the 4th floor
of Run Run Shaw building. DO NOT COPY. L
MATH1853 (13/14 Semester 2) Assignment 4 (0%)
(Due date: NOT to be handed in)
30-04-2014
We will explain the solution to this assignment set on 08-05-2014(Thursday)
10:30am, Knowles Bldg 223.
1. Each
MATH1853 (13/14 Semester 2) Assignment 1 (0%)
(Due date: 28 Mar 2014 5pm)
21-03-2014
Please submit your solution to the assignment box located on the 4th floor
of Run Run Shaw building. DO NOT COPY. L
Introduction
1. Explain situation
CHT convenient and cheap
2. Raise problem
Exceed Tunnel Design Capacity 78000 vehicles per day < 120000
3. Choose option C
Interpretation of option C
1. Private car
\
gm Cur;
THE UNIVERSITY OF HONG KONG
BACHELOR OF ENGINEERING: LEVEL cfw_I EXAMINATION
DEPARTMENT OF CIVIL ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
ENGINEERING FOR SUSTAINABLE DEVELOPMENT (ENG
i.
THE UNIVERSITY OF HONG KONG
BACHELOR OF ENGINEERING: LEVEL (I) EXAMINATION
DEPARTMENT OF CIVIL ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
ENGINEERING FOR SUSTAINABLE DEVELOPMENT (ENGGI006)
DA
Engineering for Sustainable Development
ATMOSPHERE AND AIR POLLUTION
PROGRESS & OUTCOMES
Atmospheric Environment
Protect us from hostile environment
Absorbs cosmic rays & (some)
meteorites
Allow sun
THE UNIVERSITY OF HONG KONG
ENGG1201
Engineering for Sustainable
Development
Transportation Systems
Professor S.C. Wong
Room 6-26, Haking Wong Building
Tel.: 2859 1964
Fax: 2559 5337
E-mail: [email protected]
Student Name:
University ID#:
Faculty of Engineering
The University of Hong Kong
Dr. Kaimin Shih
1st Semester, 2017-2018
ENGG1201: Engineering for Sustainable Development
Topics 1-3 Homework Question
ENGG 1201 Engineering for Sustainable Development
Name: Lam Yin Lok
UID: 3035493751
Topic: Tsing Ma Bridge
Background
Tsing Ma Bridge is the only connection road between Tsing Yi and Lantau Island, th