Coating mPEG-amine on PDA@AuNP
Polydopamine coatings also support a variety of reactions with organic species for the creation of organic
ad-layers. For example, under oxidizing conditions, it is known that catechols react with thiols and
amines iva Micha
Chapter 4
nates
Parametric Equations and Polar Coordi-
Denition [200] If x and y are given as functions
x = f (t),
y = g (t)
over an interval I of t-values, (can think of t as the time), then the set of points (x, y ) =
(f (t), g (t) dened by these equati
Chapter 3
Applications of Derivatives
The number in [ ] refers to the page number of our textbook
Theorem 1 - The Extreme Value Theorem [139] If f is continuous on a closed interval
[a, b], then f attains both an absolute maximum value M and an absolute m
Chapter 2
Dierentiation
The number in [ ] refers to the page number of our textbook
Denition [67] The derivative of a function f at a point x0 , denoted f (x0 ), is
f (x0 + h) f (x0 )
h0
h
f (x0 ) = lim
provdied this limit exists.
Read Eg.1 [67].
[68]
If
Chapter 1
Limits and Continuity
The number in [ ] refers to the page number of our textbook
Eg. 1, 2 [4] An rock falls from a cli and the distance it falls through after t seconds is
given by y = 4.9t2 . The average velocity of the rock for the rst 2 seco
Worked Examples
July 31, 2012
1
Limits and continuity
x2 + 3x 10
by cancelling a common factor .
x 1
x2 + 5 x
1. Find the limit lim
Ans :
x2 + 3x 10
(x 2)(x + 5)
(x 2)
= lim
= lim
= 1
2 + 5x
x1
x 1
x1
x
x(x + 5)
x
lim
x2 + 9 3
2. Find the limit lim
by cre
13
Bernoulli Experiment and Its Related Distributions
An experiment is called a Bernoulli experiment if there are only two possible
outcome: success with probability p and failure with probability (1 p) where
0 < p < 1.
We say x is a Bernoulli random vari
Figure 1: St Augustine and Monica by Ary Scheer (1846). Taken from Wikipedia.
4
Some History of Probability*
This section is optional and it aims to introduce some story of probability.
With the advent of Christianity, the concept of random events develop
Chapter 7
Transcendental Functions
7.5 Indeterminate Forms and L Hpitals Rule
o
Theorem 5 - L Hpitals Rule [377] Suppose that f (a) = g (a) = 0, that f and g are
o
dierentiable on an open interval I containing a, and that g (x) = 0 on I if x = a. Then
f (
MATH 1851 - Laplace Transforms
(A)
Basic concepts
The Laplace transform of a function f (t) is defined by
L ( f (t ) ) L( f )
0
e st f (t ) dt F ( s) ,
f (t ) L1 ( F (s),
where t is usually time. The convention here is that small letter is used for the f
THE UNIVERSITY OF HONG KONG
BACHELOR OF ENGINEERING: LEVEL (I) EXAMINATION
DEPARTMENT OF CIVIL ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
ENGINEERING FOR SUSTAINABLE DEVELOPMENT (ENGG1006)
DATE: 18 December 2010
TIME: 9:30 am - 12:30 pm
(3 hours)
An
THE UNIVERSITY OF HONG KONG
BACHELOR OF ENGINEERING: LEVEL (I) EXAMINATION
DEPARTMENT OF CIVIL ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
ENGINEERING FOR SUSTAINABLE DEVELOPMENT (ENGG1006)
DATE: 9 May 2009
TIME: 9:30 am - 12:30 pm
(3 hours)
Answer A
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 system
3
If we put the coordinates as , we have a vecto
System of linear equations
A simple example: x 2 x = 1
1
2
x1 + 3 x2 = 3
x1 = 3, x2 = 2
Physical meaning: Solution is
the intersection point of two
lines
Other possibilities: No solution
or infinite many solutions
1
Y.C. WU - HKUEEE
Example of three
MATH 1851 - Ordinary Differential Equations (ODEs)
(A)
First order equations
A linear, first order ODE is always solvable by the method of integrating factor:
dy
p ( x) y q ( x) .
dx
Multiplying by (the integrating factor)
exp
p( x) dx
will turn the le
Q1. Find the average rate of change of the
function dened by P () = 3 42 + 5 on
the interval [1, 2].
Ans. Average rate of change (check denition)
is P/ which is
P (2) P (1)
=0 .
21
1
Q2. Find the tangent line to the curve y =
2 x3 at the point (1, 1).
Ans
Math1851, Tutorial 2 (for 2/10-6/10)
FLT
Please go through all 10 problems before your tutorial session.
1. (Ex1.5: #60) If functions f (x) and g (x) are continuous for 0 x 1,
could f (x)/g (x) possibly be discontinuous at a point of [0, 1]? Give
reasons
Math1851, Tutorial 1 (for 24/9-28/9)
FLT
Please work on the following 10 problems before your tutorial session.
1. (Ex1.1: #6) Find the average rate of change of the function dened by
P () = 3 42 + 5 on the interval [1, 2].
2. (Ex1.1: #12) Find the tangen
3
Complex Variables
The imaginary number i is the solution of the equation
x2 + 1 = 0.
This idea of i was introduced to answer the above question. But then it results in
many interesting results, beautiful theory and useful applications.
In general a comp
MATH 1853 Probability Theory & Statistics
(0) A Review on set theory and basic calculus.
(1) Elementary Complex Variables: Arithmetic of complex numbers; Modulus argument and conjugate; Basic properties and operations of complex numbers;
Argand diagram; A
MATH 1853 Homework (Fall 2012)
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 solutions:
x 2y =1
x y + kz = 2
ky + 4 z = 6
2. Let W be the solution s
ENGG1006 Engineering for Sustainable Development
Teaching Week Topic (Teacher) Course Learning Outcomes Assessment Task Number Main Learning Outcomes of Each Lecture
Theme: Engineering Systems
6 Engineering Systems: Past and Present Dr. S.T. Smith Infrast
ENGG1006 Engineering for Sustainable Development
Learning Outcomes of ENGG1006 (Related to Dr Smiths Lectures)
Describe the natural and built environment and argue the role engineers have played and will play, Describe modern engineering systems and discu
ENGG1006 - Engineering for Sustainable Development
RESOURCE AND WASTE MANAGEMENT
Resource Consumption and Prediction
Dr. Kaimin Shih
DEPARTMENT OF CIVIL ENGINEERING THE UNIVERSITY OF HONG KONG
Office: Rm. 6-30, Haking Wong Building x Phone: 2859-1973 x E-
ENGG1006 - Engineering for Sustainable Development Provide sustainable supply of water quantity. Protect and restore the water quality.
Keeping sustainable water resources is to.
SUSTAINABLE WATER ENVIRONMENT
Dr. Kaimin Shih
DEPARTMENT OF CIVIL ENGINEERIN
Faculty of Engineering Dr. Kaimin Shih The University of Hong Kong 1st Semester, 2010-2011 ENGG1006: Engineering for Sustainable Development
Topic 2: Atmosphere and Air Pollution
[Office Hours: Sep. 14, 21, and October 05 (Tuesdays) 5-7pm, Haking Wong Bui
ENGG1006 - Engineering for Sustainable Development
ATMOSPHERE AND AIR POLLUTION
Dr. Kaimin Shih
DEPARTMENT OF CIVIL ENGINEERING THE UNIVERSITY OF HONG KONG
Office: Rm. 6-30, Haking Wong Building Phone: 2859-1973 E-mail: kshih@hku.hk
PROGRESS & OUTCOMES
1
ENGG1006: ENGG1006: Engineering for Sustainable Development
ENGG1006: Engineering for Sustainable Development
Course Coordinator
Dr. Scott T. SMITH
(Week 6, 7, 9, 12, 13)
Dr. Kaimin SHIH
(Week 1, 2, 3, 4, 5)
Professor S.C. WONG
(Week 8)
Dr. Sam C M Hui
(W