Coating mPEG-amine on [email protected]
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
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
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
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 (
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
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
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
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
Proceedings of the 35th
Conference on Decision and Control
Kobe, Japan December 1996
FA10 950
An Automatic Choosing Control for Nonlinear Systems
Kitoshi Taka,ta,
Department of Electrical and Electronics Engineering
Kagoskima University
Korimoto, Kagoshim
Triumph Of The Lean Production System
Krafcik, John F.
Sloan Management Review; Fall 1988; 30, 1; ABI/INFORM Global
pg. 41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of
How to audit a business process excellence
implementation?
Niels Gorm Mal Rytter ([email protected])
Aalborg University, Denmark
Torben Knudby
Copenhagen University College of Engineering, Denmark
Kim Hua Tan
Nottingham University Business School, UK
Rik
9.7.2009
1/4
Less work, better forecasts:
More efficient and accurate demand
forecasting with quantitative forecasting tools!
Manufacturing companies rely on demand forecasts to control purchasing, production,
inventories, and capacity. This means that fo
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
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
ENGG1006 Engineering for Sustainable Development
Measurement and Conversion Tables
Dr. Scott Smith Department of Civil Engineering The University of Hong Kong E: [email protected], T: 2241 5699, Office: 6-10 (Haking Wong Building) Consultation Times: Thursda
ENGG1006 Engineering for Sustainable Development
Theme: Engineering Systems Topic: Infrastructure Development 1 Teaching Week: 7 (2010-11 S1)
Dr. Scott Smith Department of Civil Engineering The University of Hong Kong E: [email protected], T: 2241 5699, Offi
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-