I_
SUBJECT: CHEMISTRY FOR ENGINEERS
Dean of School of Biotechnology
THE INTERNATIONAL UNIVERSITY. (1U) VIETNAM NATIONAL UNIVERSITY HCMC
FINAL EXAMINATION
Exam code: X):
Date: January 5&1? , 21113
.; Duration: 120 minutes
Name: . Student ID:
Score

Tangent Planes and
Linear Approximations
By
Assoc.Prof. Mai Duc Thanh
Tangent Planes
Find tangent plane to a surface z = f(x,y)
at (a,b,f(a,b)
z f ( x, y )
General Case
Consider graph z = f(x,y) at (a,b,f(a,b). To
find the equation for the tangent plane
w

Directional Derivatives
and the Gradient Vector
By
Assoc.Prof. Mai Duc Thanh
Contour map of the temperature T.
Tx at a location such as Reno is the rate of change of
temperature with respect to distance if we travel east from Reno;
Ty is the rate of chang

Double Integrals in
Polar Coordinates
By
Assoc.Prof. Mai Duc Thanh
1. Polar Coordinates
(Chap 10 of Textbook)
Polar coordinate system consists of
-a pole O
-a polar axis: a ray from O horizontal
to the right
Polar coordinates of a point P is P(r, )
r =dis

Chapter 5:
Line and Surface Integrals
Lecture 1
Vector
Fields
Line Integrals
1. Vector Fields
Velocity field
Air velocity vectors that indicate the wind speed
and direction at points
Let D be a set in R2 (a plane region). A vector
field on D is a function

Maximum and
Minimum Values
By
Assoc.Prof. Mai Duc Thanh
Local maximum and minimum
Definition 1. A function of two variables f(x,y) has a
local maximum at (a,b) if f(x,y) f(a,b) when (x,y)
near (a,b).
r 0 s.t. f ( x, y ) f (a, b),
( x, y ), ( x - a) 2 ( y

Surface Area and
Triple Integrals
By
Assoc.Prof. Mai Duc Thanh
1. Surface Area
Divide domain D of z=f(x,y) into subrectangles
Parts of tangent plane above each subrectangle
approximate patches in the graph
Approximation gets better and better when
subr

Chapter 5:
Line and Surface Integrals
Lecture 2
The
Fundamental Theorem for Line Integrals
Greens Theorem
Curl and Divergence
1. The Fundamental
Theorem for Line Integrals
Motivation
Recall that the Fundamental Theorem of
Calculus can be written as
b
F

Chapter 2: Geometry of Space
and Vector Functions
Lecture 2:
Vector Functions and Space Curves
Definitions
Introduction
A parametric curve in space or space curve is a set
of ordered (x, y, z), where
x = f(t), y = g(t), z = h(t)
(1)
Vector-Valued Funct

Outline
Integral and Comparison Tests
Absolute and Conditional Convergence
Chapter 1: Sequences and Series
Lecture 3: Convergence Tests
Assoc. Prof. Mai Duc Thanh
September 15, 2015
Assoc. Prof. Mai Duc Thanh
Chapter 1: Sequences and Series Lecture 3: Con

Chapter 3: Partial derivatives
Lecture 1: Functions of Several
Variables
Example 1.
Ohms law: Voltage drop across resistor
V=RI
We say that V is a function of two variables
R and I
Example 2
The volume V of a circular cylinder depends
on its radius and it

Partial Derivatives
By
Assoc.Prof. Mai Duc
Thanh
Partial Derivatives
Rate of change of a function f(x,y)
depends on the direction
Begin by measuring the rate of
change if we move parallel to the x
or y axes
These are called the partial
derivatives of the

Sequences Convergence & Divergence of Sequences Limit Laws of Sequences Monotone Sequences Bounded S
Chapter 1: Infinite Sequences and Series
Lecture 1: Sequences
Assoc. Prof. Mai Duc Thanh
February 14, 2016
Assoc. Prof. Mai Duc Thanh
Chapter 1: Infinite

Lecture: Iterated Integrals
by
Assoc.Prof. Mai Duc Thanh
How to evaluate double integrals?
Motivations
Let a function f(x,y) be defined on a rectangle
R=[a, b]x[c, d]
We can take integral with respect to x and y
separately:
b
d
a
c
f ( x, y)dx g ( y), f

Chapter 4: MULTIPLE INTEGRALS
Lecture: Double
Integrals over
Rectangles
How can you evaluate the water amount in a lake?
CHAPTE
R
4
Assoc.Prof. Mai Duc Thanh
07:38:15 AM
Volumes and Double Integrals
2
Consider a function of two variables defined on a
clos

Double Integrals over
General Regions
Double Integrals over Bounded Region
Let D be a bounded region
D can be enclosed in a rectangle R
We define a new function F with domain R by
f ( x, y ), if ( x, y ) D
F ( x, y )
if ( x, y ) D
0,
R
D
Definition
If t

Outline
Power Series
Representing Functions as a Power Series
Chapter 1: Sequences and Series
Lecture 4: Power Series
Assoc. Prof. Mai Duc Thanh
September 22, 2015
Assoc. Prof. Mai Duc Thanh
Chapter 1: Sequences and Series Lecture 4: Power
Outline
Power S

Lagrange Multipliers
By
Assoc.Prof. Mai Duc Thanh
Example
The profit from the sale of x units of radiators
for automobiles and y units of radiators for
generators is given by
P(x,y)= -x2 y2 + 4x + 8y
Problem: Find values of x and y that lead to a
maximum

LIMITS AND CONTINUITY
By
Assoc.Prof. Mai Duc Thanh
Definition
lim
( x , y ) ( a ,b )
f ( x, y ) L if for every 0, there exists 0
such that if 0 ( x a) 2 ( y b) 2 then f ( x, y) L
That is, we can make f(x,y) as close to L as we like by
taking (x,y) suffic

Triple Integrals in
Cylindrical and
Spherical Coordinates
By
Assoc.Prof. Mai Duc Thanh
Cylindrical Coordinates
A point P(x, y, z)
is represented by
the ordered triple
(r, , z) ,
where:
r and are polar
coordinates of the
projection of P
onto the xy-plane
M

Applications of Double Integrals
By
Assoc.Prof. Mai Duc Thanh
Density and Mass
A lamina occupies a region D of the xy-plane and its
density (in units of mass per unit area) at a point (x, y)
in D is given by (x, y), where is continuous on D.
This means:
m

Series
Chapter 1: Sequences and Series
Lecture 2: Series
Assoc. Prof. Mai Duc Thanh
Department of Mathematics
International University Ho Chi Minh City
February 14, 2016
Assoc. Prof. Mai Duc Thanh
Chapter 1: Sequences and Series Lecture 2: Series
Series
S

Chapter 5:
Line and Surface Integrals
Lecture 3
Parametric Surfaces and Their Areas
Surface Integrals
Parametric Surfaces and
Their Areas
We use vector functions to describe
general surfaces, called parametric
surfaces, and compute their areas
Definition

The Chain Rule
By
Assoc.Prof. Mai Duc
Thanh
Recall
We recall that the Chain Rule for functions of
a single variable gives the rule for
differentiating a composite function: If y=f(x)
and x=g(t), where f and g are differentiable
functions, then y is indir

Outline
Taylor and Maclaurin Series
Binomial Series
Chapter 1: Sequences and Series
Lecture 5: Taylor and Maclaurin Series
Assoc. Prof. Mai Duc Thanh
September 7, 2015
Assoc. Prof. Mai Duc Thanh
Chapter 1: Sequences and Series Lecture 5: Taylor
Outline
Ta

Chapter 5:
Line and Surface Integrals
Lecture 4
Stokes Theorem
Divergence Theorem
1. Stokes Theorem
Positive Orientation of a Boundary Curve
Let S be an oriented surface. The orientation of S induces the
positive orientation of the boundary curve C: if y

Fallacies
How many legs does this elephant have?
Is this wave moving?
We will learn.
1. Fallacies
of Relevance
Common mistakes in reasoning
(frequently committed and often
psychologically persuasive)
What
mistake!
2. Fallacies of
Insufficient
Evidence
Wha

Introduction to Critical
Thinking
Dr. Pham Huynh Tram
Department of Industrial & Systems Engineering
RA2.602 phtram@hcmiu.edu.vn
Today class
What this course is about
Course aim & Expected Learning
Outcomes
How we work together
How your performance is

Chemistry for Engineers - Tuesday classe
QUIZ 1: MEASUREMENT, MATTERS
1) In _ solids, particles randomly distributed without any long-range
pattern
a) crystalline
b) armosphous
c) Both crystalline and armosphous
d) Not listed here
.
2) As a solid element

School of Biotechnology, International UniversityHCMC
Department: Applied Chemistry
Course Syllabus
CHEMISTRY FOR ENGINEERS
(Code: CH011IU)
COURSEOVERVIEW
This onesemester course is designed for engineering students those who are pursuing a non
chemi

THE INTERNATIONAL UNIVERSITY (IU) VIETNAM NATIONAL UNIVERSITY HCMC
FINALEXAMINATION
Exam code:
Date:
Duration:
Name:.
01
June 9th, 2014
120 minutes
Student ID: .
SUBJECT: Chemistry for Engineers
Head of
Academic Affairs
Dean of School of
Biotechnology
Lec

Fallacies of Insufficient Evidence
Arguments in which the premises, though
logically relevant to the conclusion, fail
to provide sufficient evidence to support
the conclusion.
Fallacies of Insufficient Evidence
Inappropriate Appeal to
Authority
Questionab

Our very eyes are sometimes,
like our judgments, blind
- Shakespeare
Evaluating Arguments
What good argument does not mean?
Good argument does not mean agrees with my view
Mistake: confuse good argument with argument whose conclusion I
agree with
Good ar