2007/2008 SEMESTER 1 - SUPPLEMENTARY EXAMINATION
Course
:
Diploma in Business Management
Diploma in Marketing
Diploma in Sport & Wellness Management
Diploma in Accountancy & Finance
Diploma in Banking & Financial Services
Module
:
BM0003 Principles of Acc
NANYANG POLYTECHNIC
SCHOOL OF BUSINESS MANAGEMENT
Microeconomics (BM 0007)
Tutorial 5
Discussion Questions:
1.
Calculate the price elasticity of demand of a Nissan March car when price of the car
rises from $65,000 to $70,000 and quantity demanded decreas
(1-5) Value and compensation
i
.
FM
Answer: d
MEDIUM
The primary operating goal of a publicly-owned firm trying to best serve its stockholders should be to
a.
b.
c.
d.
e.
Maximize managers' own interests, which are by definition consistent with maximizing
Todays lecture
Critical points of multi-variable functions:
Local maxima, minima, and saddle points
Finding the absolute maximum and minimum
of a multi-variable function on a given domain
1
First topic:
Critical points of multi-variable
functions: Local
MH1402 Algorithms & Computing II
Lecture 4 Functions (Part1)
Wu Hongjun
1
Overview
Functions
Declaration, definition, function call
Variables
Local and Global Variables
Passing by Reference
Function Overloading
Separate Compilation and Libraries
M
Todays lecture
Vectors in 3-dimensional space (review)
Vectors in n-dimensional space Rn
(Euclidean n-space)
Linear combinations of vectors in Rn.
The span of a collection of vectors in Rn.
1
Overview of this part of the course
We have already seen th
MH1402 Algorithm & Computing II
Lecture 1 Data Types
Wu Hongjun
1
Overview
Identifier, Keyword
Variables
Data Types
2
Identifier and Keyword
Any item being defined in a C+ program must have an identifier
Identifiers are names for variables, functions
Todays Lecture:
Properties of matrix multiplication
Writing linear systems as matrix
equations
The inverse and determinant of a
square matrix
Reminder
An m x n matrix is an array of numbers with m rows
and n columns:
a11 a12 ! a1n
a21 a22 ! a2 n
A
Todays lecture
Vectors in 3-dimensional space (review)
Vectors in n-dimensional space Rn
(Euclidean n-space)
Linear combinations of vectors in Rn.
The span of a collection of vectors in Rn.
Overview of this part of the course
We have already seen that
Todays Lecture:
More properties of the determinant
The transpose of a matrix
Formula for the inverse of a square matrix
Cramers Rule for solving linear systems
Facts about determinants
The following facts are not proved in this course. But they are
ea
Todays Lecture:
Review of properties of the determinant
Determinant formula for the inverse matrix
(reminder from last lecture)
Solution of linear systems by Cramers Rule
Powers of matrices
Diagonalization of matrices. Eigenvectors
and eigenvalues.
R
Why attend the lectures?
The lectures are video recorded, so you could stay home and
watch them online. But that is not a good idea!
Attending the lectures is more efficient timewise.
Can ask questions during or after the lecture. And
discuss with other
Todays lecture
Introduction to functions of several variables
Partial derivatives
Chain rule for differentiation of functions of
several variables.
1
First topic:
Introduction to functions of several
variables
Examples of functions of several variables
March29,2016
Isotopes
H
Isotopes
Li
B
N
O
Na Mg
Al
P
S
K
Ca
Sc
Cr Mn Fe
Co
Rb
Rh
Cs
Ir
3/29/2016
He
Isotopes
Ni
Cu Zn Ga
Se
Ag
Te
Hg
Churchill AdvancedInorganicChemistry
Tl
Pb
Cl
I
1
Mainpointsoflastclass
Explainformationconstants,versusEquilibrium
const
Delta bond ()
Also, a glimpse at chromocene.
The options.
Molecular orbitals.
More about the radical anions.
Resonance structures.
of perchlorate.
Hydrogen chromate.
Ligand non-innocence!
Metalloids: What and Where!?
Cyclooctatetraene (Cyclo octa
CH107 College Chemistry
Prologue: Scientific Method
Prologue: Scientific Method
First Steps: Formation of a
hypothesis
Starts with observations, discoveries
or accumulation of data
Hypothesis a tentative explanation
of observations or data
Prologue: Scien
COLLEGE CHEMISTRY CH107 FALL SEMESTER 2009
QUIZ 1 (Chapters 1 3).
Answer all 12 questions, choosing a single letter for each.
Time allowed: 10 minutes
1. Heat energy flows from a region of high temperature to a region of cooler
temperature spontaneously.
Todays lecture
Directional derivatives and gradient
Critical points of multi-variable functions.
Local maxima, minima and saddle points.
Finding the maximum and minimum of a
multivariable function in a given domain.
1
First topic:
Directional derivativ
Todays lecture
Subsets vs. Subspaces of Rn
Linear (in)dependence of vectors in Rn.
Basis and dimension for a subspace of Rn
and for Rn itself.
Subsets versus subspaces
Here are some subsets of R2. Which of them are subspaces?
2
Reminder about subspaces
Todays lecture
Dot product and orthogonality for vectors
We generalize the geometric concepts of length
and angles from R2 and R3 to vectors in Rn.
Vectors in 2- and 3-dimensional space have length
(and direction). Also have an angle between two vectors.
Todays Lecture:
How to solve systems of linear equations
Solving linear systems whose augmented
matrix is in row-echelon form. (Review)
Solving linear systems in general by Gaussian
Elimination.
How to determine whether a linear system has
solutions, a
Todays lecture
Dot product and orthogonality for vectors
We generalize the geometric concepts of length
and angles from R2 and R3 to vectors in Rn.
Vectors in 2- and 3-dimensional space have length
(and direction). Also have an angle between two vectors.
Todays Lecture:
Properties of matrix multiplication
Writing linear systems as matrix
equations
The inverse and determinant of a
square matrix
1
Reminder
An m x n matrix is an array of numbers with m rows
and n columns:
a11 a12 a1n
a21 a22 a2 n
A
Todays lecture
Introduction to functions of several variables
Partial derivatives
Chain rule for differentiation of functions of
several variables.
1
First topic:
Introduction to functions of several
variables
Examples of functions of several variables
Todays Lecture:
Method for solving a system of linear equations
Bringing the augmented matrix into rowechelon form
Solving a linear system whose augmented
matrix is in row-echelon form
1
General idea for solving a linear system
a11x1 a12 x2 a1n xn b1
Todays lecture
Basis and dimension for a subspace of Rn
and for Rn itself.
Finding a basis for a subspace
Hyperplanes in Rn : Generalization of
planes to higher dimensions
Basis for a subspace
Let V be a subspace of Rn. A basis for V is a collection of
Todays Lecture:
An application of linear algebra:
Coupled harmonic oscillators
Coupled oscillators
There are many physical systems where the components are
coupled in a way that causes them (or allows them) to oscillate
with the same frequency. Here is a
Todays lecture
Bases for subspaces of Rn.
Hyperplanes in Rn:
Generalization of planes to higher dimensions.
1
Reminder: Subspaces
Subspaces are subsets of Rn that are closed under addition and
scalar multiplication.
Theorem: A subset is a subspace if an
Chapter 8
Modern Atomic Theory
Setting the Stage Emission of
Light
The beautiful color of fireworks comes from
the particular elements used.
The colors are characteristic of the elements
and can be used to understand their
properties.
Malone and Dolter -
Chapter 10
The Gaseous State
Setting the Stage The
Atmosphere
The atmosphere protects the planet and provides chemicals
necessary for life.
Oxygen supports metabolism and provides energy to living
things.
Nitrogen is incorporated into living organisms as
Chapter 9
The Chemical Bond
Setting the Stage Salt and Water
Earth is a complex world of chemicals
We will focus on two basic types of
compounds:
Salt (sodium chloride) is a typical ionic
compound
Water is a typical molecular compound
These substances are
Chapter 11
The Solid and Liquid States
Setting the Stage Ice floating on
Water
We all know that ice floats in water.
This turns out to be very unusual
behavior, since most solids sink in
their liquids (the solids are more
dense than the liquids).
Life on
Chapter 14
Oxidation-Reduction Reactions
Setting the Stage Electron Flow
The flow of electrons is common.
It occurs naturally (lightning) and as a
result of human activity (electricity).
Early electrical experiments involved
chemically generated electrici