Turk J Chem
34 (2010) , 593 602.
ITAK
c TUB
doi:10.3906/kim-0907-124
Synthesis and characterisation of vanadium(III)
complexes of biphenylphenols
Neeraj SHARMA, Maridula THAKUR and Subhash Chand CHAUDHRY
Department of Chemistry, Himachal Pradesh Universi
MANUAL PENGURUSAN PENTADBIRAN, TUGAS RASMI GURU & TAKWIM 2014
MAKLUMAT GURU & SENARAI TUGAS 2014
Nama : .
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No. Kad
Pengenalan : .
Alamat Rumah :
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.
.
.
.
No. Telefon (R) : . No. Telefon
(B) : .
Jawatan
: .
Jawatan : .
Gred
No . Fail JPN : .
SPP : .
NUMBER SYSTEM
Learning outcomes:
At the end of the lesson the student should be
able to
define complex numbers.
represent a complex number in Cartesian form.
understand the equality of two complex numbers.
understand the conjugate of a complex number.
per
Number System
Indices
1
Learning outcomes
At the end of the lesson, student should be able to
(a) define indices.
(b) state the rules of indices such as am x an = am+n,
am an = am - n and (am )n = amn .
(c) solve equations which involve index
2
The index
CHAPTER 2:
EQUATIONS,
INEQUALITIES &
ABSOLUTE VALUES
1
2.1 QUADRATIC
EXPRESSIONS &
EQUATIONS
2
LEARNING OUTCOMES:
At the end of the lesson, the students should
be able to:
(a)Define quadratic equation
(b)Solve quadratic equations by
(i) Factorization
(ii)
CHAP.1: NUMBER SYSTEM
Real number
1
Learning Outcomes
(a)
(b)
(c)
(d)
(e)
(f)
(g)
To define and understand natural, whole, integers, prime
numbers, rational and irrational numbers.
To represent rational and irrational numbers in decimal
form,
To represent
LOGARITHMS 2012
- The number 100 can be expressed as , that is =
- An equivalent form of = is
=
- = is said to be in index form.
- = is equivalent logarithmic form.
- Definition: Let > , and is a positive real number
such that = . Then,
=
that is is
SYSTEM OF REAL NUMBERS
(Chapter 1 Part 3)
Dr. Hjh. Noraini Abdullah
Faculty of Science and Natural Resources
In this chapter, you will
define number systems based on
those numbers that anyone is
familiar with: the natural numbers.
define - the 'real numb
COMPLEX NUMBER
(Chapter 1 Part 4)
Dr. Hjh Noraini Abdullah
3rd Floor, Room 48
Faculty of Science and Natural Resources
In this chapter, you will
see how the real number system is only a
part of a larger number system; call the
"complex" numbers.
see how t
Introduction
Refer to the American Heritage Dictionary of the English Language,
mathematics is the study of the measurement, properties, and relationships
of quantities and sets, using numbers and symbols. Mathematical had been
invented early in ancient E
HYPERBOLIC FUNCTIONS
Stan Wagon riding his tricycle with square wheels
(a mathematician at Macalester College in St. Paul)
HYPERBOLIC FUNCTIONS
Definitions
and
Identities
HYPERBOLIC FUNCTIONS
x
e e
cosh( x)
2
x
x
e e
sinh( x)
2
x
We pronounce
cosh(x)
si
SYSTEM OF REAL
NUMBER
(Chapter 1 Part 3)
Dr Hjh Noraini Abdullah
Faculty of Science and Natural
Resources
In this chapter, you will
define
number systems based on
those numbers that anyone is
familiar with: the natural numbers.
define - the 'real number
10/8/2014
Discrete Mathematics/Set theory/Answers - Wikibooks, open books for an open world
Discrete Mathematics/Set theory/Answers
Contents
1 Answers to Set Theory Exercise 1
2 Answers to Set Theory Exercise 2
3 Answers to Set Theory Exercise 3
4 Answers
10/30/2014
3. Graphical Representation of Complex Numbers
interactive mathematics
Learn math by playing with it!
Home
Complex Numbers
3. Graphical Representation
3. Graphical Representation of Complex Numbers
by M. Bourne
We can represent complex number
10/8/2014
Discrete Mathematics/Set theory/Exercises - Wikibooks, open books for an open world
Discrete Mathematics/Set theory/Exercises
Contents
1 Set Theory Exercise 1
2 Set Theory Exercise 2
3 Set Theory Exercise 3
4 Set Theory Exercise 4
5 Set Theory E
SJ10103
10/18/2014
Definition to elasticity
Elasticity measures the magnitude of responsiveness
of any variable to a change in one of the determinants
factors.
Formula of elasticity
The value of elasticity can be
measured by:
Elasticity , E =
For example
Logarithm and Exponential
Functions
Overview of logs and exponential functions
Logarithm is an exponent
Inverse functions
Log functions and exponential functions are
inverses of one another
Properties of logarithms
Logarithms/exponentials in scientific
Logic and Truth Tables
What is a Truth Table?
A truth table is a tool that helps you analyze statements or arguments in order to verify
whether or not they are logical, or true. There are five basic operations that you will utilize
when creating a truth t
Set Theory
(Chapter 1 Part 2)
Dr Hjh Noraini Abdullah
Faculty of Science and Natural Resources
In this chapter, you will
learn
the basic terms and facts about sets
see how sets can be combined to yield other sets.
LEARNING OUTCOMES
At the end of this chap
COMPLEX NUMBER
(Chapter 1 Part 4)
Dr Hjh Noraini Abdullah
Faculty of Science and Natural Resources
In this chapter, you will
see
how the real number system is only a
part of a larger number system; call the
"complex" numbers.
see how the interpretations
2.1 Introduction-Functions and Inverses
A function is a rule that assigns a unique value to every member in
its domain.
3
2
9
3
5
1 7
0
f
Notation: f (2) = 1, f (3) = 7, f (5) = 3 and f (9) =0
f consists of ordered pairs (2,1) (3, 7) (5, 3) (9, 0)
3
2
9
3
SJ10103
10/18/2014
INTRODUCTION
Consumer Choice Theory is important in economic
activities because producers are always competing
with each other to get consumers to buy their
products. Consumer Choice Theory further explains
the existing behaviour of con
10/30/2014
4. Polar Form of Complex Numbers
interactive mathematics
Learn math by playing with it!
Home
Complex Numbers
4. Polar Form
4. Polar Form of a Complex Number
by M. Bourne
We can think of complex numbers as vectors, as in our earlier example. [
190
Chapter 9 Applications of Integration
It is clear from the gure that the area we want is the area under f minus the area
under g, which is to say
9
1
2
2
2
g(x) dx =
f (x) dx
1
1
f (x) g(x) dx.
It doesnt matter whether we compute the two integrals on
10/3/2014
Sets, Subsets, and Set Operations
Sets, Subsets, and Set Operations Summary
Sets | Subsets | Set Operations
Sets
A set is a collection of items which can be anything. A set is denoted with braces
or "curly brackets," such as:
cfw_2, 4, 6, 8, 10,
SJ10103
10/3/2014
Definition of market equilibrium
Equilibrium price and output
Market equilibrium is a situation where
quantity demanded and quantity
supplied are equal and there is no
price or quantity to change.
Market equilibrium is determined by the
Limits
Continuity
Derivative
Calculus for the Life Sciences I
Lecture Notes Limits, Continuity, and the Derivative
Joseph M. Mahay,
mahaffy@math.sdsu.edu
Department of Mathematics and Statistics
Dynamical Systems Group
Computational Sciences Research Cent
*Please write up ONLY the final answer.
No need to show your calculation. Due
DATE 12/12/14 before 00:00 AM.
NAME:
MATRIC NUM:
PROGRAMME:
Exercises - Area
Example
1. Find the area of the finite region bounded by the curves
ANS:
2. Find the area of the fin
12/8/2014
3.Areabetween2Curves
interactivemathematics
Learnmathbyplayingwithit!
Home
ApplicationsofIntegration
3.AreaBetween2Curves
3.AreaBetween2Curves
byM.Bourne
Wearetryingtofindtheareabetween2curves,y
f x andy
f x ,andthelinesx
aandx
b.
Weseethatifwes