Applied Mathmatics

3. Assignment&Presentation:
Applied Mathematics
Prepared By:
Royal Benchers
Submitted To:
Sir Zeeshan Ghani Sahib

4. Royal Benchers
The

5. Group Members
Zubair Mughal (Group Leader)
Nabeel Ahmed
Waqar Ali
Abdul Qayyum
Khadija Majeed
Zara Munir
Soha Mazher

6. Algebra is the branch of mathematics that
uses letters in place of some unknown
numbers.
Basic Algebra
Definition:
The part of mathematics in which letters
and other general symbols are used to
represent numbers and quantities in
formulae and equations.
Basic Definition:

7. The word algebra originated from the title
of the book ilm al-jabr w'almuqabala, a
book written during the ninth century the an
Arabian mathematician named al-
Khworizimi. The original title was translated
as the science of restoration and
reduction, basically meaning transposing
and combining similar terms of equations.
Translated in Latin toal-jabr (the union of
broken parts) led to the term we now refer
to as Algebra. Algebra was brought from
ancient.
Introduction To Algebra
History:

8. Fundamentals:
Essentially, Algebra evolved from the rules
and operations of arithmetic which begins
with the four operations: addition,
subtraction, multiplication and division of
numbers. Operations in algebra follow the
same rules as those in arithmetic. Algebra
uses variables which is a symbol that
represents a number and expressions
which are mathematical statements that
use numbers and or variables. The second
example below is an example of an
expression. Algebra involves equations
which are statements that two numbers or
expressions are equal.

9. 5 + 5 = 2 x 5
5 + 5 = 10
n + n = 2 x n
5 + 5 = 2n
(When 2n is written, it is understood that 2
is multiplied by n)
Example:
In Algebra, symbols or letters are
introduced as a sort of shorthand which is
used to abbreviate and simplify long and
often complicated statements.
Algebra is illustrated by many formulas
used in science, computer programs and
the workplace industry.

10. - 2 = 4
What is the missing number?
OK, the answer is 6, right?
Because 6 − 2 = 4.
Well, in Algebra we don't use blank boxes,
we use a letter (usually an x or y, but any
letter is fine). So we write
x – 2 = 4
It is really that simple. The letter (in this
case an x) just means "we don't know this
yet", and is often called the unknown or
the variable.
X = 6
Puzzle:

11. Why Use a Letter?
It is easier to write "x" than drawing empty
boxes (and easier to say "x" than "the
empty box").
If there are several empty boxes (several
"unknowns") we can use a different letter
for each one.

12. How to Solve:
Algebra is just like a puzzle where we start
with something like "x − 2 = 4" and we
want to end up with something like "x = 6".
But instead of saying "obviously x=6", use
this neat step-by-step approach:
Work out what to remove get "x = ..."
Remove it by doing the opposite (adding
is the opposite of subtracting).
Do that to both sides.

13. Example:
We want to
remove the "-
2“ To remove it, do
the opposite, in
this case add 2:
Do it to both
sides:
Which is ...
Solved!

14. Why we add 2 to both sides?
To keep the balance,
what we do to one side of the "="
we should also do to the other side!
In Balance Out of
Balance
Balance
Again
X-2 = 4
+2 4
x-2
+2 +2
x-2 4

15. Algebraic Expressions
Definition:
An algebraic expression is a
mathematical phrase that can contain
ordinary numbers, variables (like x or y)
and operators (like add,subtract,multiply,
and divide).

16. Types of Algebraic Expressions
 Monomial
 Polynomial
 Binomial
 Trinomial
 Multinomial

17. Monomial:
An algebraic expression which consists of
two non-zero terms is called a binomial.
Examples of Monomial:
1) 10ab2 is a monomial in two variables a
and b.
2) 5m2n is a monomial in two variables m
and n.
3) -7pq is a monomial in two variables p
and q.

18. Polynomial:
An algebraic expression which consists of
one, two or more terms is called a
polynomial.
Examples of polynomials:
1) 2a + 5b is a polynomial of two terms in
two variables a and b.
2) 3xy + 5x + 1 is a polynomial of three
terms in two variables x and y.
3) 3y4 + 2y3 + 7y2 - 9y + 3/5 is a
polynomial of five terms in two variables
x and y.

19. Binomial:
An algebraic expression which consists of
two non-zero terms is called a binomial.
Examples of binomials:
1) m + n is a binomial in two variables m
and n.
2) a2 + 2b is a binomial in two variables a
and b.
3) 5x3 – 9y2 is a binomial in two variables
x and y.

20. Trinomial:
An algebraic expression of three non-
zero terms only is called a trinomial.
Examples of trinomial:
1) x + y + z is a trinomial in three variables
x, y and z.
2) 2a2 + 5a + 7 is a trinomial in one
variables a.
3) xy + x + 2y2 is a trinomial in two
variables x and y.

21. Multinomial:
An algebraic expression of two terms or
more than three terms is called a
multinomial.
Examples of multinomial:
1) p + q is a multinomial of two terms in
two variables p and q.
2) a + b + c is a multinomial of three terms
in three variables a, b and c.
3) a + b + c + d is a multinomial of four
terms in four variables a, b, c and d.

22. Important Terms
Integral:
If the algebraic expression doesn′t contain
the division by variables (i.a.
exponentiation with a fractional exponent),
then it is called integral.

23. Fractional:
If algebraic expression consists of numbers
and variables with the helping of
operations of addition, subtraction,
multiplication, exponentiation with the
natural exponent and division, and besides
division by expression with variables, then
it is called fractional.

24. Rational:
The integral and fractional expressions are
called rational expressions.
Irrational:
If we use root extraction from variables (or
raising to fractional power) in the algebraic
expression, then such expression is
called irrational.