This presentation is about the application of so many branch of mathematics in Business purpose. Here we are trying to describe this topic with short details. I think everyone likes this presentation .

1. Welcome
To our Presentation

2. SPECIAL THANKS tO
Dr. Md. Jamal Hossain
Associate Professor
Department of Applied Mathematics,
Noakhali Science and Technology University

3. SL NO: NAME STUDENT ID
01 SABIR AHMED ASH2006011M
02 IFTEKHAR JAHAN TANJIL MUH2006012M
03 MD.ABUL KALAM AZAD MUH2006013M
04 RIDILA KAISER NIHA BFH2006014F
05 JAHIDUL ISLAM HASAN MUH2006015M
06 ANAMIKA ROUTH BFH2006016F
Group
Members
G r o u p N a m e : I n f i n i t y

4. PREGENTATION title
Application of mathematics in business

5.  Set Theory is a branch of mathematical logic where we learn sets and
their properties. A set is a collection of objects or groups of objects.
These objects are often called elements or members of a set.
For example: Number of workers in RFL group.
 TYPES OF SET:
 Finite set
 Infinite set
 Empty set
 Equal set
 Equivalent set
 Power set
 Universal set
Set Theory
 Sets can be represented in two
ways:
1) Roster Form or Tabular form.
2) Set Builder Form.

6. APPLICATIONOF SET THEORY IN BUSINESS
 In business operations there are a lot of interactions between people
and objects. With a good knowledge of sets theory, its rules and
operations such as unions, complements and intersections, businesses
could find ways to save cost and increase profit.
Solution: Let A = Set of people who
like cold drinks.
B = Set of people who like hot drinks.
Given, (A ∪ B) = 60 n(A) = 27
n(B) = 42
then; n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
= 27 + 42 - 60
= 69 - 60
= 9
 In a group of 60
people, 27 like cold
drinks and 42 like hot
drinks and each
person likes at least
one of the two drinks.
How many like both
coffee and tea?

7. STRAIGHT LINE
 WHAT IS STRAIGHT LINE ?
 STRAIGHT LINE IS A GEOMETRIC FIGURE DESIGNED BY A POINT
MOVING IN A FIXED DIRECTION.
y = Total cost
mx = Variable
cost
c = Fixed cost
m = Marginal cost
x = number of

8. 1. MOST STRAIGHTFORWARD
METHOD FOR
CALCULATING DEPRECIATION.
2. EASY TO CALCULATE AND
UNDERSTAND.
3. REDUCE THE VALUE OF A
TANGIBLE ASSET.
Importance of Straight Line :
Straight Line Depreciation =
Cost of Asset − Salvage Value
Useful Life of Asset

9.  WHAT IS DETERMINANTS?
 Adeterminantis a factor or cause that makes something
happen or leads directly to a decision.
Determinants
 APPLICATIONS OF DETERMINANTS
 The application of determinants helps in various professions.
In business,Determinants are essential tools for solving many
businesses and economic problems & Cramer’s rule are also
used in business problem. It can be exceptionally frequently
used to search for an optimal explanation of the maximization
profit or minimization loss.

10.  PROFIT MAXIMIZATION CASE
 In business, profit maximization is a
good thing, but it can be a bad thing
for the client if, for example, lower-
quality materials and labours are used
or if the business decides to raise the
prices for executing projects, all in
pursuit of profit maximization.
LOSE MINIMIZATION CASE
 The loss minimization rule applies when
a company's short-run economic loss is
less than its entire fixed cost. This
happens when the price paid is lower
than the average total cost but higher
than the average variable cost.

11. ANNUITY
 A sequence of fixed annual payments made at
uniform(or equal) time intervals is called Annuity.
Mathematics of Finance
TYPES OF ANNUITY
 Annuity Certain
1) Annuity Due
2) Annuity ordinary(or Immediate)
 Contingent Annuity
 Deffered Annuity

12.  PRESENTVALUE
 Present value describes how much a future sum of
money is
worth today.
 FUTURE VALUE
 Refers to a method of calculating how much the
present
value (PV) of an asset or cash will be worth at a
specific time in
the future.
 SIMPLE INTEREST
 A quick method of calculating the interest charge
on a loan.
Simple interest is determined by multiplying the
interest rate by
the principal by the number of periods.

13.  COMPOUND INTEREST
 Interest which is calculated not only on the initial principal but also
the accumulated interest of prior periods. Compound interest differs
from simple interest in that simple interest is calculated solely as a
percentage of the principal sum.
 DEPRECIATION
 The principle value is diminished every year by a certain constant
amount,
and in the subsequent period the diminished value becomes the
principle
value 𝐴𝑛 = 𝑃(1 − 𝑖)𝑛

14.  WHAT IS DIFFERENTIATION?
Differentiation & Integration
 PURPOSE OF DIFFERTIATION
DIFFERENTIATION ALLOWS US TO FIND RATES OF
CHANGE. FOR EXAMPLE, IT ALLOWS US TO FIND
THE RATE OF CHANGE OF VELOCITY WITH
RESPECT TO TIME (WHICH IS ACCELERATION).
 Power Rule: (d/dx) (xn )
= nxn-1
 Derivative of a constant,
a: (d/dx) (a) = 0.
 Derivative of a constant
multiplied with function
f: (d/dx) (a. f) = af'
 Sum Rule: (d/dx) (f ± g)
= f' ± g'
 Product Rule: (d/dx)
(fg)= fg' + gf'
 Quotient Rule: d d x ( f g
) = g f ′ – f g ′ g 2.
 LIST OF DIFFERTIATION
FORMULAS
 DIFFERENTIATION IS A METHOD USED TO
COMPUTE THE RATE OF CHANGE OF A
FUNCTION F(X) WITH RESPECT TO ITS INPUT
X . THIS RATE OF CHANGE IS KNOWN AS THE
DERIVATIVE OF F WITH RESPECT TO X.

15.  Technique of finding a function
g(x) the derivative of which,
Dg(x), is equal to a given
function f(x).
 PURPOSE OF INTEGRATION
 WHAT IS INTEGRATION?
Technique of finding a function
g(x) the derivative of which, Dg(x),
is equal to a given function f(x).
 ∫ 1 DX = X + C.
 ∫ A DX = AX+ C.
 ∫ XN DX = ((XN+1)/(N+1))+C ;
N≠1.
 ∫ SIN X DX = – COS X + C.
 ∫ COS X DX = SIN X + C.
 ∫ SEC2X DX = TAN X + C.
 ∫ CSC2X DX = -COT X + C.
 ∫ SEC X (TAN X) DX = SEC X +
C.
 LIST OF INTEGRAL FORMULAS

16. Application of differential calculus
 To determine the exact rate of growth in a
bacterial culture when temperature, food
source are changed
 REAL LIFE APPLICATION
 Maxima, minima of a function :
 Maxima will be the highest peak on the curve within
the given range, while minima will be the lowest
 Application :
1) area of a rectangle
2) Maximizing area,minimizing cost,maximizing profit

17.  RELATION BETWEEN THEM : PROPORTIONAL
 ONE OF FORMULA : M=1/(1-MPC)
 MARGINAL PROPENSITY of
consumer and multiplier:
 Marginal propensity to
consume is the extra money
we spend, ultimately
creating an increase in
demand and spending.
 The consequence of the
extra spending and
producing is an overall
increase in income which is
called the Multiplier.
APPLICATION OF PARTIAL
DERIVATIVES :
A PARTIAL DERIVATIVE OF A
FUNCTION OF SEVERAL VARIABLES
IS ITS DERIVATIVE WITH RESPECT
TO ONE OF THOSE VARIABLES WITH
THE OTHERS HEALTH CONSTANT
USED IN: VECTOR CALCULUS,
DIFFERENTIAL GEOMETRY

18. ANY QUESTION
?

19. THANK YOU