This document provides an overview of the practical applications of mathematics in daily life and various fields. It discusses how basic math is used for everyday tasks like shopping and bills. More advanced topics covered include relations and functions and their uses in physics, biology, and economics. Other mathematical concepts like matrices, determinants, derivatives, and probability are explained with examples of how they are applied in fields such as cryptography, engineering, medicine, chemistry, and weather forecasting. The document encourages feedback on understanding the practical uses of mathematics.

1. PRACTICAL
APPLICATION
OF
MATHEMATICS-
BASICS
By, C Eng. Shameem. P
B.E, MBA.

2. OBJECTIVE
 Lecture on subject practical application
of mathematics in real world- Basics.

3. What is mathematics
 Simply stated as study of numbers,
equation , functions, geometry etc.

4. What are the daily life
application of mathematics
 Buying snacks or goods from shop.
 Paying taxi fare.
 Paying bills.
 Buying bus tickets.
 Paying petrol bill.
These are common and simple application
of mathematics, which a layman or
common man doing in daily life.

5. Advance mathematics.
 Relation and functions.
 Inverse trigonometric function.
 Matrices and determinants.
 Limits and continuity.
 Application of derivatives.
 Differential equation
 Vector algebra
 3D Geometry
 Linear Programming
 Probability

6. Relation and function –
Practical app.
 In physics,
1. Einstein's famous equation E= mc2,
E= energy , M= mass , C= velocity of light.
 In biology,
2. Plants growth rate as a function of sun &
water availability.
3. Economics, inflation as a function of the
price of oil.
4. Business, sales as a function of price.

7. Inverse Trigonometric
Function.- Practical app.
 Rahim is making a scale model of the
tower bridge. He knows the distance to
the sides but the want to calculate the
angle.( Refer the picture)
 Abdulla want to make a bike lunching
ramp. What will be angle ? ( Refer the
picture).

8. Matrices and determinants-
Practical App.
 There are many application , one of the is
 Cryptography-
Cryptography involves encrypting (coding) data so that a
third party cannot intercept and read the data.
In the early days of satellite television the video signals weren't
encrypted and anyone with an satellite dish could watch
whatever the show on air. So the companies were not getting
enough profit. They start encrypting( coding) the video signal
with a system called video cipher.
Video cipher encryption system is to convert the signal to
digital form, encrypt it and send data over satellite. If the
satellite dish owner had as video cipher box and paid for the
channel then the box would unencrypt(decode) the signal
and return ti to its original useful form.
Now how to use matrices???

9. Limits and continuity- Practical
App.
 A real life example of a continuous function is
representation of the thermodynamic features
throughout the day.
 The concept of limits is used in the measurement
of instantaneous speed of the vehicles like bike,
car, truck etc.
 Calculating area of complex geometrical shapes,
where basic geometry fails.
 In the field of astronomy and time travel.
 Earth’s ability of maintaining and sustaining various
species is also a real life example of limits.

10. Derivatives- Practical App.
 Vibration analysis of underwater pipeline.
Underground pipeline are subject to
various fatigues. Derivatives are helps to
build underwater pipe line so that they do
not break.
 Certain small vibration is not visible, to
calculate the fatigue, we need to know
how much the pipe is curved. It turns out
that strain is the first derivative of
curvature.

11. Differential equation- Practical
App.
 In medicine , for modelling cancer growth
or the spread of diseases.
 In chemistry, for modelling chemical
reaction.
 In economics, to find the optimum
investment strategies.
 In physics, to describe the motion of
waves.
 To find out the population growth.

12. Vector algebra- Practical
App.
1.Used in Navigation system.
Navigation by air and by boat is generally
done using vector. Planes are given a
vector to travel and they use their speed to
determine how far they need to go before
turning or landing. Flight plans are made
using a series of vector.
2. Sports coaching using computer uses
vector .

13. 3D Geometry- Practical App.
 One of the application of 3D geometry is
in design of computer graphics.

14. Linear Programming- Practical
App.
 Mr. Alvin is going to bake some cookies for the guest. Two
different kinds of cookies
(a) Oat meal, cost 50 rupees
(b) Chocolate cookies, 30 rupees.
Conditions are ,
The number of chocolate cookies must be at least twice the
number of oat meat cookies. Mr. Alvin make 6 dozen of
cookies of that chocolate cookies shall not be more than 5
dozen.
What is the minimum cost to bake the cookies? How many
dozens of each kind will be able to bake for that cost?
Using linear programming we can easily find the solution for
such kind of problems.

15. Probability- Practical App.
 Future cannot be predicted, but probability can be
used to make better decision making.
 Medical decision making. When a patient is advised
to undergo surgery , they often want to know the
success rate of the operation done by that hospital ,
which is nothing but a probability rate. Based on that
patient can take decision.
 Weather forecast. When planning an outdoor
activity people generally check the probability of
rain. Meteorologists also predict the weather based
on the patterns of the previous year, temperature,
etc.
 Insurance – Life expectancy is based on the number
of years the same group of people lived in past .

16. END
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