This presentation discusses the application of mathematics in various engineering sectors. It provides examples of how matrix mathematics is used in cryptography to encrypt messages by converting text to numerical values, arranging them in a matrix, and multiplying by an encoding matrix. It also discusses uses of geometry, graphs, and pathfinding in computer games. Trigonometry is discussed as applied in fields like surveying. Integration and differentiation are explained through their relationship to displacement, velocity, and acceleration as applied in engineering problems.

1. WELCOME
TO
OUR PRESENTATION

3. PRESENTATION ON
APPLICATION OF MATHEMATICS
IN
ENGINEERING SECTORS

4. APPLICATION OF MATRIX IN
CRYPTOGRAPHY…
 Cryptography is the process of encrypting
data so that third party can’t read it and
privacy can be maintained.
 It was started with the TV cable industries
where even people who were not the
customer could watch the TV programs.
 To prevent this, It was so much necessary to develop a system that can keep the privacy unbroken
and only paid customers can watch the programs of corresponding TV channels.

5. HOW MATRIX IS USED FOR
CRYPTOGRAPHY
 Convert the text of the message into a stream of numerical values.
 Place the data into a matrix.
 Multiply the data by the encoding matrix.
 Convert the matrix into a stream of numerical values that contains the encrypted message.
 Suppose the message is “SUBMIT HER YOUR PLANS”
We assign a number for each letter of the alphabet. Such that A is 1, B is 2, and so on. Also, we assign the number
27 to space between two words.
Thus the message becomes:

6. NEXT STEPS TO FIND THE REQUIRED
MESSAGE

7. MATHEMATICS IN COMPUTER GAMES
Examples of Computer Games
# First Person Shooters # Strategy Games # Simulation Games
Wolfenstein Age of Empires Need For Speed

8. First Person Shooters
Geometric Figure: In this type of
games Geometry is the study of
shapes of various sort.
3D graphics: The basic idea of 3D
graphics is to turn a mathematical
description of a world into a picture
of what that world would look like
to someone inside the world.

9. Strategy Games
 Nodes , Edges and Graphs : To explain how the
computer works out the best route, We need to know
what nodes , edges and graphs are.
 Path Finding : All the stuff about graphs help the
computer guide troops around levels are done by it. Because.
It makes a graph where every interesting point is a node
on the graph, and every way of walking from one node
to another is an edge, then it solves the problem We
solved above to guide the troops.

10. FIELDS OF TRIGONMETRY…
Plane Trigonometry
In many applications of trigonometry the essential
problem is the solution of triangles. If enough sides
and angles are known, the remaining sides and
angles as well as the area can be calculated, and the
triangleis then said to be solved. Triangles can be
solved by the law of sines and the law of cosines.
Surveyors apply the principles of geometry and
trigonometry in determining the shapes, measurements
and position of features on or beneath the surface of
the Earth. Such topographic surveys are useful in the
designof roads, tunnels, dams, and other structures.

11. Ancient Egypt and the Mediterranean
world…
Several ancient civilizations in particular, the Egyptian, Babylonian, Hindu, and Chinese
possessed considerable knowledge of practical geometry, including some concepts of
trigonometry.
A close analysis of the text, with its accompanying figures, reveals that this word means
the slope of an incline,
essential knowledge for huge
construction projects such as
The pyramids. It shows that
the Egyptians had at least some
knowledge of the numerical
relations in a triangle, a kind of
“proto-trigonometry.”

12. Sine waves in nature
 Sound waves are sine waves whenever we listen
to music, we are actually listening to sound waves.
 Light waves are also sine waves.
 Radio waves are sine waves.
 Simple harmonic motion of a spring when pulled
and released is a sine wave.
 Alternating current (AC) is a sine wave.
 Pendulum clock oscillations are sinusoidal in nature
 Waves of ocean are sinusoidal .
 The vibrations of guitar strings when played are sinusoidal
in nature.

13. some applications of integration and
differentiation in engineering sector…
The best real life application that can be used to describe integration
and differentiation is the relation between the displacement , velocity
and acceleration and the explanation can be extended to Newton
laws.
We can explain integration and differentiation by two ways
analytically, by equations, and graphically and Leave students to
figure out the relation between them.
Imagine there is car start Moving from rest V= 0 , at position = 0 with
acceleration = 5 m^2/s

14. since the car moves with constant acceleration So the graph
is constant Line and If we calculate the Integration on this
graph which is the area under the Line we will get the
Second graph which is Logically true since the acceleration
is the rate of Change of Velocity.

15. THANKS FOR WATCHING…