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APPLICATION OF MATHEMATICS IN ENGINEERING SECTORS

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 industrieswhere 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.

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:

NEXT STEPS TO FIND THE REQUIRED MESSAGE

And finally the message is…

MATHEMATICS IN COMPUTER GAMES

Examples of Computer Games

# First Person Shooters # Strategy Games # Simulation Games

Wolfenstein Age of Empires Need For Speed

First Person Shooters

Geometric Figure: In this type of games Geometry is the study ofshapes 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.

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 nodeon the graph, and every way of walking from one node to another is an edge, then it solves the problem Wesolved above to guide the troops.

FIELDS OF TRIGONMETRY…

Plane TrigonometryIn 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.

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.”

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.

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

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.

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