Salman Izaz Ahmed.RAnd

Vikram Ragu.N.P

APPLICATION OF MATHEMATICS IN

Race cars Aerodynamics Communications Imaging Forsenic Science Biomedical

Engineering Manufacturing Agriculture

Environmental Engineering

Ecosystem

In a simplified non-mathematical explanation, Bernoulli’s equation basically means that if velocity (the speed of motion) of a fluid increases, the pressure within (the force per unit area applied to an object) the fluid decreases.

Racecars use a spoiler shaped so that pressure stays on top of the car holding down.

Bernoulli’s principle to keep the car on the ground, and allow the car to make sharper turns

The spoiler of the car is shaped so that the velocity of air on the top of the spoiler is moving slower, thus creating more pressure on the top of the car pushing the car downward. The velocity of air on the bottom of the spoiler is much faster, thus having less pressure pushing upward on the car.

The top of an airplane’s wings are shaped so that the velocity of air moves faster over the top and slower on the bottom.

Since the velocity of air is faster on top that means the pressure on top is low.

The velocity of air is slower on the bottom so the pressure on bottom is greater helping give lift (the force that pulls an object outward, or upward.) to the airplane keeping it up in the air.

•Airplane wings are shaped opposite of racecars to have pressure on the bottom of the wing to give it lift.

Methods based on the Fourier transform are used in virtually all areas of engineering and science and by virtually all engineers and scientists. For starters:

Circuit designers Spectroscopists Crystallographers Anyone working in signal

processing and communications

Signal is composed of sine-waves of different frequencies

Maths is also being used for imaging process

For imaging, vector algebra is used by 3-dimensional coordinate axes

Example: Graphical Representation

Application of maths in biomedical engineeringBiomedical engineering is

the recent advanced technique to cure and diagnosis the diseases using machines and instruments.

TomographyX-rays are light, too, and

when they pass through murky stuff (your body) along a straightline they are attenuated and reach a detector on the other end at a reduced intensity.

It is also used to reconstruct the fractured bones

Concept of fourier transform is used in reconstruction of fractured bone.

How are mathematics used to monitor manufacturing?

Quality Control Rate

Production Rate

Quality control rate can be expressed as a rate that tells what portion of the “bolt objects” that were made passed inspection. Rates can be expressed either in the form of a ratio, fraction, percent or all three (total made ÷ total that passed inspection x 100).

Production rate is the number of quality “bolt objects” produced per minute.

16

1. Modelling plant growth and development

18

Isolated tree

Central tree

Tree on the edge

Trees in competition for light

Method of intersections of projected areas

Maths plays a important role environmental engineering

Especially in making eco-friendly Making the unwanted lands to cultivate Vector algebra is used in making

desirable landscapes

19

20

Mechanical constraints Tree growth in a constrained environment

Fourcaud et al., 2003

Simulation and visualization of ecological process dynamics at landscape scale (from 100 to 10000 km²). E.g.: water resource allocation.

Vector algebra is used in confining 2D into 3D multi-platform

Visualization of dynamics and image post-treatments

Le Chevalier et al., 2007