This document discusses various applications of mathematics across multiple domains. It provides examples of how Bernoulli's principle is applied in aerodynamics for race cars and airplanes. It also mentions applications in communications through signal processing, imaging through vector algebra and coordinate systems, biomedical engineering for diagnosis and treatment, and environmental engineering for landscape design and modeling plant growth. Overall, the document outlines the wide use of mathematical concepts and methods in fields like engineering, science, manufacturing, and ecology.

1. Salman Izaz Ahmed.R
And
Vikram Ragu.N.P

2.  APPLICATION OF
MATHEMATICS IN
 Race cars
 Aerodynamics
 Communications
 Imaging
 Forsenic Science
 Biomedical Engineering
 Manufacturing
 Agriculture
 Environmental
Engineering
 Ecosystem

3.  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.

4.  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.

5.  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.

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

7.  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

8. Signal is composed of sine-waves of different
frequencies

9.  Maths is also being
used for imaging
process
 For imaging, vector
algebra is used by 3-
dimensional
coordinate axes
 Example: Graphical
Representation

10. Applicatio n o f m aths in
bio m e dicale ng ine e ring
Biomedical engineering is
the recent advanced
technique to cure and
diagnosis the diseases using
machines and instruments.
Tomography
X-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.

11. 
It is also used to
reconstruct the
fractured bones
Concept of
fourier
transform is
used in
reconstruction
of fractured
bone.

13.  How are mathematics used to
monitor manufacturing?
Quality Control Rate
Production Rate

14. 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).

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

16. 16
1. Modelling plant growth
and development

17. 18
Isolated tree
Central
tree
Tree on the
edge
Trees in competition for light
Method of intersections of
projected areas

18.  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

19. 20
Mechanical constraints Tree growth in a constrained environment
Fourcaud et al., 2003

20.  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