1. and it's applications!
and it's applications!
C A L C U L U S
By: Aadya Gupta
Iram Zaheer

2. It all began when....
Sir Isaac Newtom made his breakthrough in the field
of physics which focused on gravity and laws of
motion. Newton started by trying to describe the
speed of a falling object. When he did this, he found
that the speed of a falling object increases every
second, but that there was no existing mathematical
explanation for this. Newton saw a void that needed
to be filled
"Calculus is the most powerful
weapon of thought yet devised by
the wit of man.
-Sir Isaac Newton

3. The issue of movement and the rate of change had
not yet been explored to any significant degree in
the field of mathematics. He began work on this right
away, incorporating planetary ellipses into his theory
in an attempt to explain the orbit of the planets. He
found that by using calculus, he could explain how
planets moved and why the orbits of planets are in
an ellipse. This is one of Newton’s great epiphanies:
that the gravitational force that holds us to the
ground is the same force that causes the planets to
orbit the Sun and the Moon to orbit Earth

4. What is Calculus?
The word Calculus comes from Latin meaning "small stone" Because it is like understanding
something by looking at small pieces. Derived from the Latin "ca/x' (counter) - ancient
Babylonians would use pebbles to represent units, tens, hundreds, etc, on a primitive abacus.
Later, defined as as the instantiates rate of change of one variable in respect to another
variable is called derivation of function.
Geometrically the derivative is the slop of curve at the point on the curve.
The process of finding a derivative is called differentiation. The réverse process is called
anti-differentiation. The fundamental theorem of calculus states that anti-differentiation is
the same as integration. Differentiation and integration constitute the two fundamental
operations in single-variable calculus.

5. Types of calculus:
Differential Calculus- a branch of mathematics
concerned mainly with the study of the rate of change of
functions with respect to their variables especially through
the use of derivatives and differentials.
1.
>First Branch of mathematical analysis, devised by Isaac
Newton and G.W. Leibniz, are concerned with the problem of
finding the rate of change of a function with respect to the
variable on which it depends. Thus it involves calculating
derivatives and using them to solve problems involving non-
constant rates of change

6. Types of calculus:
2. Intergral Calculus- a branch of mathematics concerned
with the theory and applications (as in the determination of
lengths, areas, and volumes and in the solution of differential
equations) of integrals and integration was the first know use
of intergral calculus circa 1741
>Integral calculus is concerned with the theory and
applications of Integrals while differential calculus
focuses on rates of change, such as slopes of tangent
lines and velocities, integral calculus deals with total
size or value, such as lengths, areas, and volumes.

7. Applications of calculus

8. Calculus in the field of engineering:
Calculus initially developed for better navigation
system.
Engineers use calculus for building skyscrapers,
bridges.
In robotics calculus is used how robotic parts will
work on given command.
Electrical and Computer engineers use calculus for
Calculus is used to improve safety of vehicles.
system design.

9. Calculus in Science
Isaac Newton developed the use of calculus in his laws
of motion and gravitation.
Astronomical science deeply depend on calculus as they
use it to determine the paths of satellites, rockets, and
space vehicles, as well as to convey signals in the global
positioning system when compressed data is sent.
Astronauts use calculus to determine how the spaceship
itself moves. For example, calculus is used to determine
the rate of speed required for the spaceship to
successfully reach space from the Earth.

10. Calculus in Biology
Calculus is used to study the interaction of
different species within an ecosystem calculus
used
The concentration of drugs in a living organism
can be answered with calculus.
Physical attributes, such as backbone length and
skull length measured by calculus.
Calculus is used for measuring growth rate of
bacteria and certain species.

11. Derivatives in Physics
In physics, the derivatives of the displacement
of a moving body with reference to time is the
velocity of the body, and the derivative of
velocity with reference to time is acceleration.
Newton's second law of motion states that the
derivative of the momentum of a body equals
the force applied to the body better known as
F = ma

12. Derivatives in Mathematics:
The most common use of the derivatives in
Mathematics is to study functions such as:
I. Extreme values of functions
II.The mean value theorem
IlI.Concavity & curve sketching

13. A tech company which wants to produce a cooling system for their
processors that can cool down the processors from a temperature
of 50°C to 27°C in just half an hour when the temperature outside
is 20°C but they don't know what kind of materials they should use
or what the surface area and the geometry of the shape are. So
what should they do?
They simply have to use the general formula of Newton's law of
cooling
Computer Processor Manufacture

14. And by substituting the numbers they get
27 = 20 + (50 - 20) e^-0.5k
Solving for k we get k=2.9
so they need a material with k=2.9 (k is a
constant that is related to the heat capacity,
thermodynamics of the material and also the
shape and the geometry of the material)
Computer Processor Manufacture

15. In an automobile there is always an odometer
and a speedometer. These allow the driver to
determine his speed and his distance that he
has traveled. Electronic versions of these
gauges simply use derivatives to transform the
data sent to the electronic motherboard from
the tires to miles per hour(MPH) and (KM).
Automobiles

16. Economic research uses calculus
functional relationships.
Relation of income, market prediction etc.
Differentiation is used to find optimum
solutions of economics.
Calculus also used for maximising the
efficiency or products or to minimize their
costs.
Credit card companies use calculus for
monthly payments.
Calculus in Economics

17. Business and politicians often conduct
surveys with the help of calculus.
Investment plans do not pass unless
approved by mathematicians
Doctors often use calculus in the estimation
of the progression of the illness.
Global mapping is done with the help of
calculus.
Calculus also used to solve paradoxes.
Other fun facts:

18. Thank you everyone!
Presentation by Iram & Aadya