This document discusses applications of differential and integral calculus in engineering. It begins by defining calculus as the study of rates of change and outlines its two main types: differential calculus and integral calculus. Differential calculus determines rates of change while integral calculus finds quantities from known rates of change. Several real-world examples are provided, including using Newton's Law of Cooling in forensic investigations and manufacturing. Additional applications discussed include using calculus in astronomy, architecture, graphics, robotics, vehicle safety, and other fields. The document concludes that calculus gives us power to model and control systems.

1. SUBMITTED TO:
Mr. Mir Kaosar Ahamed
Lecturer
Department of Mathematics
Daffodil International University
SUBMITTED BY:
Name:Shohan Ahmed
ID:171-23-4986
B.S.C In Textile Engineering
Date of submission: 05th April, 2017

2. Applications of Differential and
Integral Calculus in Engineering
sector

3. What is Calculus ?
Calculus is the study of 'Rates of Change'.
Calculus as we know it today was developed
in the later half of the seventeenth century
by two mathematicians, Gottfried Leibniz
and Isaac Newton.

4. Types of Calculus
There are two type of calculus.
 Differential Calculus
 Integral Calculus
Differential calculus determines the rate of
change of a quantity, integral calculus finds
the quantity where the rate of change is
known.

5. What is Differential and Integral?
Differential calculus determines the rate of
change of a quantity, its like cutting
something into small pieces to find how it
changes.
Integral calculus finds the quantity where
the rate of change is known, its like joining
(integrates) the small pieces together to
find how much there is.

6. We are surrounded by Calculus
Calculus is everywhere. The differentiation and
integration of calculus have many real-world
applications from sports to engineering to
astronomy and space travel

7. Differential Calculus
Newton’s Law of Cooling
Newton’s observations: He observed
that the temperature of the body is
proportional to the difference between its
own temperature and the temperature of
the objects in contact with it .
Formulating: First order separable DE
Applying Calculus:
Where “k” is the positive proportionality constant

8. Investigations.
It can be used to
determine the time of
death.
Computer
manufacturing
.
• Processors.
• Cooling
systems
Calculating
the surface
area of an
object
Applications on Newton’s Law of Cooling

9. Applications of calculus
Finding the Average of a Function ,A function can
represent many things. One example is the path of
an airplane. Using calculus you can calculate its
average cruising altitude, velocity and acceleration.
Same goes for a car, bus, or anything else that
moves along a path.

10. Use of calculus in Astronomy
• Calculus has been used in astronomy since the 17th
century to calculate the orbits of the planets around
stars .
• Calculus is also necessary to accurately calculate the
variable speed of moving objects in space, including
asteroids, comets and other celestial bodies

11. An architect will use integration to determine the
amount of materials necessary to construct a
curved dome over a new sports arena, as well as
calculate the weight of that dome and determine the
type of support structure required.
Use of Calculus in Architect

12. Uses of calculus in graphics
A graphics artist uses calculus to determine how
different three-dimensional models will behave when
subjected to rapidly changing conditions. This can
create a realistic environment for movies or video
games.

13. Use of Calculus in other fields
Engineers use calculus for building
skyscrapers, bridges.
In robotics calculus is used how robotic parts
will work on given command.
Engineers use calculus for system design.
Calculus is used to improve Safety of vehicles.

14. Conclusion
With calculus, we have the ability to find the effects of
changing conditions on a system. By studying these,
we can learn how to control a system to make it do
what we want it to do. Because of the ability to model
and control systems, calculus gives us extraordinary
power over the material world.

15. That’s All
ANY QUESTION ?

16. Thank You