SUBMITTED TO:Mr. Mir Kaosar AhamedLecturerDepartment of MathematicsDaffodil International University

SUBMITTED BY:Name:Shohan AhmedID:171-23-4986B.S.C In Textile Engineering

Date of submission: 05th April, 2017

Applications of Differential and Integral Calculus in Engineering sector

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.

Types of CalculusThere 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.

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.

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

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

Investigations.

It can be used to determine the time of

death.

Calculating the surface area of an

object

Applications on Newton’s Law of Cooling

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.

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 

 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

Uses of calculus in graphicsA 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.

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.

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.

That’s All

ANY QUESTION ?

Thank You