Seventeenth Century shall be considered as the century of genius because it is during this period brilliant discoveries were made.
Though some concepts of calculus were developed in ancient Greece and India, the modern use of calculus began in Europe, during the 17th century when Isaac Newton and Gottfried Wilhelm Leibniz built on the works of earlier mathematicians to introduce the basic principles of calculus.
Sir Isaac Newton, through his attempt to understand nature, discovered law of gravitation. Based on the concept of rates of change, he discovered the fundamental principles of Differential Calculus between 1673 and 1676 and Integral Calculus as the reverse process.
The calculus and its basic tools of differentiation and integration serve as a foundation for the larger branch of mathematics known as analysis. The methods of calculus are essential to modern physics and to most other branches of modern science and engineering.
In this chapter, we learn how the value of changes as gets closer and closer to a particular value what we call as limit. This is one of the most important concepts in the study of calculus.
For example: Consider a polygon inscribed in a circle. We are going to find the area of the circles by increasing the number of sides of the polygon.
Area of the polygon will never be more than the area of the circle as the polygon is inscribed in a circle. As the number of sides of the polygon is increased, the polygon is closer to the circle. Therefore the limit of the area of the polygon is the area of the circle.