Calculus: A gateway to mathematical analysis
Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. Calculus is a gateway to advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient. Calculus has two major branches, differential calculus and integral calculus.
Isaac Newton (1642-1727) and German philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716) invented calculus independently. Historically calculus is known as infinitesimal calculus. It constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus.
In differential calculus, the term’ derivative’ is used to denote the ‘rate of change’. In simple term it describes how quickly a variable changes with respect to another variable. For example, the velocity of a car can be calculated using the concept of derivative which is the rate of change of distance with respect to time ( ). Historically, it helped dealing with many problems in physics.
Conceptually, the integral calculus is the opposite to differential calculus and hence it is also called ánti-derivative. In integral calculus, the term ‘integral’ is used to denote the summation of values. This is represented by an elongated ‘S’ symbol ò.
For example, the concept of integration can be used to calculate the area of irregular shapes.
The area of DEF cannot be solved similar to the area of ABC. Calculus helps solving such problems. Area under DEF can be broken into an infinite number of recognisable areas (infinitesimals) and then summing up all those small areas—this is the concept of integral calculus. Historically this is known as method of exhaustion. Greek mathematician Archimedes developed this idea in the 3rd century BC while calculating the area of a parabolic segment.