Calculus is one of the major fields of Mathematics. Sir Isaac Newton, a British scientist has invented this new field of mathematics. Coming to the origin, ‘Calculus’ is a Latin word, which means ‘small stone.’ For the counting of infinitely smaller numbers, Romans used stones as an indication. Mathematicians also began using the same term for counting. There are a large number of applications of calculus in day to day existence. Statisticians can also use calculus to evaluate data obtained from the survey to help business plans to develop for different companies. Since a survey can have different types of questions with a specified range of possible responses or answers hence the calculus allows a more accurate estimation for the appropriate action.
Mathematics
In mathematics education, calculus represents the courses of elementary mathematical analysis, which mainly involves the study of functions and limits. Limits are all about approaching because sometimes we can’t work something which has to be found directly, but we will be able to check what it should be as we get closer and closer.
Students can learn about two main branches of calculus namely differential calculus and integral calculus in their mathematics courses. They will be introduced with different methods of differentiation in their senior secondary classes. We know that differentiation deals with finding the rate of change or slope of a function. Whereas integration can be used to find the area under the curve, the volume of shape and many geometries related measures.
In order to analyze the rate of change of a quantity and making predictions over its future behavior we can use the process of differentiation. We can find the exact instantaneous rate of change at any given point just by finding its derivative. We get a straight line if a function has a constant rate of change and it is simple to just find the rate of change using the formula rise overrun. When a function changes its rate multiple of times we can find exactly what its instantaneous rate of changes at each and every point or any given point in the given period of time using differentiation.
Mathematically, the process of finding a derivative of a given function is called differentiation.
It is possible to produce a new function just by finding the derivative of a given function at every point in its domain. This is often called the derivative of the original function or the derivative function. Similarly, partial differentiation is used in case of multiple variables where the derivative of one of these variables is required to find while other variables will be treated as constants. This technique can be used in solving calculus-based optimization problems.
The study of definitions, properties, and applications of two major concepts namely definite and indefinite integrals is called integral calculus. Integration is the opposite process of differentiation. Also, it can be termed as ant differentiation for easy understanding. With the help of integration, we can find the area of a two-dimensional region and to find the volume of a three-dimensional shape which has curved boundaries.
