Question

What are the four concepts of calculus?

Answer 1

Hint: The solution of the given question is a descriptive form. Here we have to discuss the four major concepts of calculus. So first we know the definition of the calculus and then the four concepts of the calculus. So we define the four different concepts of calculus.

Complete step-by-step answer:
The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences is known as calculus.
The 4 main concepts of calculus are:
I.Limits
II.Differential Calculus (Differentiation)
III.Integral Calculus (Integration)
IV.Multivariable Calculus (Function theory)

Let us understand the above concepts briefly.

I.Limits:
A limit is a value that a function or sequence which “approaches” as the index or input “approaches” some specific value may be finite or infinite. Also, limits are used to determine the continuity of the given function or sequence, derivatives and integrals (definite integrals).

II.Differential Calculus:
Differential calculus deals with the rate of change of one quantity concerning another. The derivative of a function at a certain point describes the rate of change of the function at that input. Also, the method of getting a derivative of a function is called differentiation. In differentiation the limit will approach 0. It is also called a decreasing function.

III.Integral Calculus:
Integral calculus is another important concept of calculus. The process of evaluating the integral of a function is called integration. Integrals can be categorized into two types namely definite integral and indefinite integral. The integration is the reverse process of differentiation. Thus, the integral of a function is also called the antiderivative of the function. In an integration the limit will approach infinity.

IV.Multivariable Calculus:
Multivariable calculus is the extension of calculus functions of one variable to calculus with functions of several variables. Also, the differentiation and integration operations will be performed on functions involving several variables or two or more variables rather than just one. Thus, it is also called multivariate calculus.

Note: The application of differentiation, the application of integration and differential equation will also come under the topic of calculus. Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired.