What is Calculus
Calculus is one of the important branches of mathematics. Calculus has enriched many other branches of mathematics and it’s application is seen in other subjects such as Physics, Chemistry, Economics, Commerce, and Management studies. Sir Isaac Newton and G.W. Leibnitz laid the foundation of modern day calculus. Calculus not only deals with numbers but it uses fundamental arithmetic operations such as addition, subtraction, multiplication, and division. All the fundamentals are implemented by the concepts of functions, limits, derivatives, integrals and infinity. Basics of algebra, trigonometry, and series are mandatory for understanding calculus. Calculus is huge and it is complex too. Hence, it was subdivided into two branches:1. differential calculus2. integral calculus Differential CalculusDifferential calculus deals with derivatives. A derivate is represented by d(y)/d(x). Where, y is a function of x and represented as f(x). The concept of mathematical function is very simple as every value of x corresponds to a value of y. Functions are used to plot graph which has two scales,y and x, value of y and x are plotted and its shows the projected of the related values. Example of a function y=f(x), where f(x)= 2x+3Operation of Differential Calculus on a function is known as differentiation.
Expressions are differentiated by using some standard set of rules. These standard rules are set of formulas and results which decides the outcome of any mathematical expression. Study of Differential Calculus starts with the basics of real numbers and functions. Then basic fundamentals of Differentiation is taught which includes Limit and Continuity. All the formulas and rules are understood and defined by the rules of Limits. Then Differentiation is taught, which is of many types such as partial and second order differentiation. Basically, differentiation means separation of expression and find the lowest value of an algebraic or trigonometric expression. Integral CalculusJust like Differential Calculus, Integral Calculus also has its set of formulas and rules. This rules define the outcome of the Integral Calculus. Its operation on functions within specified intervals is known as Integration. For understanding Integral Calculus one has to again understand the fundamentals of functions and how they work.
Methods of substitution of variables are taught followed by integration by parts. These two sections form the core of Integral Calculus. Advanced Integration includes new techniques of integration such as integration of special form. Integration of some functions is very complex and can become unsolvable. This lead to the development of integration of special form of function. This is followed by real time Integration or Definite Integration where all the operations work on two sets of value or intervals. Integration means combining an expression by using the set of rules and formulasRelation between Integral Calculus and Differential CalculusThe two branches of calculus are related by the set of rules and formulas If you check closely the operation of Integration is opposite to Differentiation and vice versa. Integration is also known as anti-derivate.