Introduction Calculus

Calculus is a branch of Mathematics that deals with the study of limits, functions, derivatives , integrals and infinite series . The subject comes under the most important branches of applied Mathematics, and it serves as the basis for all the advanced mathematics calculations and engineering applications.

Categories of Calculus

There are two major categories of Calculus:

  •  Differential Calculus
  •  Integral Calculus

In this content, we will focus majorly on different solving techniques of Calculus and will also throw some light on a wide range of concepts associated with the subject.


Before we jump into the detailed study of the subject, we must be familiar with some basic terms that are associated with the course. A good understanding of Calculus requires you to have a basic knowledge of:


These functions are further characterized as

  •  Polynomials
  •  Rational Functions
  •  Logarithms
  •  Exponentials
  •  Trigonometric

Throughout this course, we will be making use of these terms frequently, so it is better if you have a good understanding of the terms listed above. These are not very difficult-to-understand concepts. You may study them on your own before you proceed further into learning concepts of Calculus. Next we move to the core concepts and examples of Calculus.


A polynomial function has the form `f(x)=a_n x^n`=`a_(n-1) x^(n-1)+...+a_1 x+a_0`, where `a_n ,a_(n-1),...,a_0` are real numbers and n is a nonnegative integer. In other words, a polynomial is the sum of one or more monomials with real coefficients and non-negative integer exponents. The degree of the polynomial function is the highest value for n where n is not equal to 0.

Polynomial functions of only one term are called monomials or power functions. A power function has the form `f(x)=ax^n`.

For a polynomial function f, any number r for which `f(r)=0` is called a root of the function f. When a polynomial function is completely factored, each of the factors helps identify zeros of the function.

Rational Functions

Rational function" is the name given to a function which can be represented as the quotient of polynomials, just as a rational number is a number which can be expressed as a quotient of whole numbers. Rational functions supply important examples and occur naturally in many contexts. All polynomials are rational functions.


Logarithmic functions are used to simplify complex calculations in many fields, including statistics, engineering, chemistry, physics, and music. For example,`log(xy)=logx+logy` and `log(x/y)=log x - log y are logarithmic functions that essentially simplify multiplication to addition and division to subtraction. Logarithmic functions are the inverse of their exponential counterparts.


An exponential function is a mathematical function of the following form: `f ( x ) = a x` where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828. Thus, the above expression becomes: `f ( x ) = e x` When the exponent in this function increases by 1, the value of the function increases by a factor of e . When the exponent decreases by 1, the value of the function decreases by this same factor (it is divided by e ).


A function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, and cosecant. Also called circular function.

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