# Calculus

## Irrational Numbers and The Proofs of their Irrationality

“Irrational numbers are those real numbers which are not rational numbers!” Def.1: Rational Number A rational number is a real number which can be expressed in the form of where $a$ and $b$

## The Area of a Disk

If you are aware of elementary facts of geometry, then you might know that the area of a disk with radius $R$ is $\pi R^2$ . The radius is actually the measure(length) of

## Triangle Inequality

Triangle inequality has its name on a geometrical fact that the length of one side of a triangle can never be greater than the sum of the lengths of other two sides of the triangle.

## Numbers – The Basic Introduction

If mathematics was a language, logic was the grammar, numbers should have been the alphabet. There are many types of numbers we use in mathematics, but at a broader aspect we may categorize them in

## Everywhere Continuous Non-differentiable Function

Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of $x$ but do not possess a derivative for any value. We now consider the celebrated function

## Free Online Calculus Text Books

In this list I have collected all useful and important free online calculus textbooks mostly in downloadable pdf format. Feel free to download and use these. Elementary Calculus : An approach using infinitesimals by H.

## D’Alembert’s Ratio Test of Convergence of Series

In this article we will formulate the D’ Alembert’s Ratio Test on convergence of a series. Let’s start. Statement of D’Alembert Ratio Test A series $\sum {u_n}$ of positive terms is convergent if from