Square Integrable function or quadratically integrable function $\mathfrak{L}_2$ function A function $y(x)$ is said to be square integrable or $\mathfrak{L}_2$ function on the interval $(a,b)$ if $$\displaystyle {\int_a^b} {|y(x)|}^2 dx <\infty$$ or $$\displaystyle {\int_a^b} y(x)

# Study Notes

Study Notes on Math, Physics and Chemistry

In this article I will explain what are Integral Equations, how those are structured and what are certain types of Integral Equations. What is an Integral Equation? An integral equation is an equation in which

Every student or graduate knows how hard the first experience of passing exams is. Preliminary preparation starves the nervous system and the physical condition of the human body, however, the exam itself is always a

This is a continuation of the series of summer projects sponsored by department of science and technology, government of India. In this project work, I have worked to collect and expand what Ramanujan did with

Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function $ f: \mathbb{N} \to \mathbb{R}$ , where $ \mathbb{N}$ is the set of natural numbers and $

These study notes on Set Theory, Functions and Real Numbers were written by Gaurav Tiwari when he was studying as a Math undergraduate in 2012-2013. The language is sought to be simple and easy to

The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were correct to limited extent but still stun the mathematicians. The

“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$