# Category Math

## TeXStudio is the most complete LaTeX Editor

A detailed and practical review of one of the most amazing LaTeX editors available for all desktop platforms like Windows, Mac and Linux. TeXStudio is a team project of Benito van der Zander, Jan Sundermeyer, Daniel Braun and Tim Hoffmann, forked from the TeXMaker application, a non-open source application, which open-source development stalled in 2009.

## Abel Prize for 2014 to Yakov Sinai

Mathematical Physicist Yakov Gregory Sinai, (b. 21st September 1935, 78 years old) has been awarded the prestigious Abel Prize for 2014 by the Norwegian Academy of Science and Letters (NASL). The President of the NASL, Nils C. Stenseth, announced the winner of the 2014 Abel Prize at the Academy in Oslo on 26 March 2014. The Abel Prize recognizes contributions of…

## How to change Differential Equations into Integral Equations?

This post explains the basic method of converting an integral equation into a corresponding differential equation.

Consider two natural numbers $n_1$ and $n_2$, out of which one is twice as large as the other. We are not told whether $n_1$ is larger or $n_2$, we can state following two propositions: PROPOSITION 1: The difference $n_1-n_2$, if $n_1 >n_2$, is different from the difference $n_2-n_1$, if $n_2 >n_1$. PROPOSITION 2: The difference $n_1-n_2$, if $n_1 >n_2$, is the same…

## What’s the question, if the answer is ‘No!’

Infinitely many answers questions are possible to the answer, “No”. So, our real task should be to find one of THOSE many, which seems to be a perfect one. A simple and the first ever logical approach of giving answers to a question is to derive answers from the question, that is, replace some words of the question with reasonable ones and…

## Square Integrable Functions, Norms, Trial Method in Integral Equations

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 $$\displaystyle {\int_a^b} y(x) \bar{y}(x) dx <\infty$$. For further reading, I suggest this Wikipedia page. $y(x)$ is then also called ‘regular function’. The kernel $K(x,t)$ , a function of two variables is…

## Definitions & Types of Integral Equations

If you have finished your course in Calculus and Differential Equations, you should head to your next milestone: the Integral Equations. This marathon series (planned to be of 6 or 8 parts) is dedicated to interactive learning of integral equations for the beginners —starting with just definitions and demos —and the pros— taking it to the heights of problem solving.…

## 11-12-13 – Last such sequence of the century

11th December 2013 (or in short 11-12-13) is just a few hours away here. It’s the last date of the 21st century with  such an extraordinary pattern of numbers.  In any calendar of the world, such date will be seen in 22nd century after 87 years and 54 days from today — on February 3, 2101, if all kind of date…

## We are now using MathJax!

The very first trouble I faced, while moving the blog from WordPress.com hosting to WordPress.org, was due to a bug in WordPress’s OPML importer. The ‘importer’ messed up with all LaTeX equations on this site — just by deleting a single but very important string from all LaTeX codes. If you are really moving your WordPress content from one blog…

## Examination Strategies : Tactics & Tips

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 stressful situation, which requires a candidate a great manifestation of mental and physical abilities. Therefore, just the knowledge of a subject is not enough for…

## Some good, OK, and useless revision techniques

Exam have been haunting student since forever, and although you’re willing to do whatever you can to retain essential information, sometimes you end up spending weeks studying with useless revision techniques. We’re accustomed to employ our own techniques when it comes to studying such as making sticky notes, highlighting, or drawing charts. However, recent studies conducted in the US have…

## Complete Elementary Analysis of Nested radicals

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 Nested Radicals and summarized all important facts into the one article. In the article, there are formulas, formulas and only formulas — I think this…