Symmetry in Physical Laws
‘Symmetry’ has a special meaning in physics. A picture is said to be symmetrical if one side is somehow the same as the other side.…
Study Notes
Macrostates and Microstates and their relations with Thermodynamic Probability
Here’s a concept that confused me for months in statistical physics: the difference between macrostates and microstates. Textbooks make it sound complicated. It’s not. Once…
How to change Differential Equations into Integral Equations?
This post explains the basic method of converting an integral equation into a corresponding differential equation.
Square Integrable Functions, Norms, Trial Method in Integral Equations
In this article, I will teach you about Square Integrable Functions, Norms and the solution of Integral Equations by the trial method. Don’t forget to…
Definitions and Types of Integral Equations
In this article, I will explain what Integral Equations are, how they are structured and what are certain types of Integral Equations. What is an…
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…
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…
Study Notes on Real Sequences (Definitions and Examples)
In this study note, I have discussed and explained about real sequences — a very important topic in Real Analysis and Calculus. I will cover…
Euler’s (Prime to) Prime Generating Equation
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…
Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can’t just look at a number and declare it irrational. You can’t check infinitely many decimal…
The Area of a Disk
The area of a disk with radius \( R \) is \( \pi R^2 \). You probably memorized this in middle school. But do you…
Triangle Inequality
The triangle inequality is one of those results that sounds obvious until you try to prove it rigorously. Here’s the geometric intuition: no side of…
