# Study Notes

Study Notes on Math, Physics and Chemistry, and other related sciences for students in colleges and those seeking admission in graduate courses.

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## Macrostates and Microstates and their relations with Thermodynamic Probability

In this article we will define what are Macrostates and Microstates in Statistical Physics with examples and illustrations. Consider some (4, say) distinguishable particles. If we wish to distribute them into two exactly similar compartments in an open box, then the priori probability for a particle of going into any one of the compartments will…

## 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

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…