## Best Time Saving Mathematics Formulas & Theorems

Formulas are the most important part of mathematics and as we all know one is the backbone of the latter. Considering there are thousands of mathematical formulas to help people develop analytical approach and solve problems easily — there are some that go beyond. Some formulas aren’t just timesaving but those also do wonders. In this article I have collected…

## Interesting Facts about Blood and Blood Cells

Like all humans have red colored blood, there are few organisms which have varying blood colors. Spiders and octopus have blue color blood, cockroaches have white/colorless blood, grasshopper, leeches, and some varieties of earthworm have green color blood and so on. Apart from these, there are more facts about the blood. In this article, few interesting facts about Blood and…

## How to convert Integral Equations into Differential Equations?

Introduction In earlier parts we discussed the basics of integral equations and how they can be derived from ordinary differential equations. In second part, we also solved a linear integral equation using trial method. Now we are in a situation from where main job of solving Integral Equations can be started. But before we go ahead to that mission, it will be better…

## Definitions in Functional Analysis

Linear Space or Vector Space over a field K Definition: The linear space over a field K is a non-empty set along with a function $+ : X \times X \to X$ called linear/vector addition  (or just, ‘addition‘) and another function $\cdot : K \times X \to X$ called scalar multiplication, such that for all elements \$x, y, z,…

## 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. Precisely, a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation. For example, if we look at a base that is left and…

## Statistical Physics: Macrostates and Microstates

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 exactly 1/2 as both compartments are identical. If the four particles are named as a , b, c and d and the compartments…