Eareindel

The number 'e' appears very commonly in a lot of natural processes. In fact, it is bested only by 𝜋 as far as its number of times of appearance is concerned. But it is indeed quite mysterious as to why nature has such a preference for a number that is neither a whole number but also  irrational . So in this article we are going to find about the discovery about this mysterious number. Let's see how the number 'e' arises from calculating the interest of 1 unit of currency annually. Suppose we have 1 dollar and we get 100%  interest annually. We deposit 1 dollar on the New Year's Day. Then at the end of one year, the total amount stands to be 2 dollars. This is because of the 1 dollar initially deposited plus the interest obtained. Pretty, simple. Now if we calculate the interest twice every year, then after six months, the interest calculated is 1 plus one-half of one i.e. 3/2(one-half because only half of the year has passed). After another six months the inter...

  The study of the second order Simple Harmonic motion(SHM)  ODE is very interesting. It shows not only how oscillations generate from relatively simple physical laws but their mathematical analysis reveals also how deeply oscillations are related to complex exponentials and thereby the inseparable relation of complex numbers to the real world. Simple Harmonic Motion is the most basic physical oscillatory motion. The important thing is to get a physical understanding of the concepts and the equations involved. Mathematical understanding will help in solving the mathematical formulation of the physical phenomena. But another important thing that is required is the Physical understanding of the concept or phenomena. That alone will help in deriving a proper and ideal mathematical formulation. Computers and calculators merely do what their name suggests, they calculate only. But proper understanding is needed to tell the computer what to calculate. Using a few mathematical mani...