Functional Analysis

-
Beamer Presentation

Topic :Introduction to normed space, properties of normed spaces, Riesz lemma,theorems on compactness and completeness.

Comments

Post a Comment

Popular posts from this blog

Happy Friendship Day

-
As it was "Friendship Day" two days ago. I had come to know about a theorem known as " Friendship Theorem ." Let's see what does it says? The “Friendship Theorem” states that, in a party of n persons, if every pair of persons has exactly one common friend, then there is someone in the party who is everyone else's friend. Further one can also get a " Friendship Graph ."
Read more

A Real Friendship between 220 and 284

-
Mathematician Ramanujam didn’t have any close friends and someone asked him the reason. He replied that although he wanted to have close friends but nobody was up to his expectations. When pressed how he expected his friend to be,  he replied,  "like numbers 220 and 284!" The person got confused and asked what is the connection between friendship and these numbers! Ramanujam asked him to find the divisors of each number! With much difficulty, the person derived and listed them as, 220 → 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 284 →1, 2, 4, 71, 142, 284 Ramanujam then asked the person to exclude the numbers 220 and 284 and asked the sum of the remaining divisors. The person was astonished to find, 220 → 1+2+4+5+10+11+20+22+44+55+110=284 284 →1+2+4+71+142=220 Ramanujam explained that an ideal friendship should be like these numbers, to complement each other. Even when one is absent, the other should represent the friend! Hats off to...
Read more

Happy 'e' - day

-
Hello friends , Today is 2nd of July , 2018 that is 2-7-18 (2.7.18). We know 'e' as Euler's number/ The Value of 'e' : 'e' is an irrational number with value            e = 2.718... The few digits are: 2.7182818284590452353602874713527.... It is often called Euler's number after Leonhard Euler (Pronounced "Oiler"). 'e' is the base of the Natural Logarithms which was invented by "John Napier". Calculating : There are many ways of calculating the value of e , but none of them ever give a totally exact value, because e is irrational. But it is known to over 1 trilllion digits of accuracy. For example, the value of $(1 + \frac{1}{n})^n$ approaches e as n gets bigger and bigger. i.e.$e = \displaystyle  \lim_{n\to\infty}(1+ \frac{1}{n})^n $ Another Calculation : The value of e is equal to $\frac{1}{0!} +\frac{1}{1!} +\frac{1}{2!} +\frac{1}{3!} +\frac{1}{4!} +\frac{1}{5!} +\frac{1}{6!} +\fr...
Read more