Fractional Calculus

Calculus is the manipulation of one basic operator: the derivative or . This operator operates on functions and by repeatedly applying it, you can get higher order derivatives. It’s inverse operator is known as the integral. Similar to matrix operators which have eigenvalues and eigenvectors, this operator also has eigenvalues and eigenfunctions. The eigenfunction is the function which only goes through some scalar change when acted on by the operator. This scalar that the function is scaled by is called the eigenvalue of the eigenfunction. For the derivative operator, Continue reading Fractional Calculus

Probability Distribution Transformations

Random number generators generate random numbers that tend to follow some kind of distribution. Uniform number generators generate a random number between 0 and 1 with equal likely hood everywhere in the range, Gaussian generators generate numbers that have higher probability to be near zero, etc. These distributions are given functions ( for uniform or  for Gaussian). In order to calculate the probability that any number generated will fall in the range , one would take the integral . The probability to get a specific number  would be  which is just 0. Continue reading Probability Distribution Transformations