Category: Math
-
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…
-
Space Transforms
Functions have the ability to be described in terms of the infinite summation of other functions with a common example being polynomials using Taylor series as shown below. However, functions can also be described in terms of trigonometric functions using the Fourier series
-
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…
-
Quaternions
Many are familiar with the idea of imaginary/complex numbers but in 1843, Hamilton invented hypercomplex numbers. Initially, he created three components such that they had the form where . This however raised a problem when multiplying complex numbers.
aakashl 