basic

Axioms of probability

Chance is a slippery concept. We all know that some random events are more likely to occur than…

Half Range Fourier Series

If a function is defined over half the range, say , instead of the full range from , it may…

Fourier series

A Fourier series is an expansion of a periodic function  in terms of an infinite sum of sines and cosines. Fourier series make…

power series solutions

Line Integral

Line integrals (also referred to as path or curvilinear integrals) extend the concept of simple integrals (used to find areas of flat, two-dimensional surfaces) to…

Cauchy- Riemann equations

Let (1) where (2) so (3) The total derivative of  with respect to  is then (4) (5) In terms of  and ,…

Analytic Functions

Analytic Functions are defined as per the converging series; that revolves around a particular variable x for which the…

Stokes theorem and Gauss divergence theorem (without proofs)

Green’s theorem

The idea behind Green’s theorem represents the circulation of FF around CC. If FF were the velocity field of water flow, for example, this…

Line and surface integrals