basic 5 min read
Discrete and Continuous Random Variables
A variable is a quantity whose value changes. A discrete variable is a variable whose value is obtained by counting. Examples: number of students present…
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Bayes’ Theorem
Bayes’ Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and…
basic 3 min read
Conditional Probability
The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This…
basic 3 min read
Axioms of probability
Chance is a slippery concept. We all know that some random events are more likely to occur than others, but…
basic 1 min read
Half Range Fourier Series
If a function is defined over half the range, say , instead of the full range from , it may be expanded…
basic 4 min read
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 use of…
basic 3 min read
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 integrals that…
basic 1 min read
Cauchy- Riemann equations
Let (1) where (2) so (3) The total derivative of with respect to is then (4) (5) In terms of and , (5) becomes…
basic 4 min read
Analytic Functions
Analytic Functions are defined as per the converging series; that revolves around a particular variable x for which the series has…
basic 3 min read
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 integral would…