Every story.

Laplace equation

The scalar form of Laplace’s equation is the partial differential equation (1) where  is the Laplacian. Note that the operator  is commonly written as  by…

Euler-Cauchy Equations

An Euler-Cauchy equation is where b and c are constant numbers. Let us consider the change of variable x = et. Then we have The equation…

Numerical Methods: The Trapezium Rule and Simpson’s Rule

Integrals don’t have to get very complicated before symbolic methods fail to work. Consider, for example, the integral 01cos(x3+x)dx:  there…

Correlation and regression

The word correlation is used in everyday life to denote some form of association. We might say that we have…

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…

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…

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…

Axioms of probability

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

Half Range Fourier Series

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

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…

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 integrals that…