basic 2 min read
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…
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basic 1 min read
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…
basic 3 min read
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…
basic 6 min read
Correlation and regression
The word correlation is used in everyday life to denote some form of association. We might say that we have…
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…
basic 13 min read
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…
