Mathematics

Function of the Day: Complete Elliptic Integral

Wed 24 Apr - 2019

Today's function of the day is the complete elliptic integral. These functions are included in the package "functions". The complete elliptic integral of the first kind is defined as

\(K(m) = \int_0^{\pi/2} [1-m\sin(t)^2]^{-1/2} dt\)

and can be used from Gaea as following: 

 (require :functions) (functions:ellipk 1)

The complete elliptic integral of the second kind is defined as

\(E(m) = \int_0^{\pi/2} [1-m\sin(t)^2]^{1/2} dt\)

which can used from Gaea as following: 

 (require :...
Category: 
Mathematics, Programming

Library of the day: Gaea statistics library

Thu 11 Apr - 2019

Gaea statistics library reference is out!

The statistics library contains various mathematical and statistical utilites functions such as one and two way anova, covariance, cross and dot product, multiple linear regression, autocorrelation, confidense intervals calculation and others.

A sample example is given below. We calculate the length, minimum, maximum, range, median, mode, mean, variance, standard deviation, and interquartile-range of a list of data: 

 GAEA > (require :statistics) NIL GAEA > (statistics:statistical-summary (list 1 2 3...
Category: 
Computing, Mathematics, Programming

Library of the day: Gaea random library

Tue 09 Apr - 2019

Gaea random library reference is out!

With the random library the user can use random numbers generated from several distributions sush as Normal, Bivariate Normal, Gamma, Beta, Binomial, Negative Binomial, Poisson, Multinomial and others.

The usage is very easy as illustrated in the following example. Here we get a random value from a Normal distribution of mean=0 and sigma=1: 

 GAEA > (require :random) NIL GAEA > (random:random-normal 0d0 1d0) -0.18245537813658388d0

The full reference for random library can be found here ....

Category: 
Computing, Mathematics, Programming

Coupled system of nonlinear PDE in one space dimension and time

Fri 15 Mar - 2019

While searching for a quantitative description of physical phenomena, the engineer establishes a system of ordinary or partial differential equations — valid in a certain region (or domain) — and imposes on this system suitable boundary and initial conditions. A partial differential equation (PDE) is an equation, involving an unknown function of two or more variables and certain of its partial derivatives. A PDE can be solved numerically with various methods, such as finite difference method, finite volume method, finite element method, spectral method, meshfree method, domain...

Category: 
Mathematics

The Black-Scholes equation

Tue 04 Dec - 2018

The Black-Scholes equation is a parabolic partial differential equation (PDE) for option prices discovered by Black and Scholes in 1973. This discovery revolutionized financial markets in 1990-s. In 1997 Merton and Scholes were awarded the Nobel prize in economics. For any stock price s,

\(0<s<\infty\)

and time t,

\(0<t<T\)

the price u for an option expiring at time T satisfies the following Black-Scholes PDE:

\(\frac{\partial u}{\partial t} + \frac{1}{2} s^2 \sigma^2(s,t)\frac{\partial^2 u}{\partial s^2} + s\mu\frac{\partial u}{\...

Category: 
Mathematics

New wiki

Wed 23 May - 2018

We have a fresh new wiki about mathematics, physics, engineering and computer science! It is still in its first steps but we are working to provide more information on these vast subjects. The main categories of the wiki are calculus of variations, optimal control and optimization, differential geometry, probability theory and stochastic processes, statistics, numerical analysis, computer science, mechanics of particles and systems, mechanics of deformable solids, fluid mechanics, classical thermodynamics, and heat transfer, and operations research and mathematical programming.

Category: 
Automation & Control, Computing, Engineering, Mathematics, Optimization, Programming