This page contains links to several mathematical utilities. More will be added as I write them. The algorithms underlying these utilities come from the BLAS, EISPACK, and LINPACK collection of subprograms, written by some of the brightest mathematicians and computer scientists (I have cited sources when I found them). Those subprograms incorporate excellent basic algorithms and programming techniques to optimize the routines for speed and accuracy.
Also visit the thothworks website, that contains the same features. Bookmark these sites and come back often (If one site is down, use the other as a back-up).
A note about machine precision.
Because these utilities are written in Javascript, make sure Javascript is enabled in your Internet browser.
Numerical Solver for Kepler's Equation for Elliptical Motion
Polynomial Root-finder (Real Coefficients)
Root-Finder Utility #1: f(M) = a1cos(M)sin2(M) + a2cos2(M)sin2(M) + a3
Root-Finder Utility #2: f(x) = a1/ √ (1 - x 2) - (1/x2) [( (1 + a2 x2)/(1 + a2) )a3 - 1]
Maximum-Finder Utility #1: f(M) = a1cos(M)sin2(M) + a2cos2(M)sin2(M) + a3
Quadratic Programming Utility, Three Variables
Three Equations in Three Unknowns
Four Equations in Four Unknowns
Five Equations in Five Unknowns
Simultaneous Equation Solver (up to 12 equations in 12 real unknowns)
A Downloadable Console Utility, N Equations in N Unknowns
Eigenvalues of a 2 by 2 Matrix
Eigenvalues of a 3 by 3 Matrix
Eigenvalues of a 4 by 4 Matrix
Eigenvalues of a 5 by 5 Matrix
Eigenvalues of a 6 by 6 Matrix
Eigenvalues and Eigenvectors Calculator (matrices up to size 12 X 12, real coefficients)
A Downloadable Console Utility, N X N, Real, General Matrix
Eigenvalues Only of a 3 by 3 Real, Symmetric Matrix
Numerical Integration Utility #1: f(x) = sin(x)
Numerical Integration Utility #2: f(x) = √ x sin(x)
Linear Least-Squares Data-Fitting Utility, Polynomial Fit, up to Fourth Degree
Aerodynamics Example #1: Finding the Critical Mach Number of an Airfoil
Quadratic Programming Example #1: No Constraints
Two Papers on Optimization/Quadratic Programming
A Transformation Utility for Successive Rotations Around Axes
A 2D Positioning Utility (by angulation)
A 3D Positioning Utility (by angulation)
Dynamic Arrays in C++ (source code)
If you are interested in an offline option for performing these types of math tasks--and more--consider a scientific calculator.
Check out this beauty from Hewlett-Packard, the 50g, which can be purchased on the HP site: