# Miscellaneous Mathematical Utilities

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 AKiTi.ca 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).

Because these utilities are written in Javascript, make sure Javascript is enabled in your Internet browser.

## Root-finding Routines

Numerical Solver for Kepler's Equation for Elliptical Motion

## Utilities for Finding Maxima/Minima of Functions

Maximum-Finder Utility   #1:   f(M)   =   a1cos(M)sin2(M)   +   a2cos2(M)sin2(M)   +   a3

Quadratic Programming Utility, Three Variables

## N Equations in N Unknowns

Three Equations in Three Unknowns

## Eigenvalues and Eigenvectors

Eigenvalues of a 2 by 2 Matrix

## Numerical Integration

Numerical Integration Utility   #1:   f(M)   =   sin(M)

## Data Fitting

Linear Least-Squares Data-Fitting Utility, Polynomial Fit, up to Fourth Degree

## Interpolation

Cubic Spline Interpolation Utility

## Examples of Applications of Some of These Utilities

Aerodynamics Example   #1: Finding the Critical Mach Number of an Airfoil

## Other Utilities

A Transformation Utility for Successive Rotations Around Axes