Numerical Solutions

Numerical Solutions is a library of mathematical programs which currently contains the 8 collections: Functions and Equations studies functions and equations in one or more variables to plot graphs, find roots, compute integrals (including multiple integrals), find derivatives (including partial derivatives), find maxima and minima (even of multivariable functions), solve nonlinear equations or systems of such (linear ones are better solved by LINEAR ALGEBRA), Linear Algebra performs a wide variety of computations with real matrices, including solution of linear systems of equations (even least squares solution of over-determined or inconsistent systems and solution by LU factors), matrix operations (add, subtract, multiply), finding the determinant, trace, inverse, adjoint, QR or LU factors, real eigenvalues and eigenvectors, establish the definiteness of a symmetric matrix, perform scalar multiplication, transposition, shift, create matrices of zeroes or ones, identity, symmetric or general matrices, Ordinary Differential Equations solves linear or nonlinear differential equations and systems of such, subject to boundary conditions or initial conditions which may also be linear or nonlinear and may involve not only the unknown function but also its derivatives. The solution will be a finite power or trigonometric series, depending on the program.Regression fits user-specified functionals to a given set of data points in one or more independent variables, performing linear or nonlinear regressions.Approximation and Interpolation approximates continuous or tabulated single-variable or multivariable functions by finite power, trigonometric or mixed series. Continuous functions may be defined explicitly or by a linear/nonlinear equation. Depending on the program and the user setups, the function may be fitted exactly at user-specified grid points, or it may be fitted using Least Squares methods/Fast Fourier Transform methods.Stereographer produces stereoscopic graphs, which most people are able to view without any paraphernalia. True depth perception is due to binocular vision, and the usual single view of a surface, space curve or scatter diagram is unable to provide it, but the STEREOGRAPHER does provide this interesting 3-D sensation. You can rotate and translate surfaces, graph partial derivatives, zoom in or out, etc. Aside from functions you enter directly, you can also stereograph the results of other collections such as mixed series, regression surfaces and scatter diagrams.Support provides ways to study the solutions found by programs of other collections. For instance, the Power Series and Trigonometric Series programs may be used to study the solutions found by the programs of the Differential Equations collection to find integrals, roots, maxima & minima, derivatives. Even the multivariable series produced by the Approximation and Interpolation collection can be studied by support programs to compute multiple integrals, maxima & minima, partial derivatives.Math Miscellanea is an useful and interesting addition to the library: Prime factors, base conversion, complex numbers, sorting, formulas for triangles and circles. (Source: