Freeware:

1. Numerical Solutions

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 computations associated 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, 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 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.

2. Dynamic Solver
Dynamics Solver is a powerful tool to study differential equations, (continuous and discrete) nonlinear dynamical systems, deterministic chaos, mechanics, etc. For instance, You can draw phase space portraits (including an optional direction field), Poincaré maps, Liapunov exponents, histograms, bifurcation diagrams, attraction basins, etc. The results can be watched (in perspective or not) from any direction and particular subspaces can be analyzed. It is also able to draw complex mathematical figures, including many fractals.

3. EigenMath
A computer algebra package that features bignum arithmetic, symbolic arithmetic, calculus, tensors and graphs. Symbolic results are displayed in a graphical form that approximates typeset math. Also included is a scripting feature that can be used to create math and physics demos. Several example scripts are included in the download, these can be used as models for your own projects.

4.Grapher
Grapher is a program that generates interactive graphs in any dimension. It is intended to be used as an educational tool for both students and educators. However, it's many functions make it useful for a number of other applications as well.

5.SGA-C 2.0  SGA-C 2.0 (Upgraded version from SGA-C)
SGA-C version 2.0 (Upgraded version from SGA-C by Rob Smith) is an C-language translation and extension of the original Pascal SGA code presented in the book "Genetic algorithms in search, optimization, and machine learning" by Goldberg (1989). In order to ease the readers from having to write the code from scratch upon reading the book, several features, translated based on the descriptions in the book, are added in this current version. Flexibility and  modularity are maintained throughout the code, and its operation is essentially the same as that of the original Pascal version. A concise and comprehensive user guide,together with several examples, are included to provide an extensive introduction to the software, and a guide for users in implementing it for different problems. Available also from:
 http://skynet.ee.ic.ac.uk/software/ng/sga-c20.zip

6.PrimoPDF
FREE PDF Converter - not a trial version. Print to PDF from virtually any application Optimize PDF output for print or screen . No annoying pop-up ads - no catch!. High-quality PDF creation

7.Office Free
Complete Office Suite: You don't need Microsoft Office, but if you have it already on your computer, EasyOffice will co-exist without any problem. Has many programs and features not found in Microsoft Office. Create PDF documents and spreadsheets. Powerful EasyCalculator and full ZIP program. EasyMail with artificial intelligence

Shareware:
1. Software for Neural Networks and Genetic Algorithms
Neural Networks and genetic algorithms are exciting technologies in the field of artificial intelligence. These technologies have steadily changed the way we solve "real-world" problems in science, engineering and economics. The company Neurodimensions, www.nd.com has strong ties with the world-renowned Computational Neural Engineering Lab at the University of Florida and they bring state-of-the-art neural network technology to the marketplace.