| I developed the Numerical Solutions Library on a Sunday afternoon while watching the Super Bowl. Bored at halftime, I started to think how nice it would be to have such a thing. I opened a programming tutorial and an arithmetic book and by the end of the third quarter I had the Library ready. I figured I�d throw in some instructions in case I forgot how to use the thing. By game�s end a horrifying bunch of words had materialized... The first program of the Library was Functions of one Variable and the first collection was the Functions and Equations Collection. Functions of one Variable studies one-variable functions in a given interval to find roots, maxima & minima, integral, derivatives, graph. This
program is part of the Functions and Equations
Collection of the Numerical Solutions
Library. Other programs of the Functions and Equations Collection are: Maxima and Minima (of functions of several variables), Multiple Integrals (Numerical multiple integration with constant or variable limits), Systems of Nonlinear Equations (solves systems of nonlinear equations), Partial Derivatives. Functions of one Variable studies one-variable functions in a given interval to find roots, maxima & minima, integral, derivatives, graph. Download
Functions of one Variable If you like this sort of entertainment, keep your eyes open for the many other similar ones which are on their way. Other collections of the Numerical Solutions Library are: The Ordinary Differential Equations Collection 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. The Regression Collection fits user-chosen functionals to a given set of data points in one or more independent variables, performing linear or nonlinear regressions. The Approximation and Interpolation Collection 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. The Linear Algebra Collection 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, 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. The Support Collection 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. The Math Miscellaneous Collection is an useful and interesting addition to the library: Prime factors, base conversion, complex numbers, sorting, formulas for triangles and circles. The Stereographer Collection 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. |
