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QuickPak Scientific

A Powerful Numerical Analysis Toolbox for DOS Compiled BASIC

QuickPak Scientific is a comprehensive collection of subroutines and functions that add numerical analysis to your BASIC programs. Each routine is provided in the form of a flexible and easy to use BASIC algorithm designed to help you solve practical and challenging problems in engineering, science, and other technical applications. QuickPak Scientific consists of three key components designed to simplify your numerical analysis programming:

Source code for state-of-the-art BASIC subroutines and functions:These routines perform a variety of fundamental and sophisticated numerical analysis tasks which may be too time-consuming or difficult to program and debug yourself.

Interactive BASIC demonstration programs:These sample programs illustrate the proper procedure for working with each QuickPak Scientific routine. Many of these programs also provide an example problem for solution, and each program displays information about the algorithm and its performance.

The QuickPak Scientific owner's manual:This comprehensive document describes the procedures for integrating the QuickPak Scientific algorithms into your own BASIC applications. It also serves as a tutorial about the art and science of numerical analysis and includes many programming hints and tips.

Every QuickPak Scientific algorithm includes a complete description of the required input and resultant output. Many of the demonstration programs offer an example problem for solution - the software interactively prompts you for the required inputs, and several programs also recommend typical input values. Other interactive programs allow the BASIC programmer to assess the effects of such things as step size, algorithm iterations, convergence criteria, and other factors on the behavior and performance of a particular numerical method. To illustrate this point, the following is a typical output from the QuickPak Scientific Simpson Integration program:

**Program DEMOINT5.BAS
Adaptive Integration of User-Defined Functions**

Function Lower Integration Limit | = 0 |

Upper Integration Limit | = 1 |

Solution Accuracy | = .00000001 |

Integral Value | = .74682413 |

Estimated Error | = 1.0925039D-10 |

**Systems of Linear Equations:** The Linear Algebra
routines solve systems of linear equations using the LU decomposition, Gauss-Jordan
elimination, and iterative improvement methods. An algorithm is also included for solving
tridiagonal systems of linear equations using Gaussian elimination with partial solving.

**Ordinary and Partial Differential
Equations:** QuickPak Scientific contains a complete set of algorithms for
solving first- and second-order systems of ordinary differential equations. These methods
include the classic fourth-order Runge-Kutta and Nystrom methods, three adaptive
Runge-Kutta-Fehlberg algorithms, and a variable-order Adams-Bashforth-Moulton
predicator-corrector subroutine. Efficient BASIC subroutines are also provided for solving
the Poisson heat and wave partial differential equations.

**Integration and Differentiation:**
The ability to numerically integrate user-defined analytic and tabulated functions is also
part of QuickPak Scientific. Tabular data can be integrated with either Simpson or cubic
spline subroutines. Single definite integrals of analytic user-defined functions can be
quickly and accurately evaluated with a Romberg algorithm. A Composite Simpson method is
also provided for integrating both double and triple definite integrals of analytic
functions you define. An adaptive integration method based on Simpson's method completes
this series of algorithms. The derivatives of both user-defined analytic and tabulated
functions can also be calculated with QuickPak Scientific. These three differentiation
subroutines perform numerical differentiation by the classic methods of finite-divided
differences, Lagrange's method, and cubic splines.

**Non-linear Equations and Optimization:**
QuickPak Scientific has six subroutines for non-linear equations. These solve for the real
roots of the general, quadratic, cubic, and quartic equations. This series of routines
also includes an algorithm for computing the real and complex roots of any polynomial up
to order 36. Two other routines solve single non-linear equations, both with and without
derivatives. Non-linear optimization is the most powerful numerical method for technical
applications - it's also the most difficult to implement. QuickPak Scientific provides
five flexible and powerful algorithms for this purpose. These subroutines can be used to
solve for the minimum or maximum of scalar functions of one or more variables. A complete
program is included for solving the constrained, non-linear optimization problem. (The
source is more than 20,000 lines of BASIC code!)

**Interpolation and Curve Fitting:**
Important technical information often exists in the form of empirical or experimental data
which must be carefully interpreted. To address this need, QuickPak Scientific includes
several routines for interpolating tabulated data in the form **y = f(x)** using both *natural*
and *clamped* cubic spline techniques. A subroutine is also provided which can
linearly interpolate both two- and three-dimensional tabular data. Curve-fitting of
experimental data is very important in science and engineering, and QuickPak Scientific
provides three flexible subroutines for this purpose. The first algorithm can fit data to
simple linear, log, and exponential functions. The second performs a least-squares fit to
data of the form **y = f(x)**, and the third subroutine calculates fitting coefficients
to a three-dimensional surface of the form **z = f(x, y)** using a Maclaurin series.

**Fast Fourier Transforms:**
QuickPak Scientific offers two algorithms which compute the forward and inverse Fast
Fourier transforms of real or complex data. These routines transform both one- and
two-dimensional data using the Danielson-Lanczos or bit reversal methods.

**Statistics and Complex Numbers:**
Also included are routines for computing characteristics of Normal, Chi-squared,
F-distribution, and T-distribution statistical functions. These algorithms can determine *point
x* from probability and degrees of freedom, or determine probability for *point x*
for each type of statistical distribution. QuickPak Scientific includes eight routines for
performing calculations with complex numbers. These subroutines can add, subtract,
multiply, and divide two complex numbers, raise a complex number to a power, compute its
Nth and square root, and find the reciprocal of a complex number.

**Trigonometry:** BASIC's built-in
capabilities are extended with the QuickPak Scientific trigonometry routines. These
flexible functions provide easy-to-use inverse sine, cosine, tangent, and hyperbolic
functions.

**Vectors and Matrices:** The
QuickPak Scientific matrix subprograms provide flexible algorithms for performing a
variety of calculations involving matrices. Included are subroutines for computing the
inverse and determinant of a square matrix, eigenvalues and eigenvectors, rank of a
matrix, and fundamental matrix operations, such as addition, subtraction, and
multiplication. The vector routines let you easily perform numerical calculations
involving vectors. These calculations include the dot and cross product of two vectors;
fundamental operations such as vector addition, subtraction, and multiplication; and the
triple scalar and vector products.

The Full Moon Philosophy

As with all our products, full source code is provided at no additional cost, so you can see how the routines were designed and even modify them if you want. We genuinely want you to understand how our libraries work and be able to learn from them. All of our products are reasonably priced and include free technical assistance, but they are licensed for use by only one person using one computer at a time. Royalty payments are not required when our routines are incorporated into your compiled applications. However, you may not distribute our source, object, or library files. If your customers need to rebuild your program, they will need their own copy of our product(s).

The Bottom Line

QuickPak Scientific costs **$149** and works with QuickBASIC 4.x,
PDS 7.x, and VB/DOS. Add **$8** for UPS ground shipping to US addresses only (no P.O.
boxes); Connecticut residents must add 6.0% sales tax or show proof of tax-exempt status
when ordering. Please email or call for overnight and foreign shipping costs. We accept
only prepaid orders accompanied by a check.

Sorry, no demo is available at this time.

QuickPak Scientific is a trademark of Crescent Software, Inc.