HP Solve Equation Library application card

Hewlett-Packard Journal,  June, 1991  by Eric L. Vogel

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The card contains a library of 315 equations, the periodic table of the elements, a constants library, a multiple equation solver, a finance application, and engineering utilities.

HISTORICALLY, EVERY HP programmable calculator has had programs available in some form. There are application books with printed programs and keystroke sequences for machines like the HP 55, 25, 33E, 11C, and 32S, application pacs with programs on magnetic cards for the HP 65 and 67, and pacs with programs in plug-in modules for the HP 41 and 71. These books and pacs focus on computation-intensive (as opposed to data-intensive) problems in specific science or engineering disciplines. Program size and capability are limited primarily by available memory and the single-line calculator display.

The HP Solve Equation Library application card provides this capability for the HP 48SX scientific expandable calculator, but without the limitations of previous pacs. The focus on computation-intensive solutions is preserved, but for a wider range of disciplines than in individual pacs in the past. An additional focus on data-intensive applications has been added in the form of on-line, electronic reference information (two thirds of the card contains data). The 128K-byte memory capacity of the card makes these two emphases possible, and the large display allows improved user interfaces for the interactive applications.

The card contains six major applications:

Equation Library (Fig. 1). This is the primary application for which the card was named: a collection of 315 equations organized in a catalog of 15 different subjects, each containing a catalog of equation titles. For each title, the user can examine the equations and catalogs of names, descriptions, and SI or English units for its variables. A key contribution is pictures that describe the physical situations represented by the equations. Our goal was that the subject, title, and reference information would help a user select an equation to use with the HP Solve application or the card's Multiple Equation Solver (discussed below).

Periodic Table (Fig. 2). This application contains all the chemical data (such as atomic weight and density) that appears on a standard periodic table of the elements. The primary user interface is the universally recognized grid of elements. The user can move a highlight block to see any element and its most-used properties on the grid. There is also a catalog of 23 properties available for each of the 106 elements. Properties can be plotted versus atomic number to reinforce the relationship between property and atomic structure. A molecular weight calculator allows typing chemical formulas and quickly calculating their molecular weights.

Constants Library. This is a collection of 39 commonly-used physical constants. These appear in catalogs of symbols, descriptive names, values, and SI or English units.

Multiple Equation Solver. This is a collection of commands that make it possible to use the Multiple Equation Solver to interact with the user's own equations as a group, rather than just the groups of equations from the Equation Library.

Finance. This application duplicates the basic calculations performed by HP financial calculators: time value of money (the relationship between the number of payments, interest rate, present value, payment, and future value) and amortization.

Engineering Utilities. These are engineering functions that support the computational needs of some of the equations in the Equation Library.

These applications come in two forms: interactive for working with the application and its data, and noninteractive for programmatic calculations and access to the on-line data.

Equation Library Evolution

The Equation Library concept stemmed from three observations. First, students need a wide variety of solutions because of the number of classes they take. Because application pacs are limited to specific areas, students often need several pacs to cover the different disciplines they study simultaneously. Second, most of the engineering applications for the HP 41 and its predecessors are programs that simply solve an equation for a specific variable. More sophisticated programs of this type allow interchangeable solutions in which most or all of the unknown variables can be calculated as long as they can be isolated algebraically in the equation. Some programs use iterative techniques to find a solution when an algebraic isolation is not possible. Later application pacs attempt to allow the user to select different units for the different variables.

Third, the HP Solve application in the HP 48SX takes an equation and makes it into a small, self-contained application. It solves for any variable given the others, allows units to be specified for each variable, handles unit conversions automatically, and provides a consistent, straightforward user interface for interacting with all the variables.

From these three observations, we realized that we could create a collection of small applications in most of the science and engineering disciplines of previous application pacs by combining a collection of equations with HP Solve. The HP Solve user interface allows each application to work the same way, and the ability to solve for any variable and automate unit conversions makes these applications more versatile than in previous application pacs. interacting with Groups of Equations