Main Features

- The pac takes full advantage of power and flexibility of the
HP 48, combining a strong interactive menu with a function the library, integration
analysis & tables, limit analysis, a constant library and reference data.
- Contains a set of stack-based toolkits that cover
integration, functions form , 2D and 3D plotting, differential equations and vector
analysis.

At the main level of the user interface, these features are
easily accessible to the user.

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****Function Library -** This application offers prompts for
seven functions: fitting to one point and one slope, fitting to two points and two slopes,
fitting to many points, entering a piecewise function, building a polynomial the roots,
finding the roots of a polynomial, and calculating a Taylor’s series expansion.

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****Integration Analysis -** Uses interactive methods to
compute numerically approximate value of integrals, including left, right, midpoint,
trapezoids, and Simpson’s rule.

**
****Integral Tables -** Includes an integral table with 100
integrals organized in six sections for quick reference: user-defined, rational and
irrational, trigonometric/hyperbolic, exponential/logarithmic and definite integrals.

**
****Limit Analysis -** A powerful interactive tool to examine
the limit behavior of functions, sequences, partial sums of a series, and recursive
relations. The program takes into account use of L’Hopital’s rule when needed.

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****Constant Library -** Lists 43 universal constants for
quick reference. Constant values can be displayed on the screen, copied to the stack, or
printed on an IR printer, either one at a time or all at once.

**
****Reference Data -** Includes tables of the Greek alphabet,
standard SI prefixes, trigonometric and hyperbolic functions, pictures and relations, and
vector formulas for DOT, CROSS, CURL, DIVERGENCE for 2 and 3 dimensional vectors.

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****Function Toolkit -** The function toolkit is organized as
24 programmable commands into one menu for easy access from the stack. All the commands
are designed to manipulate functions. The commands include symbolic simplification, Taylor
expansion, polynomial root finder, rational power of a function, delta function, logarithm
to any base, nth root of a number, polynomial interpolation, point-slope fit, cubic spline
fit, and trigonometric and hyperbolic functions.

**
****Integration Toolkit -** Seven programmable commands
available compute approximate integrands and store user-defined integrals.

**
****Plotting Toolkit -** Provides three plotting
environments.

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****2 Dimensional Plots -** Enhances the HP 48 plotting
environment by adding new features to those built in. The new features include tracing an
equation, jumping to any value of the indent variable, and centering the graph at the
cursor coordinates.

**
****3 Dimensional Plots -** Utilizes the da Vinci 3D graphics
environment proving a powerful way to specify, plot and trace 3D functions, parametric
curves, and parametric surfaces.

**
****Differential Equations Plotting -** Is accomplished with
a series of numerical approximation routines utilizing different variations of the Euler
method and 4^{th} order Runga-Kutta method. Among the Euler methods supported are
the original Euler method, Euler’s method using mid points, and the modified Euler
method.

From the stack, you can enter the first derivative, the
starting location, and step size to get a plot of the function.

**
****Vector Analysis -** Provides 25 programmable commands
with easy access from the stack. The software can handle symbolic or numeric input.
Available commands include simplifying symbolic results, unit vector, DOT and CROSS
products, divergence and CURL, Laplacian, unary and binary vector operation, negating a
vector, vector derivatives and integrals, vector addition, subtraction, multiplication and
division, vector evaluation, length, and vector evaluate to quotient or number.

Calculus Pac was developed with the help of seasoned
instructors from several universities with experience using graphing calculators to teach
calculus in high schools, community colleges, and universities. The Calculus Pac offers a
unique opportunity for the student to explore a large class of calculus problems,
providing invaluable insights into the foundations of calculus.