HP 15c Collector's Edition User Manual

Appendix E: A Detailed Look at f 249
Conditions That Could Cause Incorrect Results
Although the f algorithm in the HP 15c is one of the best available, in
certain situations it—like nearly all algorithms for numerical
integration—might give you an incorrect answer. The possibility of this
occurring is extremely remote. The f algorithm has been designed to
give accurate results with almost any smooth function. Only for functions
that exhibit extremely erratic behavior is there any substantial risk of
obtaining an inaccurate answer. Such functions rarely occur in problems
related to actual physical situations; when they do, they usually can be
recognized and dealt with in a straightforward manner.
As discussed on page 240, the f algorithm samples the function f(x) at
various values of x within the interval of integration. By calculating a
weighted average of the function’s values at the sample points, the
algorithm approximates the integral of f(x).
Unfortunately, since all that the algorithm knows about f(x) are its values
at the sample points, it cannot distinguish between f (x) and any other
function that agrees with f (x) at all the sample points. This situation is
depicted in the illustration on the next page, which shows (over a portion
of the interval of integration) three of the infinitely many functions whose
graphs include the finitely many sample points.

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.