HP 15c Collector's Edition User Manual

244 Appendix E: A Detailed Look at f
All 10 digits of the approximations in i 2 and i 3 are identical: the
accuracy of the approximation in i 3 is no better than the accuracy in
i 2 despite the fact that the uncertainty in i 3 is less than the
uncertainty in i 2. Why is this? Remember that the accuracy of any
approximation depends primarily on the number of sample points at
which the function f(x) has been evaluated. The f algorithm is iterated
with increasing numbers of sample points until the disparity among three
successive approximations is less than the uncertainty derived from the
display format. After a particular iteration, the disparity among the
approximations may already be so much less than the uncertainty that it
would still be less if the uncertainty were decreased by a factor of 10. In
such cases, if you decreased the uncertainty by specifying one more digit
in the display format, the algorithm would not have to consider additional
sample points, and the resulting approximation would be identical to the
approximation calculated with the larger uncertainty.
If you calculated the two preceding approximations on your calculator,
you may have noticed that it did not take any longer to calculate the
integral in i 3 than in i 2. This is because the time to calculate the
integral of a given function depends on the number of sample points at
which the function must be evaluated to achieve an approximation of
acceptable accuracy. For the i 3 approximation, the algorithm did not
have to consider more sample points than it did in i 2, so it did not
take any longer to calculate the integral.
Often, however, increasing the number of digits in the display format will
require evaluating the function at additional sample points, so that
calculating the integral will take more time. Now calculate the same
integral in i 4.
Keystrokes
Display
´ i 4
7.7858 -03
i 4 display.
) )
3.1416 00
Rolls down stack until upper
limit appears in X-register.
´ f 0
7.7807 -03
Integral approximated in
i 4.

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.