HP 15c Collector's Edition User Manual

Section 14: Numerical Integration 203
In the preceding example, the uncertainty indicated that the
approximation might be correct to only four decimal places. If we
temporarily display all 10 digits of the approximation, however, and
compare it to the actual value of the integral (actually, an approximation
known to be accurate to a sufficient number of decimal places), we find
that the approximation is actually more accurate than its uncertainty
indicates.
Keystrokes Display
®
1.3825 00
Return approximation to
display.
´ CLEAR u
1382459676
All 10 digits of approximation.
The value of this integral, correct to eight decimal places, is 1.38245969.
The calculator’s approximation is accurate to seven decimal places rather
than only four. In fact, since the uncertainty of an approximation is
calculated very conservatively, the calculator’s approximation, in most
cases will be more accurate than its uncertainty indicates. However,
normally there is no way to determine just how accurate an approximation
is.
For a more detailed look at the accuracy and uncertainty of f
approximations, refer to Appendix E.
Using f in a Program
f can appear as an instruction in a program provided that the program
is not called (as a subroutine) by f itself. In other words, f cannot be
used recursively. Consequently, you cannot use f to calculate multiple
integrals; if you attempt to do so, the calculator will halt with Error 7 in
the display. However, f can appear as an instruction in a subroutine
called by _.
The use of f as an instruction in a program utilizes one of the seven
pending returns in the calculator. Since the subroutine called by f
utilizes another return, there can be only five other pending returns.
Executed from the keyboard, on the other hand, f itself does not utilize
one of the pending returns, so that six pending returns are available for
subroutines within the subroutine called by f. Remember that if all
seven pending returns have been utilized, a call to another subroutine will
result in a display of Error 5 . (Refer to page 105.)

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.