HP 15c Collector's Edition User Manual

246 Appendix E: A Detailed Look at f
If f (x) relates to a physical situation, then the function you would like to
integrate is not f(x) but rather
F (x) = f (x) ± δ
2
(x),
where δ
2
(x) is the uncertainty associated with f (x) that is caused by the
approximation to the actual physical situation.
Since f (x) =  (x) ± δ
1
(x), the function you want to integrate is
F (x) =  (x) ± δ
1
(x) ± δ
2
(x)
or F (x) =  (x) ± δ(x),
where δ(x) is the net uncertainty associated with  (x).
Therefore, the integral you want is

b
a
F (x) dx =

b
a
[(x) ± δ(x)] dx
=

b
a
 (x) dx ±

b
a
δ(x) dx
= I ± Δ
where I is the approximation to

b
a
F (x) dx and ∆ is the uncertainty
associated with the approximation. The f algorithm places the number
I in the X-register and the number ∆ in the Y-register.
The uncertainty δ(x) of  (x), the function calculated by your subroutine,
is determined as follows. Suppose you consider three significant digits of
the function’s values to be accurate, so you set the display format to i
2. The display would then show only the accurate digits in the mantissa of
a function’s values: for example,
1.23 -04.
Since the display format rounds the number in the X-register to the
number displayed, this implies that the uncertainty in the function’s
values is
± 0.005 × 10
−4
= ± 0.5 × 10
−2
× 10
−4
= ± 0.5 × 10
−6
.

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.