HP 15c Collector's Edition User Manual

202 Section 14: Numerical Integration
If the uncertainty of an approximation is larger than what you choose to
tolerate, you can decrease it by specifying a greater number of digits in
the display format and repeating the approximation.
*
Whenever you want to repeat an approximation, you don’t need to key the
limits of integration back into the X- and Y-registers. After an integral is
calculated, not only are the approximation and its uncertainty placed in
the X- and Y-registers, but in addition the upper limit of integration is
placed in the Z-register, and the lower limit is placed in the T-register. To
return the limits to the X- and Y-registers for calculating an integral again,
simply press ) ).
Example: For the integral in the expression for J
1
(1), you want an answer
accurate to four decimal places instead of only two.
Keystrokes Display
´ i 4
1.8826 -03
Set display format to i 4.
) )
3.1416 00
Roll down stack until upper
limit appears in X-register.
´ f 1
1.3825 00
Integral approximated in i 4.
®
1.7091 -05
Uncertainty of i 4
approximation.
The uncertainty indicates that this approximation is accurate to at least
four decimal places. Note that the uncertainty of the i 4
approximation is about one-hundredth as large as the uncertainty of the
i 2 approximation. In general, the uncertainty of any f
approximation decreases by about a factor of 10 for each additional digit
specified in the display format.
*
Provided that f(x) is still calculated accurately to the number of digits shown in the
display.

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.