HP 48GII User Manual

Full Command and Function Reference 3-147
REWRITE
CAS: Display a menu or list of CAS operations that rewrite expressions.
RISCH
CAS: Perform symbolic integration on a function using the Risch algorithm.
RKF
Type: Command
Description: Solve for Initial Values (Runge–Kutta–Fehlberg) Command: Computes the solution to an initial
value problem for a differential equation, using the Runge-Kutta-Fehlberg (4,5) method.
RKF solves y
'(t) = f(t,y), where y(t
0
) = y
0
. The arguments and results are as follows:
• { list } contains three items in this order: the independent (t) and solution (y) variables, and
the right-hand side of the differential equation (or a variable where the expression is stored).
• x
tol
sets the absolute error tolerance. If a list is used, the first value is the absolute error
tolerance and the second value is the initial candidate step size.
• x
Tfinal
specifies the final value of the independent variable.
RKF repeatedly calls RKFSTEP as it steps from the initial value to x
Tfinal
.
Access: …µ
RKF
Input/Output:
L
3
/A
1
L
2
/A
2
L
1
/A
3
L
2
/I
1
L
1
/I
2
{ list } x
tol
x
T final
→
{ list } x
tol
{ list } { x
tol
x
hstep
} x
T final
→
{ list } x
tol
L = Level; A = Argument; I = item
See also: RKFERR, RKFSTEP, RRK, RRKSTEP, RSBERR
RKFERR
Type: Command
Description: Error Estimate for Runge–Kutta–Fehlberg Method Command: Returns the absolute error
estimate for a given step h when solving an initial value problem for a differential equation.
The arguments and results are as follows:
• { list } contains three items in this order: the independent (t) and solution (y) variables, and
the right-hand side of the differential equation (or a variable where the expression is stored).
• h is a real number that specifies the step.
• y
delta
displays the change in solution for the specified step.
• error displays the absolute error for that step. A zero error indicates that the Runge–Kutta–
Fehlberg method failed and that Euler's method was used instead.
The absolute error is the absolute value of the estimated error for a scalar problem, and the row
(infinity) norm of the estimated error vector for a vector problem. (The latter is a bound on the
maximum error of any component of the solution.)
Access: …µ
RKFE
Input/Output:
L
2
/A
1
L
1
/A
2
L
4
/I
1
L
3
/I
2
L
2
/I
3
L
1
/I
4
{ list } h
→
{ list } h y
delta
error
L = Level; A = Argument; I = item
See also: RKF, RKFSTEP, RRK, RRKSTEP, RSBERR

HP 48GII Specifications

General

Battery type	CR2032
Type	Scientific
Form factor	Pocket

Weight and Dimensions

Weight	220 g
Dimensions (WxDxH)	184 x 87 x 23.5 mm

Summary

RPL Programming

Understanding Programs

Programs as objects, delimiters, and basic structure.

Entering and Executing Programs

Details on how to create, store, and run programs.

Using Conditional Structures

Covers IF, CASE, IFT, IFTE structures for program decision-making.

Input and Output Commands

Details commands like PROMPT, INPUT, INFORM, CHOOSE for user interaction.

RPL Programming Examples

Fibonacci Numbers

Demonstrates recursive and loop-based Fibonacci calculations.

Minimum and Maximum Array Elements

Details finding min/max elements using MNX and MNX2.

Applying a Program to an Array

Explains the APLY command for transforming array elements.

Full Command and Function Reference

How to Access Commands and Functions

Explains key presses and menu paths to access commands.

ABS (Absolute Value)

Details the absolute value function and its array behavior.

ACOS (Arc Cosine)

Explains the inverse cosine function, domain, and range.

Computer Algebra Commands

CAS Operations

Overview of CAS operations and their categorization by menu.

Algebra commands

Lists and describes commands for algebraic manipulation.

Calculus Commands

Covers derivation, integration, and limit commands.

Equation Reference

Columns and Beams (1)

Provides equations for structural mechanics.

Electricity (2)

Lists equations related to electrical circuits and laws.

Fluids (3)

Covers equations for fluid mechanics.

The Development Library

Introduction

Explains the purpose and usage of the development library.

Tools for Development

Details APEEK, PEEK, POKE, POKEARM commands.

MASD Compiler

Discusses syntax, modes, and directives for MASD.

Error and Status Messages

Messages Listed Alphabetically

Alphabetical list of error messages.

Messages Listed Numerically

Numerical list of error messages by hex code.

System Flags

System Flags (continued)

Description of various system flags.

System Flags (continued)

Continuation of system flags description.

Reserved Variables

Contents of the Reserved Variables

Explanation of key reserved variables.

PPAR

Details plotting parameters.

Technical Reference

Object Sizes

Lists object sizes in bytes.

Symbolic Integration Patterns

Provides a table of symbolic integration patterns.

Parallel Processing With Lists

General rules for parallel processing

Explains conditions for parallel list processing.

Group 4: ADD and +

Describes how ADD and + handle parallel list operations.

Keyboard Shortcuts

Press and Hold key combinations

Lists functions performed by key combinations.

Shifted softkeys

Explains shift key effects on menu labels.

The Menu-Number Table

-- menus 0-117 are semi-compatible with 48G menus --

Menu numbers and paths for built-in menus.

-- New Library 222 commands --

Details commands available in Library 222.