HP 49g Bedienungsanleitung
HP
Taschenrechner
49g
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hp 49g+ graphing calculator
user’s manual
H
Edition 2
HP part number F2228-90001
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OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.
© Copyright 2003 Hewlett-Packard Development Company, L.P.
Reproduction, adaptation, or translation of this manual is prohibited without
prior written permission of Hewlett-Packard Company, except as allowed
under the copyright laws.
Hewlett-Packard Company
4995 Murphy Canyon Rd,
Suite 301
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Printing History
Edition 2 December 2003
Preface
You have in your hands a compact symbolic and numerical computer that will
facilitate calculation and mathematical analysis of problems in a variety of
disciplines, from elementary mathematics to advanced engineering and
science subjects.
This manual contains examples that illustrate the use of the basic calculator
functions and operations. The chapters in this user’s manual are organized
by subject in order of difficulty: from the setting of calculator modes, to real
and complex number calculations, operations with lists, vectors, and matrices,
graphics, calculus applications, vector analysis, differential equations,
probability and statistics.
For symbolic operations the calculator includes a powerful Computer
Algebraic System (CAS), which lets you select different modes of operation,
e.g., complex numbers vs. real numbers, or exact (symbolic) vs. approximate
(numerical) mode. The display can be adjusted to provide textbook-type
expressions, which can be useful when working with matrices, vectors,
fractions, summations, derivatives, and integrals. The high-speed graphics of
the calculator are very convenient for producing complex figures in very little
time.
Thanks to the infrared port and the USB cable available with your calculator,
you can connect your calculator with other calculators or computers. The
high-speed connection through infrared or USB allows the fast and efficient
exchange of programs and data with other calculators or computers. The
calculator provides a flash memory card port to facilitate storage and
exchange of data with other users.
We hope your calculator will become a faithful companion for your school
and professional applications.
Page TOC-1
Table of Contents
Chapter 1 – Getting Started, 1-1
Basic Operations, 1-1
Batteries, 1-1
Turning the calculator on and off, 1-2
Adjusting the display contrast, 1-2
Contents of the calculator’s display, 1-2
Menus, 1-3
The TOOL menu, 1-3
Setting time and date, 1-4
Introducing the calculator’s keyboard, 1-4
Selecting calculator modes, 1-6
Operating mode, 1-7
Number Format and decimal dot or comma, 1-10
Standard format, 1-11
Fixed format with decimals, 1-11
Scientific format, 1-12
Engineering format, 1-13
Decimal comma vs. decimal point, 1-14
Angle Measure, 1-14
Coordinate System, 1-15
Selecting CAS settings, 1-16
Explanation of CAS settings, 1-17
Selecting Display modes,1-17
Selecting the display font, 1-18
Selecting properties of the line editor, 1-19
Selecting properties of the Stack, 1-20
Selecting properties of the equation writer (EQW), 1-21
References, 1-21
Chapter 2 – Introducing the calculator, 2-1
Calculator objects, 2-1
Editing expressions in the stack, 2-1
Creating arithmetic expressions, 2-1
Page TOC-7
Chapter 14 – Differential Equations, 14-1
The CALC/DIFF menu, 14-1
Solution to linear and non-linear equations, 14-1
Function LDEC, 14-2
Function DESOLVE, 14-3
The variable ODETYPE, 14-4
Laplace Transforms, 14-5
Laplace transform and inverses in the calculator, 14-5
Fourier series, 14-6
Function FOURIER, 14-6
Fourier series for a quadratic function, 14-6
Reference, 14-8
Chapter 15 – Probability Distributions, 15-1
The MTH/PROBABILITY.. sub-menu – part 1, 15-1
Factorials, combinations, and permutations, 15-1
Random numbers, 15-2
The MTH/PROB menu – part 2, 15-3
The Normal distribution, 15-3
The Student-t distribution, 15-3
The Chi-square distribution, 15-4
The F distribution, 15-4
Reference, 15-4
Chapter 16 – Statistical Applications, 16-1
Entering data, 16-1
Calculating single-variable statistics, 16-1
Obtaining frequency distributions, 16-3
Fitting data to a function y = f(x), 16-4
Obtaining additional summary statistics, 16-6
Confidence intervals, 16-7
Hypothesis testing, 16-9
Reference, 16-11
Page TOC-8
Chapter 17 – Numbers in Different Bases, 17-1
The BASE menu, 17-1
Writing non-decimal numbers, 17-1
Reference, 17-2
Chapter 18 – Using SD cards, 18-1
Storing objects in the SD card, 18-1
Recalling an object from the SD card, 18-2
Purging an object from the SD card, 18-2
Limited Warranty – W-1
Service, W-2
Regulatory information, W-4
Page 1-1
Chapter 1
Getting started
This chapter is aimed at providing basic information in the operation of your
calculator. The exercises are aimed at familiarizing yourself with the basic
operations and settings before actually performing a calculation.
Basic Operations
The following exercises are aimed at getting you acquainted with the
hardware of your calculator.
Batteries
The calculator uses 3 AAA (LR03) batteries as main power and a CR2032
lithium battery for memory backup.
Before using the calculator, please install the batteries according to the
following procedure.
To install the main batteries
a. Make sure the calculator is OFF. Slide up the battery compartment cover
as illustrated.
b. Insert 3 new AAA (LR03) batteries into the main compartment. Make sure
each battery is inserted in the indicated direction.
To install the backup battery
a. Make sure the calculator is OFF. Press down the holder. Push the plate to
the shown direction and lift it.
Page 1-2
b. Insert a new CR2032 lithium battery. Make sure its positive (+) side is
facing up.
c. Replace the plate and push it to the original place.
After installing the batteries, press [ON] to turn the power on.
Warning: When the low battery icon is displayed, you need to replace the
batteries as soon as possible. However, avoid removing the backup battery
and main batteries at the same time to avoid data lost.
Turning the calculator on and off
The $ key is located at the lower left corner of the keyboard. Press it once
to turn your calculator on. To turn the calculator off, press the red right-shift
key @ (first key in the second row from the bottom of the keyboard),
followed by the key. Notice that the $ $ key has a red OFF label
printed in the upper right corner as a reminder of the OFF command.
Adjusting the display contrast
You can adjust the display contrast by holding the $ key while pressing the
+ - or keys.
The (hold) $ + key combination produces a darker display
The (hold) $ - key combination produces a lighter display
Contents of the calculator’s display
Turn your calculator on once more. At the top of the display you will have
two lines of information that describe the settings of the calculator. The first
line shows the characters:
RAD XYZ HEX R= 'X'
Page 1-3
For details on the meaning of these specifications see Chapter 2 in the
calculator’s user’s guide.
The second line shows the characters
{ HOME }
indicating that the HOME directory is the current file directory in the
calculator’s memory.
At the bottom of the display you will find a number of labels, namely,
@EDIT @VIEW @@ RCL @@ @@STO@ ! PURGE !CLEAR
associated with the six , F1 through F6: soft menu keys
ABCDEF
The six labels displayed in the lower part of the screen will change depending
on which menu is displayed. But will always be associated with the first A
displayed label, B with the second displayed label, and so on.
Menus
The six labels associated with the keys A through F form part of a menu
of functions. Since the calculator has only six soft menu keys, it only display 6
labels at any point in time. However, a menu can have more than six entries.
Each group of 6 entries is called a Menu page. To move to the next menu
page (if available), press the L (NeXT menu) key. This key is the third key
from the left in the third row of keys in the keyboard.
The TOOL menu
The soft menu keys for the default menu, known as the TOOL menu, are
associated with operations related to manipulation of variables (see section
on variables in this Chapter):
@EDIT A EDIT the contents of a variable (see Chapter 2 in this guide
Page 1-4
and Chapter 2 and Appendix L in the user’s guide for more
information on editing)
@VIEW B VIEW the contents of a variable
@@ RCL @@ C ReCaLl the contents of a variable
@@STO@ D STOre the contents of a variable
! PURGE E PURGE a variable
CLEAR F CLEAR the display or stack
These six functions form the first page of the TOOL menu. This menu has
actually eight entries arranged in two pages. The second page is available
by pressing the L (NeXT menu) key. This key is the third key from the left
in the third row of keys in the keyboard.
In this case, only the first two soft menu keys have commands associated with
them. These commands are:
@CASCM A CASCMD: CAS CoMmanD, used to launch a command from
the CAS (Computer Algebraic System) by selecting from a list
@HELP B HELP facility describing the commands available in the
calculator
Pressing the L key will show the original TOOL menu. Another way to
recover the TOOL menu is to press the I key (third key from the left in the
second row of keys from the top of the keyboard).
Setting time and date
See Chapter 1 in the calculator’s user’s guide to learn how to set time and
date.
Introducing the calculator’s keyboard
The figure below shows a diagram of the calculator’s keyboard with the
numbering of its rows and columns. Each key has three, four, or five functions.
The main key function correspond to the most prominent label in the key.
Also, the green left-shift key, , the red right-shift key, , and key (8,1) key (9,1)
Page 1-5
the blue ALPHA key, , can be combined with some of the other keys key (7,1)
to activate the alternative functions shown in the keyboard.
For example, the , has the following six functions associated P key, key(4,4)
with it:
P Main function, to activate the SYMBolic menu
„´ Left-shift function, to activate the MTH (Math) menu
… N Right-shift function, to activate the CATalog function
Page 1-6
~p ALPHA function, to enter the upper-case letter P
~„p ALPHA-Left-Shift function, to enter the lower-case letter p
~…p ALPHA-Right-Shift function, to enter the symbol π
Of the six functions associated with a key only the first four are shown in the
keyboard itself. The figure in next page shows these four labels for the P
key. Notice that the color and the position of the labels in the key, namely,
SYMB SYMB, MTH, CAT and P, indicate which is the main function ( ), and
which of the other three functions is associated with the left-shift „(MTH),
right-shift ( (… CAT ), and ~ P) keys.
For detailed information on the calculator keyboard operation refer to
Appendix B in the calculator’s user’s guide.
Selecting calculator modes
This section assumes that you are now at least partially familiar with the use of
choose and dialog boxes (if you are not, please refer to appendix A in the
user’s guide).
Press the H button (second key from the left on the second row of keys from
the top) to show the following input form: CALCULATOR MODES
Page 1-7
Press the !!@@OK#@ ( ) F soft menu key to return to normal display. Examples of
selecting different calculator modes are shown next.
Operating Mode
The calculator offers two operating modes: the Algebraic mode, and the
Reverse Polish Notation (RPN) mode. The default mode is the Algebraic
mode (as indicated in the figure above), however, users of earlier HP
calculators may be more familiar with the RPN mode.
To select an operating mode, first open the CALCULATOR MODES input form
by pressing the H button. The Operating Mode field will be highlighted.
Select the Algebraic or RPN operating mode by either using the \ key
(second from left in the fifth row from the keyboard bottom), or pressing the
@CHOOS soft menu key ( ). If using the latter approach, use up and down B
arrow keys, — ˜, to select the mode, and press the !!@@OK#@ soft menu key
to complete the operation.
To illustrate the difference between these two operating modes we will
calculate the following expression in both modes:
5.2
3
0.23
0.30.3
1
0.50.3
e+
⋅
−⋅
To enter this expression in the calculator we will first use the equation writer,
‚O. Please identify the following keys in the keyboard, besides the
numeric keypad keys:
!@.#*+-/R
Q¸Ü‚Oš™˜—`
The equation writer is a display mode in which you can build mathematical
expressions using explicit mathematical notation including fractions,
derivatives, integrals, roots, etc. To use the equation writer for writing the
expression shown above, use the following keystrokes:
‚OR3.*!Ü5.-
Page 1-8
1./3.*3.
—————
/23.Q3™™+!¸2.5`
After pressing `the calculator displays the expression:
√ (3.*(5.-1/(3.*3.))/23.^3+EXP(2.5))
Pressing `again will provide the following value (accept Approx mode on,
if asked, by pressing !!@@OK#@):
You could also type the expression directly into the display without using the
equation writer, as follows:
R!Ü3.*!Ü5.-
1/3.*3.™
/23.Q3+!¸2.5`
to obtain the same result.
Change the operating mode to RPN by first pressing the H button. Select
the RPN operating mode by either using the \key, or pressing the
@CHOOS soft menu key. Press the @@OK#@ (F ) soft menu key to complete the
operation. The display, for the RPN mode looks as follows:
Notice that the display shows several levels of output labeled, from bottom to
top, as 1, 2, 3, etc. This is referred to as the stack of the calculator. The
Page 1-9
different levels are referred to as the stack levels, i.e., stack level 1, stack level
2, etc.
Basically, what RPN means is that, instead of writing an operation such as 3
+ 2, in the calculator by using
3+2`
we write first the operands, in the proper order, and then the operator, i.e.,
3`2`+
As you enter the operands, they occupy different stack levels. Entering
3` 2`puts the number 3 in stack level 1. Next, entering pushes
the 3 upwards to occupy stack level 2. Finally, by pressing +, we are
telling the calculator to apply the operator, or program, + to the objects
occupying levels 1 and 2. The result, 5, is then placed in level 1.
Let's try some other simple operations before trying the more complicated
expression used earlier for the algebraic operating mode:
123/32 123`32/
42 4`2Q
3√ √( 27) 27`R3@»
Notice the position of the y and the x in the last two operations. The base in
the exponential operation is y (stack level 2) while the exponent is x (stack
level 1) before the key Q is pressed. Similarly, in the cubic root operation,
y (stack level 2) is the quantity under the root sign, and x (stack level 1) is the
root.
Try the following exercise involving 3 factors: (5 + 3) × 2
5`3`+ Calculates (5 +3) first.
2X Completes the calculation.
Let's try now the expression proposed earlier:
Page 1-10
5.2
3
23
33
1
53
e+
⋅
−⋅
3` Enter 3 in level 1
5` Enter 5 in level 1, 3 moves to level 2
3` Enter 3 in level 1, 5 moves to level 2, 3 to level 3
3* Place 3 and multiply, 9 appears in level 1
Y 1/(3×3), last value in lev. 1; 5 in level 2; 3 in level 3
- 5 - 1/(3×3) , occupies level 1 now; 3 in level 2
* 3× × (5 - 1/(3 3)), occupies level 1 now.
23` Enter 23 in level 1, 14.66666 moves to level 2.
3Q Enter 3, calculate 233 into level 1. 14.666 in lev. 2.
/ (3× × (5-1/(3 3)))/233
into level 1
2.5 Enter 2.5 level 1
!¸ e2.5, goes into level 1, level 2 shows previous value.
+ (3 3)))/23× (5 - 1/(3×3
+ e2.5 = 12.18369, into lev. 1.
R √ × ×((3 (5 - 1/(3 3)))/233
+ e2.5
) = 3.4905156, into 1.
To select between the ALG vs. RPN operating mode, you can also set/clear
system flag 95 through the following keystroke sequence:
H @)FLAGS —„—„—„— @@CHK@@
Number Format and decimal dot or comma
Changing the number format allows you to customize the way real numbers
are displayed by the calculator. You will find this feature extremely useful in
operations with powers of tens or to limit the number of decimals in a result.
To select a number format, first open the CALCULATOR MODES input form by
pressing the H button. Then, use the down arrow key, ˜, to select the
option Number format. The default value is Std, or Standard format. In the
standard format, the calculator will show floating-point numbers with no set
decimal placement and with the maximum precision allowed by the calculator
Page 1-11
(12 significant digits).”To learn more about reals, see Chapter 2 in this guide.
To illustrate this and other number formats try the following exercises:
• Standard format:
This mode is the most used mode as it shows numbers in the most familiar
notation. Press the !!@@OK#@ soft menu key, with the Number format set to
Std, to return to the calculator display. Enter the number
123.4567890123456 (with16 significant figures). Press the ` key.
The number is rounded to the maximum 12 significant figures, and is
displayed as follows:
• Fixed format with decimals:
Press the H button. Next, use the down arrow key, ˜, to select the
option Number format. Press the @CHOOS soft menu key ( B), and select
the option with the arrow down key Fixed ˜.
Press the right arrow key, ™, to highlight the zero in front of the option
Fix. Press the @CHOOS soft menu key and, using the up and down arrow
keys, —˜, select, say, 3 decimals.
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Press the !!@@OK#@ soft menu key to complete the selection:
Press the !!@@OK#@ soft menu key return to the calculator display. The
number now is shown as:
Notice how the number is rounded, not truncated. Thus, the number
123.4567890123456, for this setting, is displayed as 123.457, and not
as 123.456 because the digit after 6 is > 5.
• Scientific format
To set this format, start by pressing the H button. Next, use the down
arrow key, ˜, to select the option Number format. Press the @CHOOS soft
menu key ( B), and select the option Scientific with the arrow down key
˜. Keep the number 3 in front of the Sci. (This number can be
changed in the same fashion that we changed the Fixed number of
decimals in the example above).
Press the !!@@OK#@ soft menu key return to the calculator display. The
number now is shown as:
Page 1-13
This result, 1.23E2, is the calculator’s version of powers-of-ten notation,
i.e., 1.235 × 102. In this, so-called, scientific notation, the number 3 in
front of the Sci number format (shown earlier) represents the number of
significant figures after the decimal point. Scientific notation always
includes one integer figure as shown above. For this case, therefore, the
number of significant figures is four.
• Engineering format
The engineering format is very similar to the scientific format, except that
the powers of ten are multiples of three. To set this format, start by
pressing the H button. Next, use the down arrow key, ˜, to select
the option Number format. Press the @CHOOS soft menu key ( B), and
select the option Engineering with the arrow down key ˜. Keep the
number 3 in front of the Eng. (This number can be changed in the same
fashion that we changed the Fixed number of decimals in an earlier
example).
Press the !!@@OK#@ soft menu key return to the calculator display. The
number now is shown as:
Because this number has three figures in the integer part, it is shown with
four significative figures and a zero power of ten, while using the
Engineering format. For example, the number 0.00256, will be shown as:
Page 1-14
• Decimal comma vs. decimal point
Decimal points in floating-point numbers can be replaced by commas, if
the user is more familiar with such notation. To replace decimal points for
commas, change the FM option in the CALCULATOR MODES input form
to commas, as follows (Notice that we have changed the Number Format
to Std):
• Press the H ˜ button. Next, use the down arrow key, , once, and the
right arrow key, ™, highlighting the option __FM,. To select commas,
press the @@CHK@@ soft menu key (i.e., the B key). The input form will
look as follows:
• Press the !!@@OK#@ soft menu key return to the calculator display. The
number 123.4567890123456, entered earlier, now is shown as:
Angle Measure
Trigonometric functions, for example, require arguments representing plane
angles. The calculator provides three different Angle Measure modes for
working with angles, namely:
• Degrees 360 360: There are degrees ( o) in a complete circumference.
• Radians: There are 2π radians (2 π r) in a complete circumference.
Page 1-15
• Grades: There are 400 400 grades ( g) in a complete circumference.
The angle measure affects the trig functions like SIN, COS, TAN and
associated functions.
To change the angle measure mode, use the following procedure:
• Press the H ˜ button. Next, use the down arrow key, , twice. Select
the Angle Measure mode by either using the \key (second from left in
the fifth row from the keyboard bottom), or pressing the @CHOOS soft menu
key ( B). If using the latter approach, use up and down arrow
keys, (— ˜, to select the preferred mode, and press the !!@@OK#@ F)
soft menu key to complete the operation. For example, in the following
screen, the Radians mode is selected:
Coordinate System
The coordinate system selection affects the way vectors and complex numbers
are displayed and entered. To learn more about complex numbers and
vectors, see Chapters 4 and 8, respectively, in this . There are three guide
coordinate systems available in the calculator: Rectangular (RECT), Cylindrical
(CYLIN), and Spherical (SPHERE). To change coordinate system:
• Press the H ˜ button. Next, use the down arrow key, , three times.
Select the Coord System mode by either using the \ key (second from
left in the fifth row from the keyboard bottom), or pressing the @CHOOS soft
menu key ( B). If using the latter approach, use up and down arrow
keys, ( )— ˜, to select the preferred mode, and press the !!@@OK#@ F
soft menu key to complete the operation. For example, in the following
screen, the Polar coordinate mode is selected:
Page 1-16
Selecting CAS settings
CAS stands for C A Somputer lgebraic ystem. This is the mathematical core of
the calculator where the symbolic mathematical operations and functions are
programmed. The CAS offers a number of settings can be adjusted according
to the type of operation of interest. To see the optional CAS settings use the
following:
• Press the button to activate the CALCULATOR MODES input form. H
• To change CAS settings press the @@ CAS@@ soft menu key. The default values
of the CAS setting are shown below:
• To navigate through the many options in the CAS MODES input form, use
the arrow keys: š™˜—.
• To select or deselect any of the settings shown above, select the underline
before the option of interest, and toggle the @@CHK@@ soft menu key until the
right setting is achieved. When an option is selected, a check mark will
be shown in the underline (e.g., the Rigorous and Simp Non-Rational
Page 1-17
options above). Unselected options will show no check mark in the
underline preceding the option of interest (e.g., the _Numeric, _Approx,
_Complex, _Verbose, _Step/Step, _Incr Pow options above).
• After having selected and unselected all the options that you want in the
CAS MODES input form, press the @@@OK@@@ soft menu key. This will take you
back to the CALCULATOR MODES input form. To return to normal
calculator display at this point, press the soft menu key once more. @@@OK@@@
Explanation of CAS settings
• Indep var: The independent variable for CAS applications. Typically, VX
= ‘X’.
• Modulo : For operations in modular arithmetic this variable holds the
modulus or modulo of the arithmetic ring (see Chapter 5 in the calculator’s
user’s guide).
• Numeric : If set, the calculator produces a numeric, or floating-point result,
in calculations.
• Approx : If set, Approximate mode uses numerical results in calculations. If
unchecked, the CAS is in Exact mode, which produces symbolic results in
algebraic calculations.
• Complex : If set, complex number operations are active. If unchecked the
CAS is in Real mode, i.e., real number calculations are the default. See
Chapter 4 for operations with complex numbers.
• Verbose : If set, provides detailed information in certain CAS operations.
• Step/Step : If set, provides step-by-step results for certain CAS operations.
Useful to see intermediate steps in summations, derivatives, integrals,
polynomial operations (e.g., synthetic division), and matrix operations.
• Incr Pow : Increasing Power, means that, if set, polynomial terms are
shown in increasing order of the powers of the independent variable.
• Rigorous : If set, calculator does not simplify the absolute value function
|X| to X.
• Simp Non-Rational : If set, the calculator will try to simplify non-rational
expressions as much as possible.
Selecting Display modes
Page 1-18
The calculator display can be customized to your preference by selecting
different display modes. To see the optional display settings use the following:
• First, press the H button to activate the CALCULATOR MODES input
form. Within the CALCULATOR MODES input form, press the @@DISP@ soft
menu key ( ) to display the DISPLAY MODES input form. D
• To navigate through the many options in the DISPLAY MODES input form,
use the arrow keys: š™˜—.
• To select or deselect any of the settings shown above, that require a check
mark, select the underline before the option of interest, and toggle the
@CHK@@ soft menu key until the right setting is achieved. When an option
is selected, a check mark will be shown in the underline (e.g., the
Textbook option in the Stack: line above). Unselected options will show
no check mark in the underline preceding the option of interest (e.g., the
_Small, _Full page, and _Indent options in the Edit: line above).
• To select the Font for the display, highlight the field in front of the Font:
option in the DISPLAY MODES input form, and use the @CHOOS soft menu
key (B).
• After having selected and unselected all the options that you want in the
DISPLAY MODES input form, press the @@@OK@@@ soft menu key. This will take
you back to the CALCULATOR MODES input form. To return to normal
calculator display at this point, press the soft menu key once more. @@@OK@@@
Selecting the display font
First, press the H button to activate the CALCULATOR MODES input form.
Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key
Page 1-19
(D) to display the DISPLAY MODES input form. The Font: field is
highlighted, and the option Ft8_0:system 8 is selected. This is the default
value of the display font. Pressing the @CHOOS soft menu key (B), will provide
a list of available system fonts, as shown below:
The options available are three standard System Fonts (sizes 8, 7, and 6) and
a Browse.. option. The latter will let you browse the calculator memory for
additional fonts that you may have created or downloaded into the calculator.
Practice changing the display fonts to sizes 7 and 6. Press the OK soft menu
key to effect the selection. When done with a font selection, press the @@@OK@@@
soft menu key to go back to the CALCULATOR MODES input form. To return
to normal calculator display at this point, press the @@@OK@@@ soft menu key once
more and see how the stack display change to accommodate the different font.
Selecting properties of the line editor
First, press the H button to activate the CALCULATOR MODES input form.
Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key
(D) to display the DISPLAY MODES input form. Press the down arrow key,
˜, once, to get to the Edit line. This line shows three properties that can be
modified. When these properties are selected (checked) the following effects
are activated:
_Small Changes font size to small
_Full page Allows to place the cursor after the end of the line
_Indent Auto indent cursor when entering a carriage return
Instructions on the use of the line editor are presented in Chapter 2 in the
user’s guide.
Page 1-20
Selecting properties of the Stack
First, press the H button to activate the CALCULATOR MODES input form.
Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key
(D) to display the DISPLAY MODES input form. Press the down arrow key,
˜, twice, to get to the Stack line. This line shows two properties that can be
modified. When these properties are selected (checked) the following effects
are activated:
_Small Changes font size to small. This maximizes the amount of
information displayed on the screen. Note, this selection
overrides the font selection for the stack display.
_Textbook Displays mathematical expressions in graphical mathematical
notation
To illustrate these settings, either in algebraic or RPN mode, use the equation
writer to type the following definite integral:
‚O…Á0™„虄¸\x™x`
In Algebraic mode, the following screen shows the result of these keystrokes
with neither nor are selected: _Small _Textbook
With the option selected only, the display looks as shown below: _Small
With the option selected (default value), regardless of whether the _Textbook
_Small option is selected or not, the display shows the following result:
Page 1-21
Selecting properties of the equation writer (EQW)
First, press the H button to activate the CALCULATOR MODES input form.
Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key
(D) to display the DISPLAY MODES input form. Press the down arrow key,
˜, three times, to get to the EQW (Equation Writer) line. This line shows
two properties that can be modified. When these properties are selected
(checked) the following effects are activated:
_Small Changes font size to small while using the equation
editor
_Small Stack Disp Shows small font in the stack after using the equation
editor
Detailed instructions on the use of the equation editor (EQW) are presented
elsewhere in this manual.
For the example of the integral ∫∞−
0dXe X, presented above, selecting the
_Small Stack Disp in the EQW line of the DISPLAY MODES input form
produces the following display:
References
Additional references on the subjects covered in this Chapter can be found in
Chapter 1 and Appendix C of the calculator’s user’s guide.
Page 2-1
Chapter 2
Introducing the calculator
In this chapter we present a number of basic operations of the calculator
including the use of the Equation Writer and the manipulation of data objects
in the calculator. Study the examples in this chapter to get a good grasp of
the capabilities of the calculator for future applications.
Calculator objects
Some of the most commonly used objects are: reals (real numbers, written with
a decimal point, e.g., -0.0023, 3.56), integers (integer numbers, written
without a decimal point, e.g., 1232, -123212123), complex numbers (written
as an ordered pair, e.g., (3,-2)), lists, etc. Calculator objects are described in
Chapters 2 and 24 in the calculator’s user guide.
Editing expressions in the stack
In this section we present examples of expression editing directly into the
calculator display or stack.
Creating arithmetic expressions
For this example, we select the Algebraic operating mode and select a Fix
format with 3 decimals for the display. We are going to enter the arithmetic
expression:
3
0.20.3
5.7
0.1
0.1
0.5 −
+
⋅
To enter this expression use the following keystrokes:
5.*„Ü1.+1/7.5™/
„ÜR3.-2.Q3
The resulting expression is: 5*(1+1/7.5)/( ƒ3-2^3).
Press ` to get the expression in the display as follows:
Page 2-2
Notice that, if your CAS is set to EXACT (see Appendix C in user’s guide) and
you enter your expression using integer numbers for integer values, the result
is a symbolic quantity, e.g.,
5*„Ü1+1/7.5™/
„ÜR3-2Q3
Before producing a result, you will be asked to change to Approximate mode.
Accept the change to get the following result (shown in Fix decimal mode with
three decimal places – see Chapter 1):
In this case, when the expression is entered directly into the stack, as soon as
you press the calculator will attempt to calculate a value for the `,
expression. If the expression is entered between apostrophes, however, the
calculator will reproduce the expression as entered. For example:
³5*„Ü1+1/7.5™/
„ÜR3-2Q3`
The result will be shown as follows:
Page 2-3
To evaluate the expression we can use the EVAL function, as follows:
µ„î`
If the CAS is set to Exact, you will be asked to approve changing the CAS
setting to Approx. Once this is done, you will get the same result as before.
An alternative way to evaluate the expression entered earlier between quotes
is by using the option …ï.
We will now enter the expression used above when the calculator is set to the
RPN operating mode. We also set the CAS to Exact, the display to Textbook,
and the number format to The keystrokes to enter the expression Standard.
between quotes are the same used earlier, i.e.,
³5*„Ü1+1/7.5™/
„ÜR3-2Q3`
Resulting in the output
Press ` once more to keep two copies of the expression available in the
stack for evaluation. We first evaluate the expression using the function EVAL,
and next using the function NUM: µ.
Page 2-4
This expression is semi-symbolic in the sense that there are floating-point
components to the result, as well as a 3. Next, we switch stack locations √
[using ™] and evaluate using function NUM, i.e., ™…ï.
This latter result is purely numerical, so that the two results in the stack,
although representing the same expression, seem different. To verify that they
are not, we subtract the two values and evaluate this difference using function
EVAL: -µ. The result is zero (0.).
For additional information on editing arithmetic expressions in the display or
stack, see Chapter 2 in the calculator’s user’s guide.
Creating algebraic expressions
Algebraic expressions include not only numbers, but also variable names. As
an example, we will enter the following algebraic expression:
b
L
yR
R
x
L
2
12
+
+
+
We set the calculator operating mode to Algebraic, the CAS to , and the Exact
display to Textbook. To enter this algebraic expression we use the following
keystrokes:
³2*~l*R„Ü1+~„x/~r™/
„ Ü ~r+~„y™+2*~l/~„b
Press ` to get the following result:
Page 2-5
Entering this expression when the calculator is set in the RPN mode is exactly
the same as this Algebraic mode exercise.
For additional information on editing algebraic expressions in the calculator’s
display or stack see Chapter 2 in the calculator’s user’s guide.
Using the Equation Writer (EQW) to create expressions
The equation writer is an extremely powerful tool that not only let you enter or
see an equation, but also allows you to modify and work/apply functions on
all or part of the equation.
The Equation Writer is launched by pressing the keystroke combination
‚O (the third key in the fourth row from the top in the keyboard). The
resulting screen is the following. Press to see the second menu page: L
The six soft menu keys for the Equation Writer activate functions EDIT, CURS,
BIG, EVAL, FACTOR, SIMPLIFY, CMDS, and HELP. Detailed information on
these functions is provided in Chapter 3 of the calculator’s user’s guide.
Creating arithmetic expressions
Entering arithmetic expressions in the Equation Writer is very similar to
entering an arithmetic expression in the stack enclosed in quotes. The main
difference is that in the Equation Writer the expressions produced are written
in “textbook” style instead of a line-entry style. For example, try the following
keystrokes in the Equation Writer screen: 5/5+2
The result is the expression
Page 2-6
The cursor is shown as a left-facing key. The cursor indicates the current
edition location. For example, for the cursor in the location indicated above,
type now: *„Ü5+1/3
The edited expression looks as follows:
Suppose that you want to replace the quantity between parentheses in the
denominator (i.e., 5+1/3) with (5+π 2/2). First, we use the delete key (ƒ)
delete the current 1/3 expression, and then we replace that fraction with π 2/2,
as follows: ƒƒƒ„ìQ2
When hit this point the screen looks as follows:
In order to insert the denominator in the expression, we need to highlight 2
the entire π 2 expression. We do this by pressing the right arrow key (™)
once. At that point, we enter the following keystrokes:
/2
Page 2-7
The expression now looks as follows:
Suppose that now you want to add the fraction 1/3 to this entire expression,
i.e., you want to enter the expression:
3
1
)
2
5(25
5
2+
+⋅+π
First, we need to highlight the entire first term by using either the right arrow
(™) or the upper arrow (—) keys, repeatedly, until the entire expression is
highlighted, i.e., seven times, producing:
NOTE: Alternatively, from the original position of the cursor (to the right of the
2 in the denominator of π 2/2), we can use the keystroke combination ‚—
, interpreted as (‚ ‘ ).
Once the expression is highlighted as shown above, type +1/3 to
add the fraction 1/3. Resulting in:
Page 2-8
Creating algebraic expressions
An algebraic expression is very similar to an arithmetic expression, except
that English and Greek letters may be included. The process of creating an
algebraic expression, therefore, follows the same idea as that of creating an
arithmetic expression, except that use of the alphabetic keyboard is included.
To illustrate the use of the Equation Writer to enter an algebraic equation we
will use the following example. Suppose that we want to enter the expression:
∆⋅+
⋅+−
3/1
2
3
2
θ
µ
λµyx
LNe
Use the following keystrokes:
2 / R3 ™™ * ~‚n + „¸\ ~‚m
™™ * ‚¹ ~„x + 2 * ~‚m * ~‚c
~„y ——— / ~‚t Q1/3
This results in the output:
In this example we used several lower-case English letters, e.g., x
(~„x), several Greek letters, e.g., λ (~‚n), and even a
combination of Greek and English letters, namely, ∆y (~‚c
~„y). Keep in mind that to enter a lower-case English letter, you need
to use the combination: followed by the letter you want to enter. ~„
Page 2-9
Also, you can always copy special characters by using the CHARS menu
(…±) if you don’t want to memorize the keystroke combination that
produces it. A listing of commonly used keystroke combinations is ~‚
listed in Appendix D of the user’s guide.
For additional information on editing, evaluating, factoring, and simplifying
algebraic expressions see Chapter 2 of the calculator’s user’s guide.
Organizing data in the calculator
You can organize data in your calculator by storing variables in a directory
tree. The basis of the calculator’s directory tree is the HOME directory
described next.
The HOME directory
To get to the HOME directory, press the UPDIR function („§) -- repeat as
needed -- until the spec is shown in the second line of the display {HOME}
header. Alternatively, use . For this example, the HOME „ (hold) §
directory contains nothing but the CASDIR. Pressing will show the J
variables in the soft menu keys:
Subdirectories
To store your data in a well organized directory tree you may want to create
subdirectories under the HOME directory, and more subdirectories within
subdirectories, in a hierarchy of directories similar to folders in modern
computers. The subdirectories will be given names that may reflect the
contents of each subdirectory, or any arbitrary name that you can think off.
For details on manipulation of directories see Chapter 2 in the calculator’s
user’s guide.
Page 2-10
Variables
Variables are similar to files on a computer hard drive. One variable can
store one object (numerical values, algebraic expressions, lists, vectors,
matrices, programs, etc). Variables are referred to by their names, which can
be any combination of alphabetic and numerical characters, starting with a
letter (either English or Greek). Some non-alphabetic characters, such as the
arrow (→) can be used in a variable name, if combined with an alphabetical
character. Thus, ‘ ’ is not. Valid →A’ is a valid variable name, but ‘→
examples of variable names are: ‘A’, ‘B’, ‘a’, ‘b’, ‘ ’, ‘A1’, ‘AB12’, α’, ‘β
‘A12’,’Vel’,’Z0’,’z1’, etc.
A variable can not have the same name as a function of the calculator. Some
of the reserved calculator variable names are the following: ALRMDAT, CST,
EQ, EXPR, IERR, IOPAR, MAXR, MINR, PICT, PPAR, PRTPAR, VPAR, ZPAR,
der_, e, i, n1,n2, …, s1, s2, …, Σ ΣDAT, PAR, π, ∞
Variables can be organized into sub-directories (see Chapter 2 in the
calculator’s user’s guide).
Typing variable names
To name variables, you will have to type strings of letters at once, which may
or may not be combined with numbers. To type strings of characters you can
lock the alphabetic keyboard as follows:
~~ locks the alphabetic keyboard in upper case. When locked in this
fashion, pressing the „ before a letter key produces a lower case letter,
while pressing the ‚ key before a letter key produces a special character.
If the alphabetic keyboard is already locked in upper case, to lock it in lower
case, type, „~
~~„~ locks the alphabetic keyboard in lower case. When locked
in this fashion, pressing the „ before a letter key produces an upper case
letter. To unlock lower case, press „~
Page 2-11
To unlock the upper-case locked keyboard, press ~
Try the following exercises:
³~~math`
³~~m„a„t„h`
³~~m„~at„h`
The calculator display will show the following (left-hand side is Algebraic
mode, right-hand side is RPN mode):
Creating variables
The simplest way to create a variable is by using the . The following K
examples are used to store the variables listed in the following table (Press
J if needed to see variables menu):
Name Contents Type
α -0.25 real
A12 3×10 5 real
Q ‘r/(m+r)' algebraic
R [3,2,1] vector
z1 3+5i complex
p1 « » → r 'π*r^2' program
• Algebraic mode
To store the value of –0.25 into variable α: 0.25\
K ~‚a. AT this point, the screen will look as follows:
Page 2-12
Press ` to create the variable. The variable is now shown in the
soft menu key labels:
The following are the keystrokes required to enter the remaining
variables:
A12: 3V5K~a12`
Q: ³~„r/„Ü
~„m+~„r™™ K~q`
R: „Ô3‚í2‚í1™ K~r`
z1: 3+5*„¥ K~„z1` (Accept
change to mode if asked). Complex
p1: ‚å‚é~„r³„ì*
~„rQ2™™™ K~„p1`..
The screen, at this point, will look as follows:
You will see six of the seven variables listed at the bottom of the
screen: p1, z1, R, Q, A12, α.
Page 2-13
• RPN mode
(Use H\@@OK@@ to change to RPN mode). Use the following
keystrokes to store the value of –0.25 into variable α:
0.25\` ~‚a`. At this point, the screen
will look as follows:
This expression means that the value –0.25 is ready to be stored into
α. Press K to create the variable. The variable is now shown in
the soft menu key labels:
To enter the value 3×10 5 into A12, we can use a shorter version of
the procedure: 3V5³~a12` K
Here is a way to enter the contents of Q:
Q: ³~„r/„Ü
~„m+~„r™™ ³~q` K
To enter the value of R, we can use an even shorter version of the
procedure:
R: „Ô3#2#1™ ³K
Notice that to separate the elements of a vector in RPN mode we can
use the space key ( ), rather than the comma ( ) used # ‚í
above in Algebraic mode.
z1: ³3+5*„¥ ³~„z1 K
Page 2-14
p1: ‚å‚é~„r³„ì*
~„rQ2™™™ ³ ~„p1™` K.
The screen, at this point, will look as follows:
You will see six of the seven variables listed at the bottom of the
screen: p1, z1, R, Q, A12, α.
Checking variables contents
The simplest way to check a variable content is by pressing the soft menu key
label for the variable. For example, for the variables listed above, press the
following keys to see the contents of the variables:
Algebraic mode
Type these keystrokes: J ` `@@z1@@ @@@R@@ @@@Q@@@ `. At this point, the
screen looks as follows:
RPN mode
In RPN mode, you only need to press the corresponding soft menu key label to
get the contents of a numerical or algebraic variable. For the case under
consideration, we can try peeking into the variables z1 A12, R Q, , , , α
created above, as follows: J@@z1@@ @@@R@@ @@@Q@@ @@A12@@ @@ª@@
At this point, the screen looks like this:
Page 2-15
Using the right-shift key followed by soft menu key labels
This approach for viewing the contents of a variable works the same in both
Algebraic and RPN modes. Try the following examples in either mode:
J‚@@p1@@ ‚ ‚ ‚ ‚ @@z1@@ @@@R@@ @@@Q@@ @@A12@@
This produces the following screen (Algebraic mode in the left, RPN in the
right)
Notice that this time the contents of program are listed in the screen. To p1
see the remaining variables in this directory, use:
@@@ª@@ @@@A@@ L ‚
Listing the contents of all variables in the screen
Use the keystroke combination to list the contents of all variables in ‚˜
the screen. For example:
Press $ to return to normal calculator display.
Page 2-16
Deleting variables
The simplest way of deleting variables is by using function PURGE. This
function can be accessed directly by using the TOOLS menu ( ), or by I
using the FILES menu „¡@@OK@@ .
Using function PURGE in the stack in Algebraic mode
Our variable list contains variables p1, z1, Q, R, and α. We will use
command PURGE to delete variable p1. Press I @PURGE@ J@@p1@@ `.
The screen will now show variable p1 removed:
You can use the PURGE command to erase more than one variable by placing
their names in a list in the argument of PURGE. For example, if now we
wanted to purge variables and R Q, simultaneously, we can try the following
exercise. Press :
I @PURGE@ „ä³ J@@@R!@@ ™ ‚í ³ J@@@Q!@@
At this point, the screen will show the following command ready to be
executed:
To finish deleting the variables, press . The screen will now show the `
remaining variables:
Page 6-10
Then, enter the SOLVE environment and select Solve equation…, by using:
‚Ï@@OK@@. The corresponding screen will be shown as:
The equation we stored in variable EQ is already loaded in the Eq field in the
SOLVE EQUATION input form. Also, a field labeled x is provided. To solve
the equation all you need to do is highlight the field in front of X: by using
˜, and press @SOLVE@. The solution shown is X: 4.5006E-2:
This, however, is not the only possible solution for this equation. To obtain a
negative solution, for example, enter a negative number in the X: field before
solving the equation. Try 3\@@@OK@@˜@SOLVE@. The solution is now X: -
3.045.
Solution to simultaneous equations with MSLV
Function MSLV is available in the menu. The help-facility entry for ‚Ï
function MSLV is shown next:
Page 6-11
Notice that function MSLV requires three arguments:
1. A vector containing the equations, i.e., ‘[SIN(X)+Y,X+SIN(Y)=1]’
2. A vector containing the variables to solve for, i.e., ‘[X,Y]’
3. A vector containing initial values for the solution, i.e., the initial values
of both X and Y are zero for this example.
In ALG mode, press to copy the example to the stack, press @ECHO ` to run
the example. To see all the elements in the solution you need to activate the
line editor by pressing the down arrow key ( ) ˜ :
In RPN mode, the solution for this example is produced by using:
Activating function MSLV results in the following screen.
You may have noticed that, while producing the solution, the screen shows
intermediate information on the upper left corner. Since the solution provided
Page 6-12
by MSLV is numerical, the information in the upper left corner shows the
results of the iterative process used to obtain a solution. The final solution is X
= 1.8238, Y = -0.9681.
Reference
Additional information on solving single and multiple equations is provided in
Chapters 6 and 7 of the calculator’s user’s guide.
Page 7-3
Note: If we had entered the elements in lists L4 and L3 as integers, the infinite
symbol would be shown whenever a division by zero occurs. To produce the
following result you need to re-enter the lists as integer (remove decimal
points) using Exact mode:
If the lists involved in the operation have different lengths, an error message
(Invalid Dimensions) is produced. Try, for example, L1-L4.
The plus sign ( ), when applied to lists, acts a + concatenation operator,
putting together the two lists, rather than adding them term-by-term. For
example:
In order to produce term-by-term addition of two lists of the same length, we
need to use operator ADD. This operator can be loaded by using the function
catalog ( ). The screen below shows an application of ADD to add ‚N
lists L1 and L2, term-by-term:
Functions applied to lists
Real number functions from the keyboard (ABS, e x, LN, 10 x, LOG, SIN, x 2, , √
COS, TAN, ASIN, ACOS, ATAN, y x) as well as those from the
MTH/HYPERBOLIC menu (SINH, COSH, TANH, ASINH, ACOSH, ATANH),
and MTH/REAL menu (%, etc.), can be applied to lists, e.g.,
Page 7-4
ABS INVERSE (1/x)
Lists of complex numbers
You can create a complex number list, say, L5 = L1 ADD i*L2 (type the
instruction as indicated before), as follows:
Functions such as LN, EXP, SQ, etc., can also be applied to a list of complex
numbers, e.g.,
Lists of algebraic objects
The following are examples of lists of algebraic objects with the function SIN
applied to them (select Exact mode for these examples -- See Chapter 1):
The MTH/LIST menu
The MTH menu provides a number of functions that exclusively to lists. With
system flag 117 set to CHOOSE boxes, the MTH/LIST menu offers the
following functions:
Page 7-5
With system flag 117 set to SOFT menus, the MTH/LIST menu shows the
following functions:
The operation of the MTH/LIST menu is as follows:
∆LIST : Calculate increment among consecutive elements in list
ΣLIST : Calculate summation of elements in the list
ΠLIST : Calculate product of elements in the list
SORT : Sorts elements in increasing order
REVLIST : Reverses order of list
ADD : Operator for term-by-term addition of two lists of the same length
(examples of this operator were shown above)
Examples of application of these functions in ALG mode are shown next:
SORT and REVLIST can be combined to sort a list in decreasing order:
Page 7-6
The SEQ function
The SEQ function, available through the command catalog ( ), takes ‚N
as arguments an expression in terms of an index, the name of the index, and
starting, ending, and increment values for the index, and returns a list
consisting of the evaluation of the expression for all possible values of the
index. The general form of the function is
SEQ(expression, index, start, end, increment)
For example:
The list produced corresponds to the values {1 2, 2 2, 3 2, 4 2}.
The MAP function
The MAP function, available through the command catalog ( ), takes ‚N
as arguments a list of numbers and a function f(X), and produces a list
consisting of the application of function f or the program to the list of numbers.
For example, the following call to function MAP applies the function SIN(X) to
the list {1,2,3}:
Reference
For additional references, examples, and applications of lists see Chapter 8 in
the calculator’s user’s guide.
Page 8-1
Chapter 8
Vectors
This Chapter provides examples of entering and operating with vectors, both
mathematical vectors of many elements, as well as physical vectors of 2 and 3
components.
Entering vectors
In the calculator, vectors are represented by a sequence of numbers enclosed
between brackets, and typically entered as row vectors. The brackets are
generated in the calculator by the keystroke combination „Ô ,
associated with the key. The following are examples of vectors in the *
calculator:
[3.5, 2.2, -1.3, 5.6, 2.3] A general row vector
[1.5,-2.2] A 2-D vector
[3,-1,2] A 3-D vector
['t','t^2','SIN(t)'] A vector of algebraics
Typing vectors in the stack
With the calculator in ALG mode, a vector is typed into the stack by opening
a set of brackets („Ô) and typing the components or elements of the
vector separated by commas (‚í). The screen shots below show the
entering of a numerical vector followed by an algebraic vector. The figure to
the left shows the algebraic vector before pressing . The figure to the right `
shows the calculator’s screen after entering the algebraic vector:
In RPN mode, you can enter a vector in the stack by opening a set of brackets
and typing the vector components or elements separated by either commas
Page 8-3
The @EDIT key is used to edit the contents of a selected cell in the
Matrix Writer.
The @VEC@@ key, when selected, will produce a vector, as opposed to a
matrix of one row and many columns.
The ←WID key is used to decrease the width of the columns in the
spreadsheet. Press this key a couple of times to see the column width
decrease in your Matrix Writer.
The @WID→ key is used to increase the width of the columns in the
spreadsheet. Press this key a couple of times to see the column width
increase in your Matrix Writer.
The @GO→ key, when selected, automatically selects the next cell to
the right of the current cell when you press `. This option is
selected by default. This option, if desired, needs to be selected
before entering elements.
The @GO↓ key, when selected, automatically selects the next cell below
the current cell when you press `. This option, if desired, needs to
be selected before entering elements.
Moving to the right vs. moving down in the Matrix Writer
Activate the Matrix Writer and enter 3`5`2`` with the
@GO→ key selected (default). Next, enter the same sequence of numbers with
the @GO↓ key selected to see the difference. In the first case you entered a
vector of three elements. In the second case you entered a matrix of three
rows and one column.
Activate the Matrix Writer again by using „², and press L to check
out the second soft key menu at the bottom of the display. It will show the
keys:
@+ROW@ @-ROW @+COL@ @-COL@
@→STK@@ @GOTO@
Page 8-4
The @+ROW@ key will add a row full of zeros at the location of the
selected cell of the spreadsheet.
The @-ROW key will delete the row corresponding to the selected cell of
the spreadsheet.
The @+COL@ key will add a column full of zeros at the location of the
selected cell of the spreadsheet.
The @-COL@ key will delete the column corresponding to the selected
cell of the spreadsheet.
The @→STK@@ key will place the contents of the selected cell on the stack.
The @GOTO@ key, when pressed, will request that the user indicate the
number of the row and column where he or she wants to position the
cursor.
Pressing L once more produces the last menu, which contains only one
function @@DEL@ (delete).
The function @@DEL@ will delete the contents of the selected cell and
replace it with a zero.
To see these keys in action try the following exercise:
(1) Activate the Matrix Writer by using „². Make sure the @VEC and
@GO→ keys are selected.
(2) Enter the following:
1`2`3`
L @GOTO@ 2 @@OK@@ @@OK@@ @@OK@@ 1
4`5`6`
7`8`9`
Page 8-5
(3) Move the cursor up two positions by using ——. Then press @-ROW.
The second row will disappear.
(4) Press @+ROW@. A row of three zeroes appears in the second row.
(5) Press @-COL@. The first column will disappear.
(6) Press @+COL@. A column of two zeroes appears in the first column.
(7) Press @GOTO@ @@OK@@ @@OK@@ @@OK@@ 3 3 to move to position (3,3).
(8) Press @→STK@@. This will place the contents of cell (3,3) on the stack,
although you will not be able to see it yet. Press ` to return to normal
display. The number 9, element (3,3), and the full matrix entered will be
available in the stack.
Simple operations with vectors
To illustrate operations with vectors we will use the vectors u2, u3, v2, and v3,
stored in an earlier exercise. Also, store vector A=[-1,-2,-3,-4,-5] to be used in
the following exercises.
Changing sign
To change the sign of a vector use the key \, e.g.,
Addition, subtraction
Addition and subtraction of vectors require that the two vector operands have
the same length:
Page 8-6
Attempting to add or subtract vectors of different length produces an error
message:
Multiplication by a scalar, and division by a scalar
Multiplication by a scalar or division by a scalar is straightforward:
Absolute value function
The absolute value function (ABS), when applied to a vector, produces the
magnitude of the vector. For example: ABS([1,-2,6]) ABS(A), ,
ABS(u3), will show in the screen as follows:
Page 8-7
The MTH/VECTOR menu
The MTH menu ( ) contains a menu of functions that specifically to „´
vector objects:
The VECTOR menu contains the following functions (system flag 117 set to
CHOOSE boxes):
Magnitude
The magnitude of a vector, as discussed earlier, can be found with function
ABS. This function is also available from the keyboard ( ). Examples „Ê
of application of function ABS were shown above.
Dot product
Function DOT (option 2 in CHOOSE box above) is used to calculate the dot
product of two vectors of the same length. Some examples of application of
function DOT, using the vectors A, u2, u3, v2, and v3, stored earlier, are
shown next in ALG mode. Attempts to calculate the dot product of two vectors
of different length produce an error message:
Page 9-1
Chapter 9
Matrices and linear algebra
This chapter shows examples of creating matrices and operations with
matrices, including linear algebra applications.
Entering matrices in the stack
In this section we present two different methods to enter matrices in the
calculator stack: (1) using the Matrix Writer, and (2) typing the matrix directly
into the stack.
Using the Matrix Writer
As with the case of vectors, discussed in Chapter 8, matrices can be entered
into the stack by using the Matrix Writer. For example, to enter the matrix:
first, start the Matrix Writer by using . Make sure that the option „²
@GO→ is selected. Then use the following keystrokes:
2.5\` 4.2` 2`˜ššš
.3` 1.9` 2.8 `
2` .1\` .5`
At this point, the Matrix Writer screen may look like this:
,
5.01.02
8.29.13.0
0.22.45.2
−
−
Page 9-2
Press ` once more to place the matrix on the stack. The ALG mode stack is
shown next, before and after pressing , once more:
If you have selected the textbook display option (using H@)DISP! and checking
off Textbook), the matrix will look like the one shown above. Otherwise,
the display will show:
The display in RPN mode will look very similar to these.
Typing in the matrix directly into the stack
The same result as above can be achieved by entering the following directly
into the stack:
„Ô
„Ô 2.5\ ‚í 4.2 ‚í 2 ™
‚í
„Ô .3 ‚í 1.9 ‚í 2.8 ™
‚í
„Ô 2 ‚í .1\ ‚í .5 `
Thus, to enter a matrix directly into the stack open a set of brackets („Ô)
and enclose each row of the matrix with an additional set of brackets
(„Ô). Commas ( ) should separate the elements of each ‚í .
row, as well as the brackets between rows.
For future exercises, let’s save this matrix under the name A. In ALG mode
use K~a. In RPN mode, use ³~a K.
Page 9-3
Operations with matrices
Matrices, like other mathematical objects, can be added and subtracted.
They can be multiplied by a scalar, or among themselves. An important
operation for linear algebra applications is the inverse of a matrix. Details of
these operations are presented next.
To illustrate the operations we will create a number of matrices that we will
store in the following variables. Here are the matrices A22, B22, A23, B23,
A33 and B33 (The random matrices in your calculator may be differents):
In RPN mode, the steps to follow are:
{2,2} RANM 'A22' {2,2} RANM 'B22'` `K ` `K
{2,3} RANM 'A23' {2,3} RANM 'B23'` `K ` `K
{3,2} RANM 'A32' {3,2} RANM 'B32'` `K ` `K
{3,3} RANM 'A33' {3,3} RANM 'B33'` `K ` `K
Addition and subtraction
Four examples are shown below using the matrices stored above (ALG mode).
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