graphing calculator
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Preface
Table of Contents
Chapter 3 – Calculations with real numbers
Chapter 4 – Calculations with complex numbers
Chapter 5 – Algebraic and arithmetic operations
Chapter 6 – Solution to equations
Chapter 7 – Operations with lists
The SEQ function
The MAP function
Chapter 8 – Vectors
Entering vectors
Typing vectors in the stack
Chapter 10 – Graphics
Chapter 11 – Calculus Applications
Chapter 12 – Multi-variateCalculus Applications
Chapter 13 – Vector Analysis Applications
Chapter 14 – Differential Equations
Chapter 15 – Probability Distributions
Chapter 16 – Statistical Applications
Chapter 17 – Numbers in Different Bases
Warranty – W-1
Chapter
Getting started
Turning the calculator on and off
Adjusting the display contrast
Contents of the calculator’s display
@EDIT @VIEW @@RCL @@ @@STO@ ! PURGE !CLEAR
ABCDEF
Menus
The TOOL menu
@EDIT
A EDIT the contents of a variable (see Chapter 2 in this Guide
and Chapter 2 and Appendix L in the user's guide for more
information on editing)
B VIEW the contents of a variable
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~„p
~…p
SYMB
Selecting calculator modes
!!@@OK#@ F
Operating Mode
@CHOOSE
!!@@OK#@
!@.#*+-/R Q¸Ü‚Oš™˜—`
1./3.*3
/23.Q3™™™+!¸2.5`
R!Ü3.*!Ü5
1/3.*3.™
/23.Q3+!¸2.5`
3+2`
3`2`+
123`32
424`2Q
3√2727`R3@»
23`
H@)FLAGS —„—„—„—@@CHK@
Number Format and decimal dot or comma
•Standard format:
•Fixed format with decimals:
Fixed
Fix
Press the !!@@OK#@ soft menu key to complete the selection:
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Page
@CHECK
Angle Measure
Coordinate System
Selecting CAS settings
•Press the Hbutton to activate the CALCULATOR MODES input form
To change CAS settings press the
@@ CAS@@
š™˜—
_Numeric, _Approx, _Complex, _Verbose, _Step/Step, _Incr Pow
Explanation of CAS settings
•Indep var: The independent variable for CAS applications. Typically, VX = ‘X’
Modulo
Numeric
@@CHK@@
Textbook
Stack:
_Small, _Full page
_Indent
Ft8_0:system
Selecting properties of the line editor
Edit
_Small
Changes font size to small
Selecting properties of the Stack
‚O…Á0™„虄¸\x™x`
Selecting properties of the equation writer (EQW)
References
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Introducing the calculator
5*„Ü1+1/7.5™
„ÜR3-2Q3
³5*„Ü1+1/7.5™
„ÜR3-2Q3`
µ„î
…³5*„Ü1+1/7.5™
™…ï
Creating algebraic expressions
2L 1 +
2*~l*R„Ü1+~„x/~r™/„ Ü~r+~„y™+2*~l/~„b
Using the Equation Writer (EQW) to create expressions
5/5+2
The result is the expression
*„Ü5+1/3
ƒƒƒ„ìQ2
NOTE
+1/3
x + 2∝ ⋅ ∆y
λ + e
Use the following keystrokes:
2/R3™™*~‚n+„¸\~‚m
™™*‚¹~„x+2*~‚m*~‚c ~„y———/~‚tQ1/3
Organizing data in the calculator
The HOME directory
Subdirectories
Variables
Typing variable names
³~~math1~`
³~~m„a„t„h~`
³~~m„~at„h~`
Creating variables
Name
A12: 3V5K~a12`
Q:³~„r/„Ü ~„m+~„r™™K~q`
R:„Ô3‚í2‚í1™K~r`
3+5*„¥K~„z1`
p1: ‚å‚é~„r³„ì* ~„rQ2™™™K~„p1`
I\@@OK@@
0.25\`~‚a`
3V5³~a12`K
Q:³~„r/„Ü ~„m+~„r™™³~q`K
R:„Ô3#2#1™³K
p1: ‚å‚é~„r³„ì* ~„rQ2™™™³~„p1™`K
Checking variables contents
J@@ @@ `@@@R@@ `@@@ @@@ `
At this point, the screen looks like this:
J‚@@ @@‚@@ @@ ‚@@@R@@ ‚@@@ @@ ‚@@A @@
Deleting variables
„¡@@OK@@
Using function PURGE in the stack in Algebraic mode
I@PURGE@ J@@ @@ `
I@PURGE@ „ä³J@@@R!@@ ™‚í³J@@@ !@@
J„ä³@@@R!@@ ™³@@@ !@@ `
I@PURGE@
UNDO and CMD functions
CHOOSE boxes vs. Soft MENU
@@OK@@ ˜˜˜˜
@@OK@@
H@FLAGS! ———————
@CHECK
@@MEM@@)
@@DIR@@)
@ORDER
Calculations with real numbers
6.3` 8.5- 4.2` 2.5* 2.3` 4.5
3.7#5.2+ 6.3#8.5- 4.2#2.5* 2.3#4.5
„Ü5+3.2™/„Ü7- 2.2`
5`3.2`+7`2.2`
³„Ü5+3.2
„Ê\2.32`
2.32\„Ê
„º\2.3`
2.3\„º
R123.4`
‚»3‚í27`
27`3‚»
‚Ã2.45`
„Â\2.3`
2.45‚Ã 2.3\„Â
2.45`‚¹ 2.3\`„¸
S30`
T45`
U135`
30S
Real number functions in the MTH menu
Using calculator menus:
We will describe in detail the use of the
4. HYPERBOLIC
Hyperbolic functions and their inverses
„´4@@OK@@ 5@@OK@@ 2.5`
2.5`„´4@@OK@@ 5@@OK@@
@@H) P@
@@TA H@
Note:
„´@@H P@ @@TA H@ 2.5`
2.5`„´@@H) P@ @@TA H@
Operations with units
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@)SPEED
Pressing the soft menu key @)U ITS will take you back to the UNITS menu
Note: Use the Lkey or the „«keystroke sequence to navigate through the menus
Available units
Attaching units to numbers
5‚Ý‚Û8@@OK@@ @@OK@@ `
Note
5‚Û8@@OK@@ @@OK@@
5‚Ý‚ÛL@)@FORCE @@@ @@ `
123‚Ý~„p~„m
Operations with units
Page
Unit conversions
Physical constants in the calculator
~~conlib~`
‚N~c
@E GL
@U ITS
To copy the value of Vm to the stack, select the variable name, and
STK
@ UIT@
tagged value
tag
„à³~h„Ü~„x™‚Å
‚¹~„x+1™+„¸~„x`
The screen will look like this:
@@@H@@
‚@@@H@@
@@@H@@@ „Ü2`
Reference
Calculations with complex numbers
Entering complex numbers
„Ü3.5‚í\1.2`
x+iy
3.5-1.2*‚¥`
In RPN mode, these numbers will be entered using the following keystrokes:
~‚6
Simple operations with complex numbers
Complex numbers can be combined using the four fundamental operations
The CMPLX menus
CMPLX menu through the MTH menu
CHOOSE boxes
„´9@@OK@@
CMPLX menu in the keyboard
Functions applied to complex numbers
Function DROITE: equation of a straight line
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Algebraic and arithmetic operations
Simple operations with algebraic objects
³„ì*~rQ™K~a1`
³„ì*~rQ`~a1K
@@A @@
@@A @@ +@@A @@ ` @@A @@ +@@A @@ `
@@A @@ 8@@A @@ ` @@A @@ /@@A @@ `
‚¹@@A @@
„¸v
Functions in the ALG menu
IL @)HELP@ `
To complete the operation press @@OK@@. Here is the help screen for function
COLLECT:
For example, for function SUBST, we find the following CAS help facility entry:
³„¸+~x+~y`
Operations with transcendental functions
Expansion and factoring using log-expfunctions
The „Ðproduces the following menu:
Expansion and factoring using trigonometric functions
The TRIG menu, triggered by using ‚Ñ, shows the following functions:
IL@HELP
Functions in the ARITHMETIC menu
FACTORS:SIMP2:
Polynomials
The HORNER function
HORNER(‘X^3+2*X^2-3*X+1’,2)= {‘X^2+4*X+5, 2, 11}
i.e., X3+2X2-3X+1= (X2+4X+5)(X-2)+11.Also
The variable
The PCOEF function
The PROOT function
The QUOTIENT and REMAINDER functions
The PEVAL function
Fractions
The SIMP2 function
The PROPFRAC function
The PARTFRAC function
The FCOEF function
The FROOTS function
Step-by-stepoperations with polynomials and fractions
X 3 − 5X 2 + 3X −
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Solution to equations
Function SOLVE
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Function SOLVEVX
Function ZEROS
Numerical solver menu
Notes:
Polynomial Equations
‚Ϙ˜@@OK@@
„Ô3‚í2‚í0
‚í1\‚í1@@OK@@
@SOLVE@
˜„Ô1‚í5
‚í2\‚í4@@OK@@
„Ô1‚í5
—@SM @
˜„Ô1‚í3
‚í2\‚í1@@OK@@
˜@S M @
Financial calculations
Solving equations with one unknown through NUM.SLV
³„¸~„x™-S„ì*~„x/3™‚Å0™ K~e~q`
‚Ï@@OK@@
3\@@@OK@@˜@SOLVE@
Solution to simultaneous equations with MSLV
@ECHO
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Operations with lists
Addition, subtraction, multiplication, division
Functions applied to lists
ABS
INVERSE (1/x)
Lists of complex numbers
Lists of algebraic objects
The MTH/LIST menu
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The SEQ function
The MAP function
Vectors
Storing vectors into variables in the stack
Using the matrix writer (MTRW) to enter vectors
@EDIT! @VEC ←WID @WID→ @GO→ @GO↓
@VEC@@
WID
@WID
@GO
3`5`2``
@ ROW@
@ ROW
@ COL@
STK@@
@GOTO@
@GOTO@ 3@@OK@@ 3@@OK@@ @@OK@@
Simple operations with vectors
Changing sign
Addition, subtraction
Multiplication by a scalar, and division by a scalar
Absolute value function
The MTH/VECTOR menu
Magnitude
Dot product
Cross product
Matrices and linear algebra
H@)DISP
Typing in the matrix directly into the stack
„Ô 2.5\‚í4.2‚í2™ ‚í „Ô .3‚í1.9‚í2.8™ ‚í
„Ô 2‚í.1\‚í.5
‚í
Operations with matrices
'`K
Addition and subtraction
`+ A
A` `+ A ` `
Multiplication
for
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Characterizing a matrix (The matrix NORM menu)
Function DET
Function DET calculates the determinant of a square matrix. For example
Function TRACE
tr(A) = ∑aii
an2
, and
Solution with the inverse matrix
Solution by “division” of matrices
Graphics
Plotting an expression of the form y = f(x)
f (x) = 1 exp(− x 2 )
L@@@OK@@@
@ADD
@AUTO
@ERASE @DRAW
•To see labels: @EDIT L@LA EL @ME U
LL@)PICT
@TRACE @@ @@
Next, press
To accept the changes made to the PLOT SETUP screen press
and the increment (Step). Enter the following: 5\@@@OK@@@
0.5@@@OK@@@ 0.5@@@OK@@@
@CHK
Out
Decimal, Integer
Trig
With the option
zoom in
@CHOOS
š™—˜
•When done, press @E IT
•Press @CA CL to return to the PLOT WINDOW environment
• Change the Step data to read: Step Indep: 20 Depnd:
•Press @ERASE @DRAW to see the surface plot. Sample views:
•Press @CA CL to return to PLOT WINDOW
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Calculus Applications
‚N~„l
Functions DERIV and DERVX
∫f (x)dx = F(x) + C
Definite integrals
∫ab f (x)dx = F(b) − F(a)
Infinite series
(xo )
f (x) = ∑
⋅ (x − xo ) n
If the value x0 = 0, the series is referred to as a Maclaurin’s series
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Multi-variateCalculus Applications
dydx
Vector Analysis Applications
The del operator
Divergence
divF
Curl
curl
Differential Equations
Function LDEC
Function DESOLVE
y(x) = 5 ⋅ exp(−x3 / 3) ⋅ (∫ exp(x3 / 3) ⋅ dx + C0 )
The variable ODETYPE
@ODET
J @ODET
Laplace Transforms
Laplace transform and inverses in the calculator
L{ f (t)} = F (s) = ∫0∞ f (t) ⋅ e−st dt
2inπt
„(hold) §`J@)CASDI `2K@PERIOD `
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Probability Distributions
~‚2
Random numbers
The MTH/PROB menu - part
The Normal distribution
The Student-tdistribution
The Chi-squaredistribution
The F distribution
Statistical Applications
CHK@
@@@OK@@
Obtaining frequency distributions
‚Ù˜@@@OK@@@
‚Ù@@@OK@@@
Select the program
•Change X-Minto -8,Bin Count to 8, and Bin Width to 2, then press @@@OK@@@
The bins for this frequency distribution will be: -8to -6, -6to -4,…
23, 22, 22, 17, 26, 15, 20
Fitting data to a function y = f(x)
‚Ù˜˜@@@OK@@@
Obtaining additional summary statistics
•To access the summary stats… option, use: ‚Ù˜˜˜@@@OK@@@
Confidence intervals
6. Conf Interval
‚Ù—
T-INT:
Press @GRAPH to see a graphical display of the confidence interval information:
Hypothesis testing
6. Conf Interval
‚Ù——@@@OK@@@
These options are interpreted as in the confidence interval applications:
‚Ù——
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Numbers in Different Bases
@HE
Warranty
Service
Europe
Country :
Telephone numbers
Austria
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Regulatory information