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HEWLETT A 'Hm PACKARD B38G aplet views LI VIEWS NOTE ACOS ATAN x-1 BIE^ a a 11 1 1 ANSWER for entering a SKETCH aplet library -_____ 1 1 MODES ASIN Home - CHARS EEX G a...z LIST Alpha shift 7 ■ ■ X2 ^0 B, ) LOG ■ g ■ / 5 ■ CLEAR NOTEPAD SPACE K 1 'll— -fi 8 MATRIX [ shift key (turquoise) H ABS D- 2 I ___ ]_ 6 10^ The {{ok}} menu-key label (when present in the display) acts the same as the | enter] key.
HP 38G Graphing Calculator User’s Guide HEWLETT® PACKARD HP Part No.
Notice This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. Hewlett-Packard Co. shall not be liable for any eiTors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples herein.
Contents Getting Started Starting Out........................................................................... 1-1 The Keyboard........................................................................ 1-2 The Display.............................................................................1-6 Display Modes.................................................................... 1-7 Using Input Forms............................................................. 1-8 Home History.................................
Plotting and Exploring Functions Defining a Problem............................................................... 3-1 Select an Aplet.................................................................... 3-2 Define an Expression (Symbolic View)............................3-2 Evaluating Expressions..................................................... 3-5 Examples: Defining Expressions...................................... 3-6 Plotting............................................................................
Statistics Example: Finding a Linear Equation to Fit Data..............5-2 Entering Statistical Data.......................................................5-5 One-Variable Data............................................................. 5-6 Two-Variable Data.............................................................5-9 Managing Statistical Data............................................... 5-12 Analyzing the Data..............................................................
Programming The Contents of a Program...............................................8-1 Structured Programming................................................. 8-1 Using the Program Catalog..................................................8-1 Programming Commands.................................................... 8-9 Aplet Commands.............................................................. 8-10 Branch Commands..........................................................8-11 Drawing Commands................
Getting Started Read this chapter first! It will get you started using your HP 38G, from turning it on to running aplets. Starting Out The Cover The protective cover swivels to provide a base for the calculator. Be sure to protect the display by replacing the cover before transporting the calculator. Slide the cover gently so as not to hit the keys. First push the cover away from you until it catches. Then swivel the cover to the back and slide it towards you.
Demo To see a demonstration of the HP 38G's features, type DEMO into the edit line in Home. (Press | home | |a...z|D |a...z|E |A...z|M |A...z|0 I ENTER|.) To Stop the demo, press any key. Home Home is the calculator’s home base. If you want to do calculations, or you want to quit the current activity (such as an aplet, a program, or an editor), press | home |. Power To save power, the calculator turns itself off after several minutes of inactivity. All stored and displayed information are saved.
Menu Keys You can press fuBl to see this screen; Parametric Polar Sequence Solve menu labels mm menu keys « The top-row keys are called menu keys because their meanings depend on the context—that’s why their tops are blank. • The bottom line of the display shows the labels for the menu keys’ current meanings, {{save}} is the label for the first menu key in this picture. “Press {{save}}’’ means to press the leftmost top-row key. Math Keys Home (press | home |) is the place to do calculations.
MATH menu. The | math | menu is a comprehensive menu list of math operations that do not appear on the keyboard. It also includes categories for all other functions and programmable commands. The functions are grouped by category, ranging in alphabetical order from Calculus to Trigonometry. Re.3l C Stat-Tyo Symbolic — Tests ? BDBSISiaiSI CEILING DEG+RFID FLOOR FNROOT » iHamBM The arrow keys scroll through the list (Q. ®) ^^d move from the category list to the item list (0, Q).
Keys for Entry Key Meanine and Editing Pressing |ON| while the calculator is on (CANCEL) cancels the current operation. Pressing ■ first turns the calculator off. ■ (shift) Accesses the function printed in turquoise color above a key. 1 HOME 1 Home base for calculations. [M] Alphabetic entry—press before a letter key. 1 ENTER 1 Enters an input or executes an operation. In calculations, 1 enter 1 acts like “=“ When {{OK}} is present as a menu key, | enter] acts the same as {{OK}}.
The Display To adjust the contrast The Parts of the Display Simultaneously press decrease) the contrast history edit line : Annunciators B Mmsm and 0 (or0) to increase (or 6*3 8/5 18 1.6 17894 _ menu-key labels Shift in effect for next keystroke. To cancel, press ■ again. a Alpha in effect for next keystroke. To cancel, press 1 A...Z 1 again. ((•)) Low battery power. See chapter 9. i Busy. Data is being transferred via infrared or cable.
Display Modes You can set the Home modes in ^ [MODES]. You make your selections using an input form. To fill out an input form, see “Using Input Forms,” after this table. The Decimal Mark setting affects all aplets, as well as Home. When you are done setting MODES, press | home | to return to the Home screen. [MODES] Setting Options Angle Measure Angle values are: Degrees. 360 degrees in a circle. Radians. 2Tr radians in a circle. Grads. 400 grads in a circle. Number Format Standard.
To display fractions Set Fraction mode to display future results as fractions, 1. Press ■ [MODES], then press 0 to select number FORMAT. 2. Press {{CHOOS}}, highlight Fraction, and press {{OK}}. 3. Press and enter a number for the precision of the fraction. The precision number determines how many digits appear in the denominator. Press | enter |. 4. Press I HOME I to display Home. To convert a result to a fraction 1. Set Fraction mode (as in the previous procedure). 2.
Hint Whenever an input form has a list of choices for a field, you can press (T) to cycle through them instead of using {{CHOOS}}. To reset values To reset the original, default value in an input form, press I DEL |. To reset all values in the form, press ■ [CLEAR]. Home History The Home display (press | home |) shows up to four lines of history : the most recent input and output. Older lines scroll off the top of the display but are retained in memory; press m to view them.
To re-use a Press ■ [ANSWER] (last answer) to put the last result from previous result Home into an expression. Ans is a variable that is updated each time you press [ enter |. Example See how [ANSWER] retrieves and reuses the last result (50), and I ENTER I updates Ans (from 50 to 75 to 100). 50 I ENTER I 25QH [ANSWER] 50 25+flns 75 100 1 enter! I enter! You can use the last result as the first expression in the edit line without pressing ■ [ANSWER].
To search a menu list To cancel a menu list ® Press @ or 0 to scroll through the list. If you press ■ Q or ■ [^, you’ll go all the way to the end or the beginning of the list. Highlight the item you want to select, then press {{OK}} (or | enter |). • If there are two columns, the left column shows general categories and the right column shows specific contents. Highlight the category on the left, then highlight the item on the right. The list on the right changes when a different category is highlighted.
Sequence ® Sequence function i/in terms of n, or in terms of previous terms in the sequence, such a s U n ~ i and Example: i/i = 0, f/2 = l,and a = + Solve ® Finding the roots of an equation. Example: x + 1 = -x-2. Statistics e Analysis of one-variable (x) or two-variable (x and y) statistical data. Views An aplet is represented in different ways. These views compose an aplet problem and its solution. Here are illustrations of three major and six supporting aplet views. SYMB Symbolic view.
■ [SETUPSYMB] Symbolic Setup (■ |symb|). Sets parameters for the symbolic expression. FUMCTIDN SVMeOUC SETUP ANGLE MEASURE: Radian CHMSE ANGLE MEASURE ■ [SETUPPLOT] Plot Setup (■ I PLOT I). Sets parameters to plot a graph. ^^^FONCIiDN KRNG: IMÜJiii VRNG; -3. 1 KTICK! 1 RES: Faster PLDT ■ 6.5 3.2 TTICK: 1 ENTER MINIMUM HDRIZDNTAL VALUE ■ [SETUP- NUM] ■ [VIEWS] Plot-Table I [NOTE] I [SKETCH] Numeric Setup (■ | numQ. Sets parameters for building a table of numeric values.
Canceling Operations To cancel an operation within a view, press | o n | (the CANCEL key). Pressing CANCEL will cancel pending operations, but will not change the view. Exploring an Aplet View by View Example Use the Function aplet to explore the real function y = sin(l/x) using the Symbolic, Plot, and Numeric views. All the information you enter is automatically saved 1. Open the Function aplet. Press |lib|. If necessary, press 0 to highlight Function.
5. Trace the plot. Move the crosshairs along the plot by pressing 0] and B- ............................ / K:1.3 FKK 6. i'''''' .... ,.. i; .sissBas Zoom in and zoom out. Press {{MENU}} {{ZOOM}}, highlight In 4 X 4 , and press {{OK}}. To restore the original scale, select {{ZOOM}} Un-zoom. 7. Display the numbers. To display a table of data, press |num|. You see the independent (X) and dependent (FI) variables listed with sampled values.
Automatic With this example you have defined a new aplet-an aplet Saving containing data for the solution of y = sin(l/x). The data are automatically saved in the Function aplet. If you want to create another aplet based on Function, then you can give this one a new name in the Library ({{SAVE}}). To keep as much memory available for storage as possible, delete aplets you no longer need. Annotating The Note view (■ [NOTE}) attaches a note to the current with Notes aplet.
Storing £uid Recalling Variables Variables are storage locations for numbers or values. The HP 38G has different categories of variables for different kinds of data. The names for the variables are predefined. For real numbers, there are 27 variable names available, A through Z and 0. (Other categories and their names are in chapter 2.) A variable holds just one value, so if you store a new number in it, any previous number is lost.
“Deleting” Variables A variable always has a value in it, even if that value is zero. When you store another value into a variable, it overwrites the previous value. So you cannot delete a variable’s value, but you can overwrite it. The predefined variable names (such as A through Z) always exist; you cannot change or delete them. Home and Aplet Variables Most variables are Home variables, which means they are shared throughout the different contexts of the calculator.
Note Editing Keys Key Meaning {{SPACE}} Space key for text entry. {{APACE}} Displays previous page of the note. {{PAGET}} Displays next page of the note. {{A...Z}} Alpha-lock for letter entry. ■ {{A...Z}} Lower-case Alpha-lock. {{BKSP}} Backspaces cursor and deletes character. (HD Deletes current character. 1 enter! Starts a new line. H {CLEAR] Erases the entire note. 1 VAR| Menu for entering variable names, and contents of variables.
Sketch Keys To draw a sketch Key Meanine {{STO^}} Stores the specified portion of the current sketch to a graphics variable (G1 through GO). {{NEWP}} Adds a new, blank page to the current sketch set. {{APACE}} Displays previous sketch in the sketch set. Animates if held down. {{PAGET}} Displays next sketch in the sketch set. Animates if held down. {{TEXT}} Opens the edit line to type a text label. {{DRAW}} Displays the menu-key labels for drawing (below). fPEH Deletes the current sketch.
To draw a line 1. In Sketch view, press {{DRAW}} and move the cursor to where you want to start the line 2. Press {{LINE}}. This turns on line-drawing. 3. Move the cursor in any direction to the end point for the line. 4. Press {{OK}} to finish the line. To draw a box 1. In Sketch view, press {{DRAW}} and move the cursor to where you want any corner of the box to be. 2. Press {{BOX}}. This turns on box-drawing. 3. Move the cursor to mark the opposite corner for the box.
DRAW Keys Key Meaning {{DOT-f}}, {{DOT-}} Dot on, dot o f f . Turns pixels on/off as crosshairs {{LINE}} Draws a line from the cursor’s starting position to the point at which you press {{ok}}. You can draw a line at any angle by moving the cursor. {{BOX}} Draws a box from the cursor's starting position to the point at which you press {{OK}}. {{CIRCL}} Draws a circle. The cursor’s starting position is the center of the circle.
To store into a You can define a portion of a sketch inside a box, and then graphics store that graphic into a graphics variable. variable 1. In the Sketch view, display the sketch you want to copy (store into a variable). 2. Press {{STO^}}. Highlight the variable name you want to use and press {{OK}}. 3. Draw a box around the whole screen or around the portion you want to copy: move the cursor to one corner, press {{OK}}, then move the cursor to another corner and press {{OK}}.
To write a note 1. In the Notepad, press {{EDIT}} to modify the highlighted in the Notepad note or press {{new}} to start a new note. For a new note, type in a name and press {{OK}}. 2. This opens the note for you to write and edit. Use the Note editing keys as in Note view (see page 1-19). 3. When you are done, you can leave the Notepad by pressing I HOME I or an aplet view key. Your work is automatically saved. Notepad Catalog Keys Key Meaning {{EDIT}} Opens the selected note for editing.
Managing Aplets Once you have entered information into an aplet, you have defined a new version of an aplet. The information is automatically saved under the current aplet name, such as “Function.” To create additional aplets of the same type, you must give the current aplet a new name. The Library is where you go to manage your aplets. Press jiiBl. Highlight (using the arrow keys) the name of the aplet you want to act on.
To name an aplet To create a new aplet 1. Press I LIB I to open the Library. Highlight the aplet to name. 2. Press {{SAVE}} and enter a name. Press {{OK}} to confirm it, {{CANCL}} to cancel it. You can create a new aplet based on an existing aplet. 1. Open the aplet you want to start from. 2. Enter or modify its information (equations, data, settings). This defines a new version of the aplet. All information is saved until you clear it or edit it. 3.
Sending and Receiving Aplets A convenient way to distribute or share problems in class and to turn in homework is to transmit (copy) aplets directly from one HP 38G to another. This takes place via the infrared port. You can also send (copy) and receive aplets to/from a remote storage device (aplet disk drive or computer). This takes place via a cable connection and requires an aplet disk drive or specialized software running on a PC or Mac (such as a connectivity kit). To transmit an 1.
3. Receiving calculator : Open the Library and press {{RECV}}. * You have two options : another HP 38G or a disk drive (or computer). Highlight your selection and press {{OK}}. If receiving from a remote storage device (aplet disk drive or computer), you will see a list of aplets in its current directory. You can choose a different directory to copy from. Check as many items as you would like to receive.
Mathematical Calculations The most commonly used math operations are on the keyboard. Access to the rest of the math functions is via the MATH menu (press |math|). The MATH menu also contains commands to use for programming. How to Do Calculations Where to Start The home base for the calculator is Home (press |home |). You can do all calculations here, and you can access all [ MATH I operations.
Long Results If the result is too long to fit in the display line, press 0 to highlight it and then press {{SHOW}}. Negative Numbers Type [^to start a negative number or to insert a negative sign. If a negative number will be raised to a power, enclose it in parentheses. For example, (—5)^= 25, whereas - 5^= - 25. Scientific Notation powers of 10) A number like 5x10"' or 3.21x10"' is written in scientific notation, that is, in terms of powers of ten. This is simpler to work with than 50000 or 0.
Examples Algebraic Precedence (Order of Evaluation) Enterine... Calculates... [Ml 45 0 ■ [it] sin (45 -r tt) [Ml 45 eg 0 H [it] sin (45) + -IT 1 Vx 1 85 01 9 yfExQ [W1 B 55 0 9 Q] VS5x9 Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right. 1. Expressions within parentheses. Nested parentheses are evaluated from inner to outer. Prefix functions, such as SIN and LOG.
Complex Numbers Complex Results The HP 38G can return a complex number as a result for some math functions, A complex number appears as an ordered pair (x, y), where x is the real part and y is the imaginary part. For example, entering returns ( 0 , 1 ) . To enter complex numbers Enter the number in either of these forms, where x is the real part, y is the imaginary part, and i is the imaginary constant, ,JZ\e (X, y) or e X + iy , To type i, press ■ | A...
Note that pressing | enter] enters (or re-enters) the last input, whereas pressing ■ [ANSWER] copies the last result into the edit line. Continuing a You can continue calculating with your last result, Ans, Calculation simply by pressing an operator key. 50 [7] 3 I ENTER I 50-^3 [+] 25 I ENTER I flns+25 Pressing 1 ENTER 1 again updates the value of Ans and repeats the operation. ^HDME 16.6666666667 41.6666666667 »HDHE 16.6666666667 flns-E25 41.6666666667 66.
Clearing the Display History It's a good habit to clear the display history (■ [CLEAR]) whenever you are done working in Home. It saves calculator memory to clear the display history. Remember that all your previous inputs and results are saved until you clear them. Clearing the Edit Line * [ DEL I deletes single characters in the edit line. (CANCEL) clears the entire edit line. Storing in Variables You can store numbers or expressions from any previous input or result into variables.
The VAR Menu Another way to retrieve a variable is to use the VAR (variables) menu. The VAR menu contains the Home variables, as well as the aplet variables for the current aplet. The VAR menu is organized by category. For each category of variables on the left, there is a list of variables on the right. The highlighted category is the current category.
Home variables retain their values regardless of context: Home, the aplets, and the editors recognize the Home variables and retain whatever was last stored in them. This sharing allows you to work on the same problem in different places (such as Home and the Function aplet) without having to update a variable whenever it is recalculated. If you have not stored anything in a real variable, then it contains the value zero. (It is never “empty.”) To access a 1. Press | var | to display the VAR menu.
Aplet Variables The variable types in the table below are aplet variables that you use to define aplet functions and to store some kinds of aplet data. They are usually found in the Symbolic view or the Numeric view of an aplet.
To access an The {{APLET}} menu key in the VAR menu switches the menu aplet variable ¡¡st to aplet variables. The ■ symbol indicates what is "on": {{APLEb}} means that aplet variables are displayed. 1. Open the aplet whose variable you want to recall. 2. Press I VAR I to display the VAR menu. Set {{apleb}}, if necessary by pressing {{aplet}}. I^^FUNCTIBN Plot ■ Plot FCN Symbolic Numeric v fixes Connect Coord FastRes v 3. Highlight the view on the left side.
You can mix formal names and real variables. Evaluating (A*s2) ^ will substitute a number for A but not for s2. If you want to evaluate an expression like (sl*s2) ^ numerically, you can do so using the I (where} command, listed in the MATH menu under the Symbolic category. For instance, if you wanted si = 3 and s2 = 4, you would enter (sl*s2) ''2 I (sl=3, s2=4). (The = symbol is in the CHARS menu: press ■ [CHARS] {{OK}}).
Composition of You can define a function of another function using the Functions Function aplet (| lib | Function). That is, f(g(xy) can be entered into the Symbolic view of Function as F1(X) -expression! F2 (X) = expression2 F3 (X) = FI {F2 (X) ) Using Math Functions Selecting To enter a function, type it in or select its name from the Functions MATH menu. The MATH Menu The MATH menu provides access to Math Functions, Programming Commands, and Programming Constants.
To copy a function 1. Press | math | to display the MATH menu. The categories appear in alphabetical order. Use 0 and 0 to scroll through the categories. To skip directly to a starting letter, press a letter key. 2. The list of functions (on the right) applies to the currently highlighted category (on the left). Use 0 and 0 to switch between the category list and the function list. 3. Highlight the name of the function you want and press {{OK}}.
Keyboard Functions 0.Q.0.0 The most frequently used functions appear on the keyboard. The keyboard functions are the only math functions that do not appear in the MATH menu. Many of the keyboard functions also accept complex numbers as arguments. Add, Subtract, Multiply, Divide. Also accept complex numbers. value 1+ value2, etc. m iel Natural exponential. Also accepts complex numbers. e''value ■ [LN] Natural logarithm. Also accepts complex numbers. IM [value] ■ [101 Exponential (antilogarithm).
[ATAN] Arc tangent: tan^'x. Output ranges from -90° to 90°, -Tr/2 to 77/2, or -100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. AT AN (oa/ue) l[J^] Square. Also accepts complex numbers. value‘ Square root. Also accepts complex numbers. V~value [^] Pi, a constant. K’] Multiplicative inverse (reciprocal). For a complex number, the reciprocal is X + y X + y value''-! EU Negation. Also accepts complex numbers.
Calculus Functions a You will find the symbols for the calculus functions derivative and integral in the CHARS menu (■ [CHARS]) as well as the MATH menu. Differentiates expression with respect to the variable of differentiation. Use a formal variable (si, etc.) for a non numeric result. doariable(expression) Example: asl (sl^+3*sl) returns 2*sl+3 f Integrates expression from lower to upper limits with respect to the variable of integration.
ComplexNumber Functions ARC These functions are for complex numbers only. You can also use complex numbers with all trigonometric and hyperbolic functions, and with some real-number and keyboard functions. Enter complex numbers in the form (x,y), where x is the real part and y is the imaginary part. Argument. Finds the angle defined by a complex number. Inputs and outputs use the current angle format in Modes. ARG{ i r , 0 ) ) CONJ Complex conjugate.
Constants The HP 38G has an internal numeric representation for these constants. e Natural logarithm base. Internally represented as 2.71828182846. ! Imaginary value for , the complex number (0,1). MAXREAL Maximum real number. Internally represented as 9.99999999999X10“. MAXREAL MINREAL Minimum real number. Internally represented as 1 x 10 “ MINREAL n The ratio perimeter: diameter. Internally represented as 3.14159265359.
Hyperbolic Trigonometry ACOSH The hyperbolic trigonometry functions can also take complex numbers as arguments. Inverse hyperbolic cosine: cosh'r. ACOsm value) ALOG Antilogarithm (exponential). This is more accurate than 10''x due to limitations of the power function. ALOG [value] ASINH Inverse hyperbolic sine : sinh''x. ASINH (ua/ue) ATANH Inverse hyperbolic tangent: tanh~'x. If the input is ± 1, an Infinite Result occurs. ATANH (ufl/ue) COSH Hyperbolic cosine: (e'4€^')/2.
List Functions These functions are for list data stored in list variables. See chapter 7, Using Lists. Loop Functions The loop functions display a result after evaluating an expression a given number of times. ITERATE Repeatedly (the specified dimes') evaluates an expression in terms of variable. The value for variable is updated each time, starting with initialvalue.
Polynomial Functions POLYCOEF Polynomials are products of constants (coefficients) and variables raised to powers (terms). Polynomial coefficients. Returns the coefficients for the polynomial with the specified roots. POLYCOEF! [roofs] ) Example: to find the polynomial with roots 2,-3, 4, -5: POLYCOEF ( [ 2 , - 3 , 4 , - 5 ] ) returns [ 1 , 2 , - 2 5 , - 2 6 , 1 2 0 ] , representing x%2з¿-25)¿-2%x+\ 20. POLYEVAL Polynomial evaluation.
Probability Functions COMB Probability functions are often used in statistical analyses. Number of combinations (without regard to order) of n things taken rat a time, n!/(r!(n-r)). COMB (n,r) ! Factorial of a positive integer. For non-integers, ! = F(x + 1). value ! PERM Number of permutations (with regard to order) of n things taken rat a time, n\/ (_n-r)\. PERM(n,r) RANDOM Random number (between zero and 1). Produced by a pseudo random number sequence.
Real-Number Functions CEIUNG Some real-number functions can also take complex arguments. Smallest integer greater than, equal to value. CEILING (oa/ue) DEG->RAD Degrees to radians. Converts value from Degrees angle format to Radians angle format. DEG—>RA.D (VOltlB ) FLOOR Greatest integer less than or equal to value. FLOOR (value) FNROOT Function root-finder (like Solver aplet). Finds the value for the given variable at which expression most nearly evaluates to zero. Uses guess as initial estimate.
Real-Number Functions, continued MAX Maximum. The greater of two values. MAX (value!, MIN Minimum. The lesser of two values. MIN (value!, MOD value2) value2) Modulo. The remainder of valueHualue2. value! MOD value2 X percent of y; that is, Ay/100. %(x,y) %CHANGE Percent change from x toy, that is, 100(y-x)/x. %CHANGE(X,y) %TOTAL Percent total: (100)y/x What percentage of x isy. %TOTAL(X,y) RAD^DEG Radians to degrees. Converts another.
Statistics-Two These are functions for use with two-variable statistics. See chapter 5, Statistics. Symbolic Functions The symbolic functions are used for symbolic manipulations of expressions. The variables can be formal or numeric, but the result is usually in symbolic form (not a number). You will find the symbols for the symbolic functions = and 1 (where) in the CHARS menu (|P [CHARS]) as well as the MATH menu. = (equ als') Sets an equality for an equation. This is not a logical operator.
Test Functions The test functions are logical operators that always return either a 1 (true') or a 0 (false). <■ Less than. Returns 1 if true, 0 if false. value Kaalue2 ^ Less than or equal to. Returns 1 if true, 0 if false. value l^value2 —— Equals (logical test). Returns 1 if true, 0 if false. value 1 = =value2 Not equal to. Returns 1 if true, 0 if false. i= value! i=value2 > Greater than. Returns 1 if true, 0 if false. value I>value2 > Greater than or equal to. Returns 1 if true, 0 if false.
Trigonometry Functions ACOT The trigonometry functions can also take complex numbers as arguments. For SIN, COS, TAN, ASIN, ACOS, and ATAN, see the Keyboard category (all these functions have keys). Arc cotangent. ACOT (value) ACSC Arc cosecant. ACSC {value) ASEC Arc secant. ASEC {value) COT Cotangent: cosx/sinx. COT {value) CSC Cosecant: 1/sinx CSC {value) SEC Secant: 1/cosx.
Plotting and Exploring Functions Types of Plots Graphing is at the heart of the HP 38G. All of the built-in aplets do graphing. This chapter considers the four main built-in aplets: « Function, ® Parametric, e Polar, and 9 Sequence, The Solve aplet and Statistics aplet, which also include graphing, are covered in separate chapters. Defining a Problem You start with an aplet and a mathematical function to explore, like y = mx + h. General Steps 1. From the Library (| lib |), open the aplet you want.
Select an Aplet Select the aplet appropriate to your problem : Open the Library (| lib |), highlight the name of an aplet, and press {{START}} (or IENTErQ. ® Function . This aplet can define rectangular equations of the form y = f(x) . • Parametric . This aplet can define parametric expressions, which define equations over time, t. They take the forms jf = /'(0andy = g(0- ® Polar, This aplet can define polar expressions, which graph equations in terms of an angle 0. • Sequence.
To define the 1. Display the Symbolic view (| symb |). If the highlight is on expression an existing expression, scroll to an empty line—unless you don’t mind writing over the expression. Or, clear one line (I DEL I) or all lines (■ [CLEAR]). 2. Make sure your function is in the form “y = For example, given the equation 9x+y - 11=0, you would rearrange it to y = f(x) = -9x + 11. Type in just the expression (-9x+l 1) for the right side. • For a Function definition, enter an expression to define F(X).
Symbolic Keys View Key Meanine {{EDIT}} Copies the highlighted expression to the edit line for editing. Press {{OK}} when done. {{^CHK}} Checks/unchecks the current expression (or set of expressions). Only the checked expression(s) are evaluated in the Plot and Numeric views. {{X}}, {{T}}, Typing aids for the independent variable. Or, you can use the |xt6 | key on the keyboard. {{0}}. {{N}} {{U1}}...{{U9}} {{uo}} Additional typing aids for variables in the Sequence aplet.
Evaluating Expressions In Aplets In the Symbolic view, a variable is a symbol only, and does not represent one specific value. If a variable contains another variable in it, then {{EVAL}} substitutes it as shown in this example. FUNCTION SyHIDLIC MIEH In Function Symbolic view, -^FKX>=R»X''2 enter these three expressions. Highlight F3.
Examples: Defining Expressions Function Example Define - 2x + 3 . Enter this expression as the right side of the equation in the Symbolic view. In the Symbolic view of the Function aplet, highlight a line (or clear the lines) and enter the expression. I LIB I Select Function.
Polar Example Define r = 2 cos40. In the Symbolic view of the Polar aplet, highlight a line (or clear the lines) and enter the expression. |PDL*f! SVHSDUC MIEW I Select Polar ^Rli0>=2*COSi;4*0> {{START}} R3<0>= 2 a 4 a {{0}} R4i;0>= R5<0>= ENTER ■HihiBirang Sequence Example Define the Fibonacci sequence, in which each term (after the first two) is the sum of the preceding two terms ; ( = 1, /j = 1, and /3 = (,_2 for /7 ss 3.
Undefined Points If, during plotting, a real value for the expression is not found, then that point is not plotted, and no line is connected through it. Tracing a Plot When a graph is nev/ly drawn, TRACE mode is on. Pressing a cursor key will trace the crosshairs along the graph, displaying the coordinate values as they move. Scrolling a Plot In Function and Sequence aplets, you can scroll left and right beyond the edge of the window to see more of the graph.
Parametric Example Plot the expressions from the previous Parametric example, x(f) = 3 sinSi and y(i) = 2 sin4f .Before plotting, however, reset the default plot settings by clearing the Plot Setup view. I Select Parametric {{START}} Make sure the correct function is highlighted and checked, m [SETUP-PLOT] T: 0 ibn:ih ■ [CLEAR] PLOT Polar Example Plot the expression from the previous Polar example, r = 2 cos40.
Sequence Example Plot the Fibonacci sequence from the previous Sequence example, i/, = 1, = 1, and = i/„_, + . In Plot Setup, first set the SEQPLOT to Stairstep, then try a Cobweb plot. Reset the default plot settings by clearing the Plot Setup view. ® A Stairstep graph plots n on the horizontal axis and t/ on the vertical axis. e A Cobweb graph plots on the horizontal axis and on the vertical axis. I LIB I Select Sequence {{START}} Make sure the correct function is highlighted and checked.
Exploring the Plot Plot view (press [ plot | or ■ [VIEWS]) gives you a selection of menu keys to explore a graph further (for the checkmarked expressions in the Symbolic view). The options vary from aplet to aplet. PLOT View Keys Key Meaning ■ [CLEAR] Erases the plot. ■ [VIEWS] Offers additional pre-defined views for splitting the screen and for scaling (“zooming") the axes. ■a Moves cursor to far left or far right. ■ 0 ([ZOOM]} Displays ZOOM menu list. ([TRACE]} Turns Trace mode on/off.
Tracing Many aplets have a Trace mode. Trace mode is on when a plot has just been drawn. When Trace mode is on, the crosshairs cursor follows just the plotted points when you press the Q or @ keys. The cursor traces the function. The display also shows the current coordinate position (jc, y) of the cursor. If there is more than one curve displayed, press (T| or [Yl to move between curves. Note that tracing might not appear to exactly follow your plot if the resolution (in Plot Setup view) is set to Faster.
To turn on e Trace mode and the coordinate display are automatically TRACE mode set when a plot is drawn. At other times, set Trace mode by pressing {{TRACE}} to change the label to {{TRAC«}}. (If the menu labels are not displayed, press {{MENU}} first.) • Turn off Trace mode by changing the menu label back to {{TRACE}}. To turn on e To turn On the display of the coordinates' values at the coordinates current cursor position, press {{(X, Y)}}. To turn the coordinate display off again, press {{MENU}}.
{{ZOOMI} Options Select an option and press {{OK}}. Option Meanine Center Recenters the plot around the current position of the crosshairs without changing the scale. Box... Lets you draw a box to define the zoom boundaries. Use the cursor keys to draw the box, and press {{OK}} to zoom in (see below). In Divides horizontal and vertical scales by the X-factor and Y-factor (in Set Factors, below). For instance, if zoom factors are 4, then zooming in results in 1/4 as many units depicted per pixel.
To use Box The Box Zoom option lets you draw a box around the area Zoom you want to zoom in on. 1. If necessary, press {{MENU}} to turn on the menu-key labels. 2. Press {{ZOOM}} and select B o x . . . 3. Position the crosshairs into one corner of the box-to-be. Press {{OK}}. 4. Use the cursor keys (, etc.) to drag two sides of a box. 5. Press {{OK}} to zoom in on the boxed area.
Other Views for Scaling and Splitting the Graph Other Scales The preset viewing options (■ [VIEWS]) draw the plot using certain pre-defined axis scales. This is a shortcut for changing Plot Setup. For instance, if you have defined a trigonometric function, then you could select Trig to plot your function on a trigonometric scale. [VIEWS] Options Select an option and press ([OK]). Option Meaninfi Plot-Detail Splits the screen into the plot and a close-up (see the next topic).
Splitting the Screen The Split Screen view can give you two simultaneous views of the plot. 1. Press ■ [VIEWS] . Select Plot-Detail and press {{OK}}. The graph is plotted twice. You can now zoom in on the right side. 2. Press {{MENU}}{{ZOOM}} to choose the Zoom method and press {{OK}} or I ENTER ¡.This zooms the right side. Here is an example of split screen with zoom in. The Plot menu keys are available as for the full plot (for tracing, coordinate display, equation display, and so on).
Setting Up the Plot (Plot Setup) Press ■ [SETUP-PLOT] to define any of the settings shown in the next two tables. 1. Use the arrow keys to move from field to field. Highlight the field to edit. If there is a number to enter, type it in and press | enter | or {{OK}}. • If there is an option to choose, press {{CHOOS}}, highlight your choice, and press | enter | or {{ok}}. As a shortcut to {{CHOOS}}, just highlight the field to change and press to display and select the different choices.
Second-Page Those items with space for a checkmark are settings you can turn on or off. Press {{PAGET}} to display the second page. SIMULT If more than one function is being plotted, plot them simultaneously (otherwise sequentially). INV. CROSS When the crosshairs cross the plot, invert those pixels that are overlapping. CONNECT Connect the plotted points. (Sequence always connects them.) LABELS Label the axes with XRNG and YRNG values. AXES Draw the axes.
To move the cursor To change the starting position of the cursor after having selected an operation, press {{MENU}}, move the cursor, and re-select the FCN operation. To clear shading To remove the shading produced by the AREA operation, press I PLOT I to re-draw the plot. FCN Operations Root Select Root to find the root x-value nearest the crosshairs. If no root is found, but only an extremum, then the result is labeled EXTR: instead of root :. (The root-finder is also used in the Solve aplet.
Examples: Root-Finding with Plots These examples of the interactive root-finding operations use the expression f(x) = jc^-1 in the Function aplet with default plot settings. IFUNCTIDN fVHBDLIC VIEH Select the Function aplet. ^FKX>=Xa-l F2t;x> = F3 = F4 = SYMB {{X}} ■ [^] □ 1 [¡EUR] ROOT ■ VI 1/ [SETUP-PLOT] [CLEAR] PLOT {{MENU}] {{FCN}} I8IJ!III ftDDT: -1 Select Root {{OK}} The crosshairs started at (0, - 1 ) . The root nearest the crosshairs is x = -1.
AREA You move the cursor to the starting point first, then shade the area. {{MENU}} {{FCN}} Select Area. . . {{OK}} {{OK}} to set starting point Q 10 times ,, ^r [/ SELE CT END POINT RCTiroai {{OK}} ........................... \l The shaded area has a value of -0,666666666667 (to 12-digit accuracy). It is negative because the region lies below the xaxis. Enter a second expression, f(x) = in Function aplet, and find the intersection of it with f(x) = x ‘ - l .
Using a Table of Numbers Display a Table of Numbers (Numeric View) After entering and selecting (checkmarking) the expression in the Symbolic view, press | num| to view a table of data values for the independent (X, T, 0, or N) and dependent variables. To adjust the initial value or step size, change the Numeric Setup. NUM View Keys Key Meaning {{ZOOM}} Displays ZOOM menu list. {{BIG}} Toggles between two character sizes. {{DEFN}} Displays the defining function expression for the highlighted column.
Exploring the Table of Numbers Zooming Zooming redraws the table of numbers in greater or lesser detail. {{ZOOM}} Options Option Meaning In Decreases the intervals for the independent variable so a narrower range is shown. Uses the NUMZOOM factor in Numeric Setup. Out Increases the intervals for the independent variable so that a wider range is shown. Uses the NUMZOOM factor in Numeric Setup. Decimal Changes intervals for the independent variable to 0.1 unit. Starts at zero.
Splitting the Screen The Split Screen view gives you two simultaneous views. 1. In the Symbolic view of the appropriate aplet, make sure the function(s) you want are checkmarked. 2. Press ■[VIEWS}. Select Plot-Table and press {{OK}}. 1J /1 Wli X -.10625 FI -.6BB66 -.BBHIE !hOEB5-!BiHi6 .601575-.62B66 IESHB13I1I 3. The Q and 0 cursor keys move the crosshairs along the plot; the view of the table adjusts itself. The Q and [V) cursor keys move the crosshairs from one graph to another. 4.
SETUP-NUM Screen Field Meaning NUMSTART Where to start the independent variable’s first value. NUMSTEP The size of the increment from one independent variable value to the next. NUMTYPE Type of numeric table: Automatic or Build Your Own. To build your own table, you must type each independent value into the table yourself. NUMZOOM Zoom factor (multiplies the scale for Zoom Out, divides for Zoom In).
To clear data Press ■ [CLEAR] to erase the data from a table. “Build Your Own” Keys Key Meanine {{EDIT}} Puts the highlighted independent value (X, T, 0, or N) into the edit line. After you edit the number, press |enter]. {{INS}} Inserts a row of zero values at the position of the highlight. Replace the zero by typing the number you want and pressing | enter 1. {{SORT}} Automatically rearranges the left-hand column into values in ascending (getting larger) or descending (getting smaller) order.
More Examples Function Example Plot the circle, = 13. Rearrange the equation to y= . This must be entered as two expressions, y = ^(l3-x') and y = I LIB I Se/ect Function SYMB [^[D 13 □ {{X}} [x3 2Q] I ENTER I . IFUNCTIDN SVMeaUC MIEH <^Flra3-X'*'2> >/F2CX>=-Ta3-X''2> F4CX>= F5= w EU [S 0 13 □ {{X}} [13 2Q] I ENTER I ■ [SETUP-PLOT] (Check that the Plot settings are the defaults—if not, press ■ [CLEAR] .J FUNCTION PLOT SETUP KRNG: ■ 6.5 VRNG: -3. 1 3.
Function Example, continued PLOT H: 0 FliK ■ [SETUP-NUM] (Check that the Numeric settings are the defaults—if not, press miClIAR].) NUM V J ■■ 3.S0SS51 i8n;iii ^^FUNCTiDN NUMERIC fETUF NUMSTflfiT: 0 NUMSTEP: .1 NUMTVPE: flut. omat i c NUMZDDM: 4 0 .5 X FI F2 3.fi05551 -3.S055S 3.fiOH16H -3.eoHifi -3.6 3lS>130HB-3.5330H 3.5B3ERH -3.3B3E>; 3.S?i?lH -3.5?i«?l .
Parametric Plot the two sets of equations below that describe the paths of Example two particles over time. Look at the interval between f = 0 and i= 6.5 seconds. I 5e/eci Parametric *PftMMETIilC SVMEnUC ANGLE MEASURE: SETUP» ■ [SETUP-SYMB] Check that Radians is set.
Parametric Example, continued T {{ZOOM}} Select in {{ok}} 1.1?5 l.S as ill: 1.3 XI 2.2 2.133333 X2 Y1 -.3 -.2 -.1 0 iTIl'iil'l .1 .2 I.REH'IIO 1.R02113 1.B763B2 l.BHPPSR I.BIBSBS 1.7B2013 1.99999999999 You can now see that Xl=2 when T=1.25, so the particles do not collide at X=2. Now search for Yl=3 and Y2=3. You can use {{ZOOM}} Out to move more quickly through the columns, but {{ZOOM}} In again to find Y1=Y2=3. 0 0 B highlight the Y2 column to highlight Y2=3 T 1.B75 l.R l.RES 1.R5 l.
Polar Example Plot the circle, r = 3 (sin^e + cos^0). I Select Polar ■ [SETUP^YMB] Check that Radians is set. ISYMB13 g El {{6}} 0 M[A 0 miA 0 fVMEDLIC VIEH^M ^RK6>=3*c:SIN<0>a+C... R2(;0> = R3C0>= R4i;0>= R5<0>= naEBEMiaKiiE gHihisirama I cos I {{6}} 0 enter! PLOT (If your plot does not look this, check that the Plot Setup has the default settings.) R1 NUM (If your table does not look like this, make sure the Numeric Setup has the default settings.
Sequence Example Generate a sequence to calculate the square root of 2 using the iterative relationship ) X ) = \{Ul, +a), where a = 2. Define this sequence in the HP 38G as U1(N) = (Ul(N-iy + A)/(2*U1(N-1)) ,andstore2 in/t. The Sequence aplet finds the square root by evaluating this expression with successive values of N until the value for U1 stops changing. In this case, the sequence converges at a value for -Jl starting with . Start the sequence by setting U1 (1) and U1 (2) to 1.
Sequence Example, continued ■ [VIEWS] Select Auto Scale {{OK}} Explore the graph and the values for N and Ul by pressing g and [^. As you trace the graph with the cursor keys, the crosshairs jump from N:1 to N:2 to N:3, and so on. The values for Ul change by smaller and smaller amounts until they converge. Ul N NUM a 1.5 H 1.415557 l.HlHilS 5 Scroll down to see that the I.HIHBIH $ values for U] remain the same 8 1.41421356237 for N»6. Therefore, -Jl is 1.41421356237 to 12 digits of accuracy.
Solve The Solve aplet will solve an equation or an expression for its unknown variable. You define an equation or expression in Symbolic view, then supply values for all of the variables except one in Numeric view. Then Solve will find the remaining unknown. As a simple example, consider the equation force = mass x acceleration (that is, f=m*a) in the Solve Symbolic view. SVMiaUC VliHS ^EliF=M*R E3: E4! E5: mia&sosi If force is 600 N and acceleration is 9.
Solving Equations An equation contains an equals sign. Its solution is a value for the unkno^vn variable that makes both sides equal the same value. An expression does not contain an equals sign. Its solution is a root, that is, a value for the unknown variable that makes the expression equal to zero. Define the Equation You can define up to ten equations (or expressions), named EO through E9. Each equation can contain up to 27 real variables, named A through Z or 6. To define an equation 1.
Symbolic View Keys Key Meanin© {{EDIT}} Copies the highlighted expression to the edit line for editing. Press {{OK}} when done. {{^CHK}} Checks/unchecks the current expression. Only the checked expression is evaluated. {{=}} Types an equals sign into the equation. {{SHOW}} Displays the current equation in standard mathematical form. {{EVAL}} Evaluates the current equation by substituting other variables for all variables except the independent variable, which remains in symbolic form.
Solve for the Unknown Variable Assign values to all the variables except one. All of the variables must represent real values. The unknown variable cannot be an index (as for a summation), limit (as for an integral), or placeholder variable (as for a derivative). To solve for an 1. Press I NUM| for the Numeric view. This displays all the unknown variables and their values, if any. 2. For each variable except the unknown, type a number and press {{OK}}. 3.
Numeric Keys View Key Meaning {{EDIT}} Copies the highlighted value to the edit line for editing. Press {{OK}} when done. {{INFO}} Displays a message about the solution (see "Interpreting Results," next page). {{PAGE}} Displays other pages of variables, if any. {{DEFN}} Displays the current, defining expression. Press {{OK}} when done. {{SOLVE}} Finds the solution for the highlighted variable.
Plotting the Equation A plot shows you graphically where the solution(s) must be ; » If you defined an expression, then the solution (root) is where the graph intersects the x-axis. ® If you defined an equation, then there are two graphs, one for each side of the equation. The solution is where the two graphs intersect. (If one side of the equation is constant, then one of the graphs will be a straight line.) To plot an equation 1. Define the equation to solve in the Symbolic view (|symb|). 2.
Interpreting Results After Solve has returned a solution, press {{INFO}} in the Numeric view for more information. You will see one of the following three messages. Press {{ok}} to clear the message. Messcige Condition Zero The Solve aplet found a point where the value of the equation (or the root of the expression) is zero within the calculator's 12-digit accuracy.
The RootFinder at Work You can watch the process of the root-finder calculating and searching for a root. Immediately after pressing {{SOLVE}} to start the root-finder, press any key except |on|. You will see two intermediate guesses and, to the left, the sign of the expression evaluated at each guess. For example: - -.219330555745 3- -1.31111111149 You can watch as the root-finder either finds a sign reversal or converges on a local minimum/maximum or does not converge at all.
Statistics The Statistics aplet can store up to ten separate data sets at one time. It can do one-variable or two-variable statistical analyses of one or more sets of data. • In Numeric view: Enter data values for one- or two-variable statistics (IVAR or 2VAR). n Cl C2 1 5 g 3 so i H HB 1 M44»4»M4eM: C3 fiO BS ?0 ?s C4 BB 33 MH 55 52 BniHBiMBiaiBBBMSBBB In Symbolic view: Define which data columns make up a data set.
e In Home: You can also compute statistics values in Home and recall the values of specific statistics variables. The values computed in the Statistics aplet are saved in variables, and many of these variables are listed by the {{STATS}} function in Numeric view. Example: Finding a Linear Equation to Fit Data Enter and analyze the advertising and sales data below. Compute statistics, fit a curve to the data, and predict the effect of more advertising on sales.
I Select Statistics {{START}} n Cl 1 C2 C3 C4 №449«««««««« K«4444444«44{ M9»9«9«»»»««« (If necessary, use ■ {CLEAR] to clear two data columns') EgmsitHBHnsiEiHBraimHrra Make sure that {{2VARh}} is on for two-variable statistics. {{IVARb}} 2 ENTER 1 5 ENTER ENTER 3 enter! 5 ENTER 4 enter] fF} to move to next column 1400 I ENTER I 920 I ENTER I 1100 [ enter! 2265 [ ENTER I 2890 I ENTER } 2200 Ienter] SYMB If necessary, ■ {CLEAR] to clear previous definition of SI.
Find the mean advertising time (MEANX), the mean sales (MEANY), and the correlation coefficient (CORK) for the data fitting a straight line. The CORK value indicates how well the linear model fits the data. rNDKTI {{STATS}} Displays computed statistics. MEANX is about 3.3 minutes and MEANY is about $1796. Scroll down to display CORE. CORE is 0.8995 to four significant digits. a-vflftSI MEANS IK IKS MEflNV lY lYE rpim BO 17B5.B33 10775 iE53B7S5 3.
Highlight Fill {{SHOW}} Shows the full Fit! expression. The slope (m) is 425.875. The y-intercept (b) is about 376.25. 425.8?5'H+3?6.25 Now find the predicted sales figure if advertising were to go up to 6 minutes. Switch to Home and use PREDY. {{OK}} 1 HOME 1 1 MATH 1 S to highlight PREDYC6) Stat-Two {Flfy} to highlight PREDY {{OK}} 6 1 enter] 2931.5 Entering Statistical Data You typically enter your data into columns in the Numeric view. Each column represents a variable named Cl through C9 and CO.
One-Variable Data To enter TVAR data Press I LIB I and select Statistics. Press {{START}} or NUM 1, 2. Set one-variable {{IVAR»}} statistics. This menu key is a toggle; pressing IVAR changes it to 2VAR and vice-versa. 3. Enter each value and press | enter] . Put all the values for the same data set in the same column. Entering frequencies: If a value occurs more than once, you can use another column to record its frequency, rather than entering multiple copies of that value. For instance.
5. Define the data in a set named HI through H5. On the left side, specify which column of data to analyze (Cl through C9, CO). (This specification can be an expression, such as Cl +C2.) On the right side, specify which column (if any) represents the frequencies for the values in the left-hand data column. If there is no frequency data column, then the frequency for each data value is 1. data columns ^EHIsnmstics svMMLic view^^ C2 .
I LIB I Select S t a t i s t i c s {{START}} Cl n 1 C2 C3 ItiiiiitiW« C4 ■ [CLEAR] B ■ [CLEAR] [Tl to clear two data columns, if necessary Make sure that {{IVARb}} is on for one-variable statistics. If it isn't press {{2VARb}}. Cl H.C H,? H.l H.as 4.25 I ENTER I 4.6 I ENTER I 4.7 fENTER I 4.
I PLOT I The bar includes 4.10 and has a frequency of 1000. Two-Variable Data To enter 2VAR 1. Press data NUM and select S t a t i s t i c s . Press {{START}} or 2. Set two-variable {{2varb}} statistics. This menu key is a toggle: pressing IVAR changes it to 2VAR and vice-versa. 3. Enter each value and press | enter |. Enter the values for one variable in one column, then move to a second column to enter the values for the second variable.
5. Define the data in a set named SI through S5. In the left-hand column, specify which column of data (Cl through C9, CO) contains the independent (x) variable data. (This specification can be an expression, such as c 1-1-c2.) STftTISTICS SVMEBLIC «'ЗПСЗ_______ C4 ^Fiti S2! |m*X+b 1 Fit; ENTER 1 Quoits w Ш DEFINED F nSBHH independent (x) data dependent ¡y) data ® In the right-hand column, specify which column of data holds the dependent (y) variable data. 4.
Numeric Keys View Key Meanine {{EDIT}} Copies the highlighted item into the edit line. {{INS}} Inserts a zero value above the highlighted cell. {{SORT}} Sorts the specified independent data column in ascending or descending order, and sorts a specified dependent (or frequency) data column along with it. {{BIG}} Switches between larger and smaller type sizes. {{IVARh}} {{2VARh}} A toggle switch to set one-variable or twovariable statistics.
Symbolic View Keys Key Meaning {{EDIT}} Copies the column variable (or variable expression) to the edit line for editing. Press {{OK}} when done. {{'^CHK}} Checks/unchecks the current data set. Only the checkmarked data set(s) are computed and plotted. {{c}} or{{x}} Typing aid for the column variables (C) or for the Fit expressions (X). {{SHOW}} Displays the current variable expression in standard mathematical form. Press {{OK}} when done.
To edit a data In the Numeric view of the Statistics aplet, highlight the data set value to change. Type a new value and press | enter |, or press {{EDIT}} to copy the value to the edit line for modification. To delete data ® To delete a single data item, highlight it and press | dei| . ® To delete a column of data, highlight an entry in that column and press ■ [CLEAR]. Select the column name. • To delete all columns of data, press ■ [CLEAR] in Numeric view. Select All columns.
Analyzing the Data First enter your data and define which columns of data make up your data set, then compute their statistical values. You compute descriptive statistics by pressing the {{STATS}} key in the Numeric view. For two-oariable (2VAR) statistics, you must first define the regression model. Defining a Regression Model (2VAR) The Symbolic view includes an expression (Fitl through Fit5) that defines the regression model, or “fit", to use for the regression analysis of each two-variable data set.
Fit Models Reeression Hi Linear Meanine (Default.) Fits the data to a straight line, y = mx+b. Uses a least-squares fit. m*x+b Logarithmic Fits to a logarithmic curve, y = m\nx + b. m*LN(X)+b Exponential Fits to an exponential curve, y = be"“. EXP{m*X)*b Power Fits to a power curve, y = X''m*b Quadratic Fits to a quadratic curve, y = ax? +bx+c. Needs at least three points. a*X''2+b*X+c Cubic Fits to a cubic curve, y = ax^ +b^ +cx+d Needs at least four points.
To deflne your own fit 1. In Numeric view, make sure 2VAR is set ({{2VARn}}). 2. Display the Symbolic view. Highlight the Fit expression (Fitl, etc.) for the desired data set. Type in an expression and press | enter |. The independent variable must be X. Example: 1.5*COS(X)+0.3*SIN(X). This automatically changes the Fit type (SI FIT, etc.) in the Symbolic Setup to "User Defined.
One-Variable Computed Statistics n2 Number of data points. totX Sum of data values (with their frequencies). MEANS Mean value of data set. pvarS Population variance of data set. svarS Sample variance of data set. PS DEV Population standard deviation of data set. SSDEV Sample standard deviation of data set. minS Minimum data value in data set. Q1 First quartile: median of ordinals to left of median. median Median value of data set.
Two-Variable Computed Statistics MEANX Mean of X- (independent) values. 2x Sum of x-values. SX2 Sum of ^-values. MEANY Mean ofy- (dependent) values. Sy Sum ofy-values. XY2 Sum of yWalues. SXY Sum of each x*y. CORK Correlation coefficient of the independent and dependent data columns for a linear fit only (regardless of the Fit chosen). Returns a value from 0 to 1, where 1 is the best fit. COV Sample covariance of independent and dependent data columns.
Plotting You can plot: ® Histograms (IVAR). » Box-and-whisker plots (IVAR). » Scatter plots of data (2VAR). Pressing {{FIT}} draws a curve to fit the data points according to the current Fit model and calculates regression coefficients. Once you have entered your data (Numeric view), defined your data set (Symbolic view), and defined your Fit model for two-variable statistics (Symbolic Setup), you can plot your data. You can select up to five Scatter or Box-and-Whisker plots at a time.
Plot Types Histogram One-variable statistics. The numbers below the plot mean that the current bar (where the cursor is) starts at 47.3598 and ends at 48.1024 (not including 48.1024), and the frequency for this column is 1. Box and Whisker Plot Scatter Plot One-variable statistics. The left whisker marks the minimum data value (MIN) to the first quartile. The box marks the first quartile, the median, and the third quartile. The right whisker marks the third quartile to the maximum data value.
Fitting a Curve to 2VAR Data In the Plot view, press {{FIT}} to turn on {{FIT«}}. This calculates a curve to fit the checked two-variable data set(s). I PLOT I {{MENU}} {{FIT}} (assuming 2VAR is set and two data sets are defined and checked in Numeric and Symbolic views) SYMB The expression in Fit 1 shows that the slope=0.03865 and they-intercept=4.856. i^^STATISTICf fVMEDLIC VIEH^W .
Plot Settings The Plot Setup view (■ [SETUP-PLOT]) sets most of the same plotting parameters as it does for the other built-in aplets. See “Setting Up the Plot” in chapter 3. Settings unique to the Statistics aplet are: Plot Type (IVAR) STATPLOT specifies either a histogram or a box-and-whisker plot for one-variable statistics (when {{IVARb}} is set).Use {{CHOOS}} to change the highlighted setting Histogram Width HWIDTH specifies the width of a histogram bar (a IVAR plot).
Exploring the Plot The Plot view has menu keys for zooming, tracing, and coordinate display. There are scaling options under ■ [VIEWS]. These features are described in chapter 3 under "Plotting and Analyzing Equations". PLOT View Keys Key Meanine ■ [CLEAR] Erases the plot. ■ [VIEWS] Offers additional pre-defined views for splitting the screen, overlaying plots, and autoscaling the axes. Moves cursor to far left or far right.
Calculating Predicted Values The functions PREDX and PREDY will estimate (predict) values for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data according to the specified fit. To find predicted values 1. In Plot view, calculate the Fit (regression curve) for the data set: e In Symbolic view, your data set (S variable) must be defined and checkmarked.
6 Using Matrices You can do matrix calculations in Home (and in programs). The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas, such as [ [ 1 , 2 , 3 ] , [ 4 , 5 , 6 ] ] for "1 2 3“ 456 (If the Decimal Mark in MODES is set to Comma, then the separators are periods.) Vectors Vectors are one-dimensional arrays. They are composed of just one row or one column. In this calculator, a vector is represented with single brackets; for example, [ 1 , 2 , 3 ] .
Creating a 1. Press ■ [MATRIX], in Matrix Catalog Highlight the matrix variable name you want to use and press {{NEW}}. (The dimensions will change automatically after the matrix is defined.) 3. Select the type of matrix. • For a vector (one-dimensional array), select Real Vector or Complex Vector. Certain operations do not recognize a one-dimensional matrix as a vector, so this selection is important. • For a matrix (two-dimensional array), select Real Matrix or Complex Matrix. 4.
To edit a matrix In the Matrix catalog, highlight the matrix name you want and press {{EDIT}} instead of {{NEW}}. Matrix Catalog Keys Key Meaninc {{EDIT}} Opens the highlighted matrix for editing. {{NEW}} Prompts for a matrix type, then opens an empty matrix with the highlighted name. {{SEND}} Transmits the highlighted matrix to another HP 38G or a disk drive. Works like sending an aplet (chapter 1). {{RECV}} Receives a transmitted matrix from another HP 38G or a disk drive.
To display a matrix In the Matrix catalog (■ [MATRIX]), highlight the matrix name and press {{EDIT}}. In Home, enter the name of the matrix variable and press I enter!. To display one In Home, enter matrixname(roLU,column). For example, if M2 element is {{3,4,},[5,6]], then M2 ( 1 , 2 ) [ enter| returns 4. To delete a matrix In the Matrix catalog (■ [MATRIX]), highlight the matrix to delete and press |del|. The name remains. The matrix is redimensioned to 1X1 with a zero element.
Creating a Matrix in Home 1. and each row with brackets (the shifted [|] and |T| keys). 2. Separate each element and each row with a comma. Example: [ [ 1 , 2 ] , [ 3 , 4 ] ] . (Note: if the Decimal Mark in MODES is set to Comma, use periods as separators.) 3. set of brackets. Example: [ 1 , 2 , 3 ] . 4. Press I ENTER I to enter and display the matrbc. Immediately after typing in the matrbi, you can store it in a variable by typing {{STO^}} matrixname j enter |.
Matrix Arithmetic You can use the arithmetic functions (+, -, X, /) with matrix arguments. Multiplication and division have different meanings depending on whether one of the arguments is a scalar or not. Adding and For addition and subtraction, the dimensions of the matrices Subtracting must be the same. You can enter the matrices themselves or enter the names of stored matrix variables. The matrices can be real or complex. For the next four examples, store [[1,2],[3,4]] into Ml and [[5,6],[7,8]] into M2.
Multiplying Two Matrices Multiplication of two matrices is not commutative. The number of columns of the first matrix must equal the number of rows of the second matrix. Assume that Ml still contains [[1,2],[3,4]] and M2 still contains [[5,6],[7,8]]. |A...z[M 1 0 [A...z|M 2 ENTER Rns/2 m*M2 [C3,4],C5,6]] [tl9,gg3,C43,50]] Bévili The result has the same number of rows as the first matrix and the same number of columns as the second matrix.
Solving Systems of Linear Equations Remember that a system of equations can be represented by a matrix equation : Equation Form Matrix Form ax + by + cz = dx + ey + fz = kj^ gx + hy + iz = b c X K e f y = k. g h i z a d Using the matrix form, the solution is the vector of variables, as shown below. Constants Vector Coefficients Matrix Variables Vector (result) [^1» ^2*^3] [[a ,b .c]{d .e,f\[S ,h.i]] [x, y.
1039^ C6,0,6]^EC2,3,4],tl,l... _______________ n , 0 , n ifeHiia To see the full input expression, first copy it.to the edit line (press 0 0 {{COPY}}), then press [0 to scroll through the expression. Matrix Functions There are two categories of matrix operations: functions and commands. The matrix functions are given in the following table. The matrix commands are for programming; they appear in chapter 8, Programming. Functions • Functions can be used in any aplet or in Home.
Output Functions return results to the display (and to the variable Ans). Results can be displayed with single brackets (for a vector) or double brackets (for a matrix). Matrix Functions COLNORM Column Norm. Finds the maximum value (over all columns) of the sums of the absolute values of all elements in a column. COLNORM (mahrx) COND Condition Number. Finds the 1-norm (column norm) of a square matrix. COND {matrix) CROSS Cross Product of vector! X vector2.
Matrix Functions, continued LQ LQ Factorization. Factors mxn matrix into three matrices: { [ [ mXn lowertrapezoidal] ] , [ [ nxn orthogonal] ] , [ [ mxm permutation ] ]}. hQ [matrix) LSQ Least Squares. Displays the minimum norm least squares matrix (or vector). hSQ [matrix!, matrix2) LU LU Decomposition. Factors a square matrix into three matrices: {[ [lowertriangular] ] , [ [uppertriangular] ] , [ [permutation] ]} The uppertriangular has ones on its diagonal. LU [matrix] MAKEMAT Make Matrix.
SCHUR Matrix Functions, continued Schur Decomposition. Factors a square matrix into two matrices. If matrix is real, then the result is {[ [orthogonal] ], [ [upperquasi triangular] ]}. If matrix is complex, then the result is {[ [unitary] ], [ [upper-triangular] ]}. SCHUR (mato) SIZE Dimensions of matrix. Returned as a list: {rows,columns}. SIZE [matrix) SPECNORM Spectral Norm of the specified array. SPECNORM (mato) SPECRAD Spectral Radius of a square matrix.
Examples Filling Matrices You can create and fill a matrix with zeros for the diagonal elements and ones for the off-diagonal elements using the MAKEMAT (make matrix) function. For example, entering MAKEMAT (IA J, 4,4) creates a 4 X 4 matrix with ones for all elements except zeros on the diagonal. The logical operator A returns 0 when I (the row number) and J (the column number) are equal, and returns 1 when they are not equal. Identity Matrix You can create an identity matrix with the IDENMAT function.
Using Lists You can do list operations in Home (and in programs). The elements of a list appear in braces and are separated by commas, such as {A, B, c} or { 1 , 2 , 3 } . (If the Decimal Mark in MODES is set to Comma, then the separators are periods.) List Variables There are ten list variables available, named LI through L9 and LO. You can use them in calculations or expressions in Home or in a program. You can fetch the list names from the VAR menu, or just type their names from the keyboard.
List Catalog Keys List Editing Keys Key Meanina {{EDIT}} Opens the highlighted list for editing. {{SEND}} Transmits the highlighted list to another HP 38G or a disk drive. Works like sending an aplet (chapter 1). {{RECV}} Receives a transmitted list from another HP 38G or a disk drive. Works like receiving an aplet (chapter 1). CUD ■ [CLEAR] Clears the highlighted list. Clears all lists. ■ ®or0 Moves to the end or the beginning of the catalog.
To transmit a You can send and receive lists to/from other calculators just list as you can send and receive aplets, programs, matrices, and notes. After aligning the calculators’ infrared ports, open the List catalogs on both calculators. Highlight the list to send, then press {{SEND}} on the sending calculator and {{RECV}} on the receiving calculator. See "Sending and Receiving Aplets," in chapter 1. Creating a List 1. Enter the list in the edit line.
List Functions Following is a table of list functions. Use them in Home, as well as in programs. You can type in the name of the function, or you can copy the name of the function from the List category of the MATH menu. Press | math | | A...Z | L. This displays the List category. Highlight the function on the right-hand side and press {{OK}}. Function Syntax « Functions have arguments that are enclosed in parentheses and separated by commas. Example; CONCAT { L I , L 2 ) .
List Operations, continued ÄUST Creates a new list composed of the differences between the sequential elements in listl. The new list has one fewer elements than //sf7. The first differences for {x, ... xj are [x-x^ AhlSTi list I) MAKEUST Calculates a sequence of elements for a new list. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELI ST (expression, variable, begin, end, increment) ttUST Calculates the product of all elements in list.
Using Lists in You can use a list ncime or the explicit list in an expression Expressions using any of the real-number functions. Press I ENTER I to evaluate the expression. (HOME i 0,2,3>^L2 HOME ■ 01 □2g3BQ] {{STOHI bvin L2 1 ENTER 1 5 1 * 1 1 A...Z 1 L 2 1 ENTER 1 Generating Series Example a £5,10,15> The MAKEUST operation generates a series by automatically producing a list from the repeated evaluation of an expression.
Finding Statistical Values for List Elements To find values such as the mean, median, maximum, and minimum values of the elements in a list, use the Statistics aplet. Given list data in a list variable (LI, for example), store LI into a data column variable (Cl, for example), and then compute its statistics. 1. In Home, store LI into Cl. You will be able to see the list data in the Numeric view of the Statistics aplet. 2.
8 Programmiiig This chapter describes how to program using the HP 38G. In this chapter you’ll learn about • Using the Program catalog to create and edit programs. • Programming commands. ® Storing and retrieving variables in programs, • Programming variables. The Contents of a Program An HP 38G program contains a sequence of numbers, mathematical expressions, and commands that execute automatically to perform a task. These items are separated by a colon (: ).
• Open the Program catalog. • Enter commands with the Math menu, e Create a new program. ® Edit a program. ® Send and receive a program. ® Delete a program or its contents. » Run and debug a program. ® Stop a program. ® Copy a program. To open the • Press ■ [PROGRAM]. Program The Program catalog displays a list of program names. If catalog yoy haven't created any programs, the only name you'll see is Editline.
Before starting to work with programs, you should take a few minutes to become familiar with the Program catalog keys. You can use any of the following keys (both menu and keyboard), to perform tasks in the Program catalog. Program catalog keys To create a new program Key Meaning {{EDIT}} Opens the highlighted program for editing. {{NEW}} Prompts for a new program name, then opens an empty program. {{SEND}} Transmits the highlighted program from another HP 38G or from a disk drive.
3. Type your program name, then press {{ok}}. When you press {{OK}}, the Program Editor opens. 4. Enter your program. When done, start any other activity. Your work is saved automatically. To enter Until you learn the abbreviated spelling for the HP 38G commands commands, the easiest way to enter commands is to use the Math menu from the Program editor. 1. From the Program editor, press [ math | {{cmds}}. 2. On the left, highlight a command category, then press 0. l»9W««««M0-rr.
To edit a program 1. Press ■ [PROGRAM] to open the Program catalog. 2. Use the arrow keys to highlight the program you want to edit. 3. Press {{EDIT}}. The HP 38G opens the Program Editor. The name of your program appears in the title bar of the display. You can use the following keys to edit your program. Editing keys Key Meanine {{STO^}) Stores a number into a named variable. {{SPACE}} Inserts space into text. {{APACE}} Displays previous page of the program.
To send and receive a program You can send and receive programs to and from another HP 38G or disk drive—^just as you can send and receive aplets, lists, matrices, and notes. 1. Connect the storage device to the calculator by cable or align the two calculators’ infrared ports by matching up the triangle marks on the rims of the calculators. Place the calculators no more than 2 inches (5 cm) apart. 2. Sending calculator: Open the Program catalog, highlight the program to send, and press {{SEND}}.
To delete a program You can delete any program except Editline, 1. Press ■ {PROGRAM] to open the Program catalog. 2, Highlight a program to delete, then press |del|. To delete all programs « To delete the contents of a program 1. Press ■ {PROGRAM] to open the Program catalog. Press ■ {CLEAR], then press {{YES}}. 2, Highlight a program , then press {{EDIT}}. 3. Press® {CLEAR], then press {{YES}} The contents of the program are deleted, but the program name remains.
2. A flashing arrow appears in the program at the point where the error occurred. R0N6MM PRDQRftMi RRNDMRT M2j3S4! EDITMRT M2:, 4 BHSBanaii 3. The character preceding the arrow contains a syntax error. You can continue to run, then edit the program until you find and correct all errors. To stop a program You can stop the execution of a program at any time by pressing [CANCEL] (the |on| key).
Programmieg Commands This section describes the commands for programming with the HP 38G. You can enter these commands in your program by typing them or by accessing them from the Math menu. 1. Press ■ [PROGRAM] to open the Program catalog. 2. Press ({NEW}} or {{EDIT}} to open the Program editor. The Program editor is where you enter new programs or edit existing ones. 2. From the Program editor, press | math | {{CMDS}}. The HP 38G displays the Program Commands menu.
Aplet Commands These commands control aplets. CHECK Checks (selects) the corresponding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. Then a checkmark would appear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view. CHECK n SELECT Selects the named aplet and makes it the current aplet. SELECT apletn am e SETVIEWS Takes trios of arguments. Used to define entries in the VIEWS menu for aplets.
Branch Commands A programming structure allows a program to control how it should execute depending on given conditions or the values of particular arguments. The HP 38G has two kinds of control structures: e Branch structures. * Loop structures. Branch structures let a program make a decision based on the result of one or more tests. Here is a summary of the branch structures available on the HP 38G. (Unlike the other programming commands, the control structure commands work in logical groups.
CASE-END Executes a series of test-ciause commands that execute the appropriate tm e-clau se sequence of commands. Its syntax is; CASE IF test-clau se^ THEN tru e-clau se ^END IF test-clau se^ THEN tru e-clau se^ END IF test-clau se^ THEN tru e-clau se^ END END When CASE is executed, tesU lau se^ is evaluated. If the test is true, tm e-clau se^ is executed, and execution skips to END. If tesK lau se, if false, execution proceeds to test-clau se^ .
Drawing Commands The Drawing commands act on the display. The scale of the display depends on the current aplet's Xmin, Xmax, Ymin, and Ymax values. The following examples assume the HP 38G default settings with the Function aplet as the current aplet. ARC Draws an arc with center (x,y), radius, start Jingle jneasurement, and end_angle_measurement. ARC x;y; radl us; start_an gl e_iaeasu rm en t; en d_an gle_m easu rm en t Example ARC 0;0 ;2 ;0 ; 3 6 0 Draws circle centered at (0,0) of radius 2.
PIXOFF Turns off the pixel at the specified coordinates (x,y). PIXOFF x;y PIXON Turns on the pixel at the specified coordinates (x,y). PIXON x;y TUNE Toggles the pixels along the line from (xl, yl) to (x2, yZ). Any pixel that was turned off, will be turned on; any pbcel that was turned on, will be turned off. TUNE can be used to erase a line. TLINE xl;yl;x2;y2 Example TLINE 0 ; 0 ; 3 ; 3 Erases previously drawn 45 degree line from (0,0) to (3,3).
Graphic Commands The Graphic commands use the graphics variables G0-G9 as name arguments—or the Page variable from Sketch. Position arguments take the form (x,y). Position coordinates depend on the current aplet's scale which is specified by Xmin, Xmax, Ymin, and Ymax. DISPLAY-» Stores the current display in name. DISPLAY^ n am e -»DISPLAY Displays graphic from name in the display. -»DISPLAY n am e ^GROB Creates a graphic from expression , using fon t_size, and stores the resulting graphic in n am e.
PLOT-» Stores the Plot view display as a graphic in n am e. PLOT^ n am e ^PLOT Puts graph from name into the Plot view display. —»PLOT n am e REPLACE Replaces portion of graphic in n am e with another grraph i c, starting at position s tart (in form x,y). REPLACE also works for lists and matrices. REPLACE n am e;(start_x, start_y);graph ic SUB Extracts a portion of a list, matrix, or graphic (specified by start and en d —in form x,y), and stores it in n am e.
Loop Commands A programming structure allows a program to control how it should execute depending on given conditions or the values of particular arguments. The HP 38G has two kinds of control structures; ® Branch structures. • Loop structures DO...UNTIL ...END Do ... Until... End is a loop structure that executes the loopclause repeatedly until test-clause returns a true (nonzero) result. Because the test is executed after the loop>clause, the loop-clause is always executed at least once.
Matrix Commands The Matrix commands use the matrix variables M0-M9 as arguments. ADDCOL Add Column. Inserts values into a column before columnjiumber in the specified matrix You enter the values as a vector. The values must be separated by commas and the number of values must be the same as the number of rows in the matrix name. ADDCOL n am e; [valu e^ , . . ■ , valu ej ; colu m n n u m ber ADDROW Add Row.
RANDMAT Creates random matrix with number of rows and columns you specify in row s, colu m n s, and stores the result in n am e (name must be MO . . . M9). The entries will be integers ranging from -9 to 9. RANDMAT n am e;row s;colu m n s Exan®>le: RANDMAT M 2 ; 3 ; 4 : EDITMAT М2: Creates a Matrix in М2 with 3 rows and 4 columns; then starts the Matrix Editor and displays matrix М2. MS 1 г 3 -Ч 3 2 1 -2 3 г 2 -5 s 4 0 -? * -5 1^дшя™1а)И||К1иам11 REDIM Redimensions the specified matrix to size.
SUB Extracts a subobject—a portion of a list, matrix, or graphic from object and stores it into name. Start and end are each specified using a list with two numbers for matrix, using a number for vector or lists, or using (x,y) for graphics. SUB name;object;start;end SWAPCOL Swap Columns. Exchanges column! and column2 of the specified matrix SWAPCOL name;columnl;column2 SWAPROW Swap Rows.
Prompt Commands You can use the following commands to prompt users for input during your program—or to provide information to users. BEEP Beeps at the at the frequency and time you specify. BEEP frequ en cy;tim e_in _secon ds Exan®le BEEP 1024,-5 Creates a 5-second beep at 1024 Hz. CHOOSE Where name is the name of the variable from which the number of the initially-highlighted item is retrieved—and into which the number of the chosen item will be stored.
DISP Displays textjtem and a value in display lin ejiu m ber. A textjtem consists of any number of expressions and quoted strings of text. The expressions are evaluated and turn into strings. Lines are numbered from the top of the screen, 1 being the top and 7 being the bottom. DISP line_number; text_item Example 3 ; “ A i s " 2 + 2 Result: A i s 4 (displayed on line 3 ) DISPTIME Displays the current date and time.
INPUT Suspends program execution, prompt the user with title, label, and help, initializes the command line with default, and saves the resulting input in name. Use ■ [CHARS] to type the quote marks" INPUT n a m e ; t l t i e , l a b e l / h e l p ; d e f a u l t Exaxt^le INPUT R; "Circular Area"; "Radius"; "Enter Number";l: ^CmCULAR AREA RADIUS ENTER NUMDER iECHBiMm MSGBOX Suspends program execution and displays a message box containing textjtem.
You can also use the NoteText variable to provide text arguments. This can be used to insert line breaks. For example, press ■ [NOTE] and type AREA IS [ enter ]. Example MSGBOX NoteText “ " -ii*A"2: FlREfl IS 3. 14159265359 WAIT Halts program execution for specified number of seconds.
Stai-One and Stat-Two Commands Analysis of one-variable and two-variable statistical data. You can refer to chapter 5 for complete definitions of these variables. Stat-One Commands DOIVSTATS Calculates STATS using datasetname and stores the results in corresponding variables: NX, TotX, MeanX, PVarX, SVarX, PSDev, SSDev, MinX, Q1, Median, Q3, and MaxX. Datasetname can be HI, H2,..., or H5. Datasetname must define at least two data points. DOIVSTATS datasetname RANDSEED Sets random number seed to value.
Storing and Retrieving Variables in Programs The HP 38G has both Home variables and aplet variables. Home variables are used for real numbers, complex numbers, graphics, lists, and matrices. Home variables keep the same values in Home or in aplets. Aplet variables are those whose values depend on the current aplet. The aplet variables are used in programming to emulate the definitions and settings you make when working with aplets interactively.
To retrieve an aplet variable You can use this procedure to retrieve either the variable name or the variable value into your program. 1. Press [VAR] to open the Variable menu. 2. If necessary, press {{aple®}} to open the list of aplet variables. 3. Select an aplet view. Each aplet variables is associated with a view: Numeric or Numeric Setup, Symbolic or Symbolic Setup, Plot or Plot Setup, Note, or Sketch.
Plot-View Variables The following aplet variables are available in Plot View. Not all variables are available in every aplet. SI fit-S5fit, for example, are only available in Statistics. Under each variable name is a list of the aplets where the variable can be used. Area Function Contains the last value found by Area operation in Plot-FCN menu. Axes Turns axes-drawing on or off. All Aplets From Plot Setup, check (or uncheck) _AXES.
Extremum Function FastRes Solve Contains the last value found by Extremum operation in the Plot-FCN menu. Toggles resolution between plotting in every other column (faster), or plotting in every column (more detail). From Plot Setup, choose Faster or More Detail. or In a program, type 1 {{STOl^}}FastRes for faster (default). 0 {{STO^}}FastRes for more detail. Grid Turns the background grid in Plot View on or off. From Plot Setup, check (or uncheck) _grid.
InvCross Toggles between solid crosshairs or inverted crosshairs. (Inverted is useful if background is solid). AllAplets or From Plot Setup, check (or uncheck) _lnvCross In a program, type 1 {{STO^-}}InvCross to invert the crosshairs. 0 {{STO^-}}lnvCross for solid crosshairs (default). ¡sect Function Labels AllAplets Contains the last value found by Intersection operation in the Plot-FCN menu. Draws labels in Plot view showing X and Y ranges.
SlmarkSSmark Statistics Defines the mark to use for statistics 2-variable scatter plots. From Plot Setup for two-variable statistics, Slmark-SBmark, then choose a mark. or In a program, type n {{STO^}}Slmark SeqPlot Sequence Toggles type of sequence plot; Stairstep or Cobweb. From Plot Setup, select SeqPlot, then choose stairstep or Cobweb. or In a program, type 1 {{STO^-}}SeqPlot for Stairstep (default). 2 {{STO^)}SeqPlot for Cobweb.
0min/0max Polar Defines the minimum and maximum independent values. Appears as the 0rng field in the Plot Setup input form. From the Plot Setup input form, enter values for 0rng, or In a program, type n {{STO^}}0min n {{STO^)}0max □step Polar Defines the step size for an independent variable. From the Plot Setup input form, enter values for Gstep. or In a program, type n {{STO^}}0step Tmin /Tmax Parametric Defines the minimum and maximum independent variable values.
Xcross AllApkts Defines the horizontal coordinate of crosshairs. Only works with TRACE off. In a program, type n {{STO^}}Xcross Ycross All Aplets Defines the vertical coordinate of crosshairs. Only works with TRACE off. In a program, type n {{STO^}}Ycross Xtick All Aplets Defines the distance between tick marks for the horizontal axis.
Ymin / Ymax AllAplets Defines the minimum and maximum vertical values of the plot screen. Appears as the YRNG fields (vertical range) in the Plot Setup input form. From Plot Setup, enter the values for yrng. or In a program, type n ¡¡STO^))Yinin n ¡(ST0^-))Ymax Xzoom AH Aplets Sets the horizontal zoom factor. From Plot-ZOOM-Set Factors, enter the value for XZOOM. or In a program, type n {{ST0^-}}xz00M (default zoom factor is 4). Yzoom AllAplets Sets the vertical zoom factor.
Symbolic-View Variables The following aplet variables are available in Symbolic View. Angle Sets the angle mode. All Aplets From Symbolic Setup, choose Degrees, Radians, or Grads for angle measure. or In a program, type 1 {{STO^}} Angle for Degrees. 2 {{STO^}} Angle for Radians (default). 3 {{STO^}}Angle for Grads, F1...FB, FD Can contain any expression. Independent variable is X.
El ...E9, EO Can contain any equation or expression. Independent variable Solve is selected by highlighting it in Numeric View. Exainple 'X+Y*X-2=Y' {{ST0^-}}E1 SI fit...S5fit Defines the type of fit to be used by the {{FIT}} operation in Statistics (two-variable), Plot view.
Numeric-View Variables The following aplet variables are available in Numeric View. C1...C9, CO CO through C9, and CO for columns of data. Can contain lists. Statistics Digits All Aplets Number of decimal places to use for Number format. From Solve-Numeric_Setup, enter a value in the second field of Number Format. or In a program, type n {{STO^}}Digits where 0 « n « 11. Format AH Aplets Defines the number display format.
Numindep List of independent values used by Build Your Own Table, Function Parametric Polar Sequence In a program, type NumRow Defines the highlighted row in Numeric view. In a program, type All Aplets list {{STO^}}NumIndep n {{STO^}}NumRow NumStart Function Parametric Polar Sequence NumStep Function Parametric Polar Sequence Defines the starting value for table in Numeric View. From Num Setup, enter a value for NUMSTART. or In a program, type n {{STO^}}NumStart.
StatMode Statistics Toggles mode between 1-variable and 2-variable statistics. Does not appear in the Plot Setup input form. Corresponds to the {{IVAR}} and {{2VAR}} keys in Numeric View. In a program, type 1 {{STO^}}StatMode for IVAR. 2 {{STOl>-}}StatMode for 2VAR. Note Variables The following aplet variable is available in Note View. NoteText Use NoteText to recall text previously entered in Note view. All Aplets Sketch Variables The following aplet variables are available in Sketch View.
Menu Maps of the VAR menu Home Variables Comolex Graphic Library List Matrix Z1...Z9. ZO G1...G9, GO Function L1...L9, DO M1...M9, MO Parametric Polar Sequence Solve Statistics User-named Modes Noteoad Procram Real Ans User-named Editline A. . .
Parametric Variables Plot Symbolic Numeric Note NoteText Axes Tstep Angle X6 Digits Connect Xcross XI Y6 Format Coord Ycross Y1 X7 NumCol Grid Xtick X2 Y7 NumFont Sketch Indep Ytick Y2 X8 Numlndep Page InvCross Xmin X3 Y8 NumRow PageNum Labels Xmax Y3 X9 NumStart Recenter Ymin X4 Y9 NumStep Simult Ymax Y4 XO NumType Tmin Xzoom X5 YO NumZoom Tmax Yzoom Y5 Tracing Polar Variables Plot Axes Xcross Symbolic Numeric Note Angle Digits NoteText C
Sequence Variables Plot Symbolic Numeric Note Xcross Angle Digits NoteText Coord Ycross U1 Format Grid Xtick U2 NuinCol Indep Ytick U3 NumFont Sketch InvCross Xmin U4 Numlndep Page Labels Xmax U5 NumRow PageNum Nmin Ymin U6 NumStart Nmax Ymax U7 NtimStep Recenter Xzoom U8 NtmiType SeqPlot Yzoom U9 NumZoom Axes Simult UO Tracing Solve Variables Plot Symbolic Numeric Note Xcross Angle Digits NoteText Connect Ycross El Format Coord Xtick E2 Niim
Statistics Variables Plot Symbolic Numeric Stat-One Axes Angle CO,...
9 Reference Information This chapter covers the following topics: « Regulatory information * Warranty information ® Service information * Battery information * How to reset the calculator e Glossary e Selected status messages Regulatory Information U.S.A. This Handheld Calculator complies with the limits for a class B digital device as specified in Part 15 of FCC Rules, which provide reasonable protection against harmful interference in a residential installation.
Europe DECLARATIONS OF CONFORMITY according to ISO/IEC Guide 22 and EN 45014 Manufacturer’s name Hewlett-Packard Australia Limited Manufacturer’s address Australian Calculator Operation 347, Burwood Highway Burwood East, Victoria 3151 Australia declares that the following product Product Name Handheld Calculator Model number HP38G Product options All.
Limited One-Year Warranty What is Covered The calculator (except for the batteries, or damage caused by the batteries) and calculator accessories are warranted by HewlettPackard against defects In materials and workmanship for one year from the date of original purchase. If you sell your unit or give it as a gift, the warranty is automatically transferred to the new owner and remains in effect for the original one-year period.
Service Environmental Limits Customer Support « Operating temperature : 0° to 45°C (32° to 113°F). • Storage temperature : -20° to 65°C (-4° to 149°F). » Operating and storage humidity: 90% relative humidity at 40°C (104°F) max\m\im. Avoid getting the calculator wet. • Battery operated at 4.5V dc, 60mA maximum. In the United States. If you have technical questions about how to use the product that are not covered in this guide, you can contact Hewlett-Packard Calculator Support 1000 NE Circle Blvd.
Hardware Service Contact Hewlett-Packard for diagnostic instructions and other service information before you send your calculator for repair. In the United States. Send the calculator to the Corvallis Service Center listed on the inside of the back cover. Outside the U.S. Contact your Hewlett-Packard dealer or sales office for the location of the nearest service center. Do not ship the calculator for service without first contacting a Hewlett-Packard office.
Warranty on Service. Service is warranted against defects in materials and workmanship for 90 days from the date of service. Service Agreements. In the U.S., a support agreement is available for repair and service. For additional information, contact the Corvallis Service Center (inside back cover). HP Marketing Should you need to contact Hewlett-Packard, check your Headquarters local telephone directory for the HP Sales and Service Office Outside the nearest you.
Batteries When battery power is low, the ((•)) annunciator stays on, even when the calculator is off. There is also a warning message that appears when the calculator is on. Warning: Low Bat. The HP 38G uses three AAA batteries. Be sure all three are of the same brand and type. Rechargeable batteries are not recommended because of their lower capacity and more sudden demise. ■ To change the batteries 1. Turn the calculator off and place the slide cover over the keyboard to keep from pressing keys.
Resetting the HP 38G If the calculator “locks up" and seems to be stuck, you must reset it. This is much like resetting a PC. It cancels certain operations, restores certain conditions, and clears temporary memory locations. However, it does not clear stored data (variables, aplet databases, programs) unless you use the procedure below, “To erase all memory and reset defaults".
Glossary aplet A small application, limited to one topic. The built-in aplet types are Function, Parametric, Polar, Sequence, Solve, and Statistics. An aplet can be filled with the data and solutions for a specific problem. It is reusable (like a program, but easier to use) and it records all your settings and definitions. command An operation for use in programs. Commands can store results in variables, but do not display results.
show the current meanings. note Text that you write in the Notepad or in the Note view for a specific aplet. program A reusable set of instructions that you record using the Program editor. sketch A drawing that you make in the Sketch view for a specific aplet. variable The name of a number, list, matrix, note, or graphic that is stored in memory. Use {{STO^}} to store and use | var| to retrieve.
Selected Status Messages Bad Argument Type Incorrect input for this operation. Bad Argument Value The value is out of range for this operation. Infinite Result Math exception, such as 1/0. Insufficient Memory You must recover some memory to continue operation. Delete one or more matrices, lists, notes,or programs (using catalogs), or custom (not built-in) aplets (using fuBl)- Insufficient Statistics Data Not enough data points for the calculation.
Selected Status Messages, continued Too Few Arguments The command requires more arguments than you supplied. Undefined Name The global variable named does not exist. Undefined Result The calculation has a mathematically undefined result (such as 0/0). Out of Memory You must recover a lot of memory to continue operation. Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not built-in) aplets (using fllBl).
Index Special Characters TT, 2-16 IT (constant), 2-19 ttLIST, 7-5 d (derivative), 2-12, 2-17 J (integral), 2-12, 2-17 =£ (logical test), 2-27 A (warning), 1-5 a annunciator (alpha), 1-6 S annunciator (busy), 1-6 ^ annunciator (stack history), 1-6 ■ key (shift), 1-2 V“.
APLET menu key, 2-8 aplet variables, 1-18,2-10 for settings, 2-10 in Plot view, 8-28 new, 2-10 retrieving, 8-27 aplet views canceling operations in, 1-14 changing, 1-13 editline, 1-16 note, 1-13 Numeric view, 1-12 Plot view, 1-12 sketch, 1-13 split-screen, 1-13 Symbolic view, 1-12 aplets attaching notes, 1-16 attaching sketches, 1-16 calculating in, 1-16 clearing, 1-26 copying, 1-27 creating new, 1-26 defined, 1-11 deleting, 1-26 editing, 1-25 Library, 1-25 naming, 1-26 Note view, 1-18 opening, 1-25 Paramet
in aplet view, 1-16 root, 4-8 with last result, 2-5 calculator automatic turn-off feature, 1-2 protective cover, 1-1 repair service, 9-5 support, 94 warranty, 93 calculus operations, 2-17 CANCEL key, 1-1 canceling menu lists, 1-11 operation in aplet view, 1-14 canceling operations, 1-1 CASE...
decreasing display, 1-6 increasing display, 1-6 Coord variable, 8-28 coordinate display, 3-13 copying from display, 1-9 programs, 8-8 copying notes, 1-19 CORR,5-19, 5-21 correlation statistical, 5-18 correlation coefficient, 5-21 COS (cosine), 2-15 COSH, 2-20 COT (cotangent), 2-28 COV, 5-19 covariance statistical, S-18 cover calculator, 1-1 creating newaplet, 1-26 notes in Notepad, 1-23 programs, 8-3 random matrix, 8-19 set of sketches, 1-22 CROSS, 6-10 cross product vector, 6-10 crosshairs horizontal coord
date and time, 8-22 full number, 1-10 matrices, 6-4 divide, 2-15 D0.,.UNT1L.,.
Extremum variable, 8-29 F f distribution, upper-tail probability, 2-23 factorial, 2-23 factorial (!), 2-23 FastRes variable, 8-29 fit, 5-21 choosing, 5-14 definingyour own, 5-16 in Statistics, 5-23 Fitl...FitO, 5-10,5-14 Fixed display, 1-7 Fixed number format, 1-7 FLOOR, 2-24 FNROOT, 2-24 FOR I...TO...STEP...
setting min/max values for, 8-29 histogram range, 5-22 histogram variable, 5-7 histogram width, 5-22 histograms, 5-19 adjusting, 5-19 plotting limit, 5-7 Historgram plot, 8-31 history.
list keys, 7-2 math functions, 1-3 menu keys, 1-3 Notepad keys, 1-24 Symbolic view, 3-3 keying in letters, 1-2 keys inactive, 1-5 Program catalog, 8-3 keystrokes shifted, 1-2 L labeling parts of a sketch, 1-22 LABELS axes, 3-19 Labels variable, 8-30 last answer, 1-10, 24 letters keying in, 1-2 Library managing aplets in, 1-25 Library keys, 1-25 LINE.
MATH menu, 1-4,2-13 structure of, 2-13 math operations, 2-1 enclosing arguments, 2-2 in scientific notation, 2-2 negative numbers in, 2-2 matrices adding columns, 8-18 arithmetic operations in, 6-6 assembly from vectors, 6-1 creating, 6-2 creating random, 8-19 dividing by a square matrix, 6-7 editing, 6-3, 8-18 inverting, 6-7 multiplying, 6-7 multiplying by a vector, 6-7 negating elements, 6-7 redimensioning, 8-19 sending and receiving, 6-4 storing elements, 6-2 matrix commands, 6-9 creating in Home, 6-5 de
of list, 7-7 name conflict, 9-11 names formal, 2-11 naming aplets, 1-26 programs, 8-3 natural exponential, 2-15, 2-20 natural log plus 1, 2-20 NEG. See negation negation, 2-16 negative numbers, 2-2 Nmax variable, 8-30 Nmin variable, 8-30 no equations checked, 9-11 normal distribution, upper-tail probability, 2-23 NOT.
pause. See WAIT percent (%).
POLYROOT, 2-22 POS, 7-5 power, 1-2 saving with automatic turn-off, 1-2 power lit, 5-15 power function, 2-16 PRDISPLAY, 8-20 precision numeric, 2-6 predicted values statistical, 5-24 PRHISTORY, 8-20 Print commands PRDISPLAY.
redrawing table of numbers, 3-24 reduced row echelon, 6-11 regression example, 5-4 values, 5-21 regression analysis, 5-21 regression fit user-defined, 5-15 regression formula, 5-15 regression model statistical, 5-10, 5-14 regression models, 5-15 defining, 5-16 regulatory information, 9-1 relative error statistical, 5-21 RelErr, 5-21 REPLACE, 8-16, 8-19 replacing portion of a graphic, 8-16 portion of a matrix, 8-19 RES plotting, 3-18 resetting aplets, 1-26 calculator, 9-8 memory, 9-8 Resetting settings Setup
SEQPLOT, 3-18 SeqPiot variable, 8-31 sequence finding square root, 3-33 sequence aplet, 1-12 Sequence definition, 3-3 sequence example, 3-7, 3-10 sequence plots choosing type, 8-31 sequence plotting defined, 3-2 example, 3-33 Sequence variables Axes, 8-28 Coord, 8-28 Grid, 8-29 Indep, 8-29 InvCross, 8-30 Labels, 8-30 Nmax, 8-30 Nmin, 8-30 Recenter, 8-30 SeqPlot, 8-31 Simult, 8-31 Trace, 8-32 Xcross, 8-33 Ycross, 8-33 service hardware, 9-5 Set Factors (zoom), 3-14 SETDEPEND, 8-25 SETFREQ, 8-25 SETINDEP, 8-25
Connect, 8-28 Coord, 8-28 FastRes, 8-29 Grid, 8-29 Indep, 8-29 InvCross, 8-30 Labels, 8-30 Recenter, 8-30 Simult, 8-31 Trace, 8-32 Xcross, 8-33 Ycross, 8-33 solving equations, 4-2 for the unknown variable, 44 quadratic equations, 2-26 SORT, 7-5 in Statistics, 5-11 sorting, 1-26 build-your-own table, 3-27 elements in a list, 7-5 in alphabetic order, 1-26 in chronological order, 1-26 SPECNORM,6-12 SPECRAD,6-12 spectral norm matrix, 6-12 spectral radius matrix, 6-12 speed search, 1-11 square, 2-16 square root,
Axes, 8-28 computed, 5-16 Connect, 8-28 Grid, 8-29 Hmin/Hmax, 8-29 Hwidth, 8-29 InvCross, 8-30 Labels, 8-30 Recenter, 8-30 Slmark-SSmark, 8-31 StatPlot, 8-31 Trace, 8-32 Xcross, 8-33 Y cross, 8-33 Stat-One commands D01VSTATS.8-2S RANDSEED, 8-25 SETFREQ, 8-25 SETSAMPLE, 8-25 STATPLOT, 5-22 StatPlot variable, 8-31 STATS, 5-11,5-16 Stat-Two commands SETDEPEND, 8-25 SETINDEP, 8-25 status messages, 9-12 step size independent variable, 8-32 STOP, 8-12 stopping programs, 8-8 storing.
tracing functions, 3-12 tracing plots, 3-8 transmitting programs, 8-6 transmitting aplets, 1-27 transpose matrix, 6-12 Trigscaling, 3-16 trigonometric functions, 2-15 trigonometry operations, 2-28 TRN, 6-12 TRNG, 8-32 TRNG (time range), 3-18 TRUNCATE, 2-25 TSTEP plotting, 3-18 Tstep variable, 8-32 two-variable data, 5-9 two-variable statistics, 5-14 computed, 5-19 typing letters, 1-2 U UNCHECK, 8-10 undefined name, 9-12 undefined result, 9-12 un-zoom, 3-14 upper-tail probabilities, 2-23 User Defined regres
zoom options, 3-14 redrawing table of numbers, 3-24 Index-18 zoom out, 3-14 ZOOM table, 3-24
Contacting Hewlett-Packard For information about Using this Product. If you have questions about how to use the product that are not covered in this guide, you can contact Hewlett-Packard Calculator Support (970) 392-1001 Mon.-Fri. 8:00am-5:00pm Pacific time. Closed holidays. For Hardware Service. See appendix A of this user’s guide for shipping instructions and information on obtaining service.
Aplet Views VIEWS NOTE SKETCH I CAPLET Function Parametric Polar Sequence Solue LIB library ▼ Е?ша[дздз1иттд1иэдак1ет1н?та1 run". 1 l u n ¿ ( I ' l E - U L I L V I C K 4 l*^FKX>=siH<;xvx F2(X>= FSCXJ Р4<Х> F5iX> SYMB symbolic ■jatinsfirai [SETUP-PLOT] ▼ 1Н!|||В1ПДТД ^^Щринстшн PLOT SETUP VRNQ;-3.1 1 RES: Faster «TICK; 3.2 VTICK: 1 EHTER MINIMUM HDRIZDNTRL VALUE ШИН PLOT plot K:.? V: NUM numeric 1 гашп FI .ВЧ1Ч71 .ЧБЧ6ЧВ? .04704 -.1B4S01 -.1Ч17В5 -.
