HP 39G/40G GRAPHING CALCULATOR USER’S GUIDE Version 1.
Contents Preface Manual conventions............................................................................... P-1 Notice .................................................................................................... P-2 1 Getting started On/off, cancel operations........................................................................1-1 The display .............................................................................................1-2 The keyboard .......................................
3 Function aplet About the Function aplet ........................................................................3-1 Getting started with the Function aplet.............................................3-1 Function aplet interactive analysis .........................................................3-8 Plotting a piecewise defined function example ..............................3-11 4 Parametric aplet About the Parametric aplet .....................................................................
9 Inference aplet About the Inference aplet .......................................................................9-1 Getting started with the Inference aplet............................................9-2 Importing Sample Statistics from the Statistics aplet .......................9-5 Hypothesis tests ......................................................................................9-9 One–Sample Z–Test .........................................................................9-9 Two–Sample Z–Test.....
11 Variables and memory management Introduction ..........................................................................................11-1 Storing and recalling variables .............................................................11-2 The VARS menu ..................................................................................11-4 Memory Manager .................................................................................11-9 12 Matrices Introduction ...........................................
15 Programming Introduction ..........................................................................................15-1 Program catalog ..............................................................................15-2 Creating and editing programs .............................................................15-4 Using programs ....................................................................................15-7 Working with programs.....................................................................
Reference information Regulatory information .........................................................................R-1 USA .................................................................................................R-1 Canada .............................................................................................R-1 LED safety.............................................................................................R-2 Warranty .................................................................
Preface The HP 39G/40G is a feature-rich graphing calculator. It is also a powerful mathematics learning tool. The HP 39G/40G is designed so that you can use it to explore mathematical functions and their properties. You can get more information on the HP 39G/40G from Hewlett-Packard’s Calculators web site. You can download customized aplets from the web site and load them onto your calculator.
Notice This manual and any examples contained herein are provided as-is and are subject to change without notice.
1 Getting started On/off, cancel operations To turn on Press >21@ to turn on the calculator. To cancel When the calculator is on, the >21@ key cancels the current operation. To turn off Press >6+,)7@OFF to turn the calculator off. To save power, the calculator turns itself off after several minutes of inactivity. All stored and displayed information is saved. If you see the ((•)) annunciator or the Low Bat message, then the calculator needs fresh batteries.
The display To adjust the contrast Simultaneously press >21@ and > @ (or > @) to increase (or decrease) the contrast. To clear the display • Press CANCEL to clear the edit line. • Press >6+,)7@CLEAR to clear the edit line and the display history. Parts of the display Title History Edit line Menu key labels Menu key or soft key labels. The labels for the menu keys’ current meanings. 672?a is the label for the first menu key in this picture.
Annunciators. Annunciators are symbols that appear above the title bar and give you important status information. Annunciator Description Shift in effect for next keystroke. To cancel, press >6+,)7@ again. α ((•)) Alpha in effect for next keystroke. To cancel, press >$/3+$@ again. Low battery power. Busy. Data is being transferred via infrared or cable.
• On the calculator keyboard, the top row of keys are called menu keys. Their meanings depend on the context—that’s why their tops are blank. The menu keys are sometimes called “soft keys”. • The bottom line of the display shows the labels for the menu keys’ current meanings. Aplet control keys The aplet control keys are: 1-4 Key Meaning >6<0%@ Displays the Symbolic view for the current aplet. See “Symbolic view” on page 1-15. >3/27@ Displays the Plot view for the current aplet.
Entry/Edit keys Getting started The entry and edit keys are: Key Meaning >21@ (CANCEL) Cancels the current operation if the calculator is on by pressing >21@. Pressing >6+,)7@, then OFF turns the calculator off. >6+,)7@ Accesses the function printed in blue above a key. >+20(@ Returns to the HOME view, for performing calculations. >$/3+$@ Accesses the alphabetical characters printed in orange below a key. Hold down to enter a string of characters.
Shifted keystrokes There are two shift keys that you use to access the operations and characters printed above the keys:>6+,)7@ and >$/3+$@. Key Description >6+,)7@ Press the >6+,)7@ key to access the operations printed in blue above the keys. For instance, to access the Modes screen, press >6+,)7@, then press >+20(@. (MODES is labelled in blue above the >+20(@ key). You do not need to hold down >6+,)7@ when you press HOME. This action is depicted in this manual as “press >6+,)7@MODES.
Math keys HOME (>+20(@) is the place to do calculations. Keyboard keys. The most common operations are available from the keyboard, such as the arithmetic (like > @) and trigonometric (like >6,1@) functions. Press >(17(5@ to complete the operation: >6+,)7@√ 256>(17(5@ displays 16. . MATH menu. Press >0$7+@ to open the MATH menu. The MATH menu is a comprehensive list of math functions that do not appear on the keyboard. It also includes categories for all other functions and constants.
Menus A menu offers you a choice of items. Menus are displayed in one or two columns. To search a menu To cancel a menu 1-8 • The _ arrow in the display means more items below. • The A_ arrow in the display means more items above. • Press *e, or *k, to scroll through the list. If you press >6+,)7@*e, or >6+,)7@*k,, you’ll go all the way to the end or the beginning of the list. Highlight the item you want to select, then press 2.a (or >(17(5@).
Input forms An input form shows several fields of information for you to examine and specify. After highlighting the field to edit, you can enter or edit a number (or expression). You can also select options from a list (&+226a). Some input forms include items to check (_ &+.a). See below for an example of an input form. Reset input form values To reset a default field value in an input form, move the cursor to that field and press >'(/@.
Setting Options (Continued) Number Format The number format mode you set is the number format used in both HOME and the current aplet. Standard. Full-precision display. Fixed. Displays results rounded to a number of decimal places. Example: 123.456789 becomes 123.46 in Fixed 2 format. Scientific. Displays results with an exponent, one digit to the left of the decimal point, and the specified number of decimal places. Example: 123.456789 becomes 1.23E2 in Scientific 2 format. Engineering.
Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the same for changing number format and decimal mark modes. 1. Press >6+,)7@MODES to open the HOME MODES input form. The cursor (highlight) is in the first field, Angle Measure. 2. Press &+226a to display a list of choices. 3. Press*k, to select Degrees, and press 2.a. The angle measure changes to degrees. 4. Press >+20(@ to return to HOME.
Aplets are stored in the Aplet library. See “Aplet library” on page 1-15 for further information. You can modify configuration settings for the graphical, tabular, and symbolic views of the aplets in the following table. See “Aplet view configuration” on page 1-17 for further information. Aplet name Use this aplet to explore: Function Real-valued, rectangular functions y in 2 terms of x. Example: y = 2x + 3x + 5 .
Quad Explorer aplet HINT The Quad Explorer aplet is used to investigate the behaviour 2 of y = a ( x + h ) + v as the values of a, h and v change, both by manipulating the equation and seeing the change in the graph, and by manipulating the graph and seeing the change in the equation. More detailed documentation, and an accompanying student work sheet can be found at HP’s web site.
Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of y = a sin ( bx + c ) + d as the values of a, b, c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation. When the user presses 67$57a in the $3/(7a view, the screen shown right is displayed. In this mode, the graph controls the equation.
Aplet library Aplets are stored in the Aplet library. To open an aplet Press >$3/(7@ to display the Aplet library menu. Select the aplet and press 67$57_ or >(17(5@. From within an aplet, you can return to HOME any time by pressing >+20(@. Aplet views When you have configured an aplet to define the relation or data that you want to explore, you can display it in different views.
Plot-Table view The VIEWS menu contains the Plot-Table view. >9,(:6@ Select Plot-Table 2.a Splits the screen into the plot and the data table. See “Other views for scaling and splitting the graph” on page 2-13 for futher information. Plot-Detail view The VIEWS menu contains the Plot-Detail view. >9,(:6@ Select Plot-Detail 2.a Splits the screen into the plot and a close-up. See “Other views for scaling and splitting the graph” on page 2-13 for further information.
Displays pictures to supplement an aplet. See “Notes and sketches” on page 14-1 for further information. Aplet view configuration You use the SETUP keys (>6+,)7@>3/27@, and >6+,)7@>180@) to configure the aplet. For example, press >6+,)7@SETUP-PLOT (>6+,)7@>3/27@)to display the input form for setting the aplet’s plot settings. Angle measure is controlled using the MODES view. Plot Setup Press>6+,)7@SETUP-PLOT. Sets parameters to plot a graph. Numeric Setup Press >6+,)7@SETUP-NUM.
Mathematical calculations The most commonly used math operations are available from the keyboard. Access to the rest of the math functions is via the MATH menu (>0$7+@). To access programming commands, press >6+,)7@ CMDS. See “Programming commands” on page 15-14 for further information. Where to start The home base for the calculator is the HOME view (>+20(@). You can do all calculations here, and you can access all >0$7+@ operations.
Scientific notation (powers of 10) 4 –7 A number like 5 × 10 or 3.21 × 10 is written in scientific notation, that is, in terms of powers of ten. This is simpler to work with than 50000 or 0.000000321. To enter numbers like these, use EEX. (This is easier than using >;@10>[N@.
Parentheses You need to use parentheses to enclose arguments for functions, such as SIN(45). You can omit the final parenthesis at the end of an edit line. The calculator inserts it automatically. Parentheses are also important in specifying the order of operation. Without parentheses, the HP 39G/40G calculates according to the order of algebraic precedence (the next topic). Following are some examples using parentheses. Algebraic precedence order of evaluation Entering... Calculates...
Clearing numbers Using previous results • >'(/@ clears the character under the cursor. When the cursor is positioned after the last character, >'(/@ deletes the character to the left of the cursor, that is, it performs the same as a backspace key. • CANCEL (>21@) • >6+,)7@CLEAR clears all input and output in the display, including the display history. clears the edit line. The HOME display (>+20(@) shows you four lines of input/ output history.
See how >6+,)7@ANS retrieves and reuses the last result (50), and >(17(5@ updates ANS (from 50 to 75 to 100). Example 50>(17(5@ > @ 25 >(17(5@>(17(5@ You can use the last result as the first expression in the edit line without pressing >6+,)7@ANS. Pressing > @, > @, >;@, or >j@, (or other operators that require a preceding argument) automatically enters ANS before the operator.
Storing a value in a variable You can save an answer in a variable and use the variable in later calculations. There are 27 variables available for storing real values. These are A to Z and θ. See Chapter 11, “Variables and memory management” for more information on variables. For example: 1. Perform a calculation. 45> @8 >[8@3 >(17(5@ 2. Store the result in the A variable. 672a?a >$/3+$@A >(17(5@ 3. Perform another calculation using the A variable.
Clearing the display history It’s a good habit to clear the display history (>6+,)7@CLEAR) whenever you have finished 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. Using fractions To work with fractions in HOME, you set the number format to Fractions, as follows: Setting Fraction mode 1. In HOME, open the HOME MODES input form. >6+,)7@MODES 2.
Setting fraction precision The fraction precision setting determines the precision in which the HP 39G/40G converts a decimal value to a fraction. The greater the precision value that is set, the closer the fraction is to the decimal value. By choosing a precision of 1 you are saying that the fraction only has to match 0.234 to at least 1 decimal place (3/13 is 0.23076...). The fractions used are found using the technique of continued fractions. When converting recurring decimals this can be important.
Fraction calculations When entering fractions: • You use the >j@ key to separate the numerator part and the denominator part of the fraction. • To enter a mixed fraction, for example, 11/2, you enter it in the format (1+1/2). For example, to perform the following calculation: 3(23/4 + 57/8) 1. Set the mode Number format to fraction. >6+,)7@MODES *e, &+226a Select Fraction >(17(5@*A,4 2.a 2. Return to HOME and enter the calculation. 3>;@> @> @2> @3 >j@4> @> @> @5> @7 >j@8> @> @ 3.
Converting a number to a fraction When converting a number to a fraction, keep the following points in mind: • When converting a recurring decimal to a fraction, set the fraction precision to about 6, and ensure that you include more than six decimal places in the recurring decimal that you enter. In this example, the fraction precision is set to 6. The top calculation returns the correct result. The bottom one does not.
Storing complex numbers There are 10 variables available for storing complex numbers: Z0 to Z9. To store a complex number in a variable: • Enter the complex number, press 672a?a, enter the variable to store the number in and press >(17(5@. > @4> @5> @ 672a?_ >$/3+$@Z 0 >(17(5@ Catalogs and editors The HP 39G/40G has several catalogs and editors. You use them to create and manipulate objects. They access features and stored values (numbers or text or other items) that are independent of aplets.
Differences between the HP 38G and the HP 39G/40G CAS The HP 40G is packaged with a computer algebra system (CAS). Refer to the CAS Manual for further information. Memory manager The HP 39G/40G incorporates a memory manager that you can use to see how much memory the objects that you have created or loaded are occupying. See “Memory Manager” on page 11-9 for more information.
2 Aplets and their views Aplet views This section examines the options and functionality of the three main views for the Function, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views. About the Symbolic view The Symbolic view is the defining view for the Function, Parametric, Polar, and Sequence aplets. The other views are derived from the symbolic expression. You can create up to 10 different definitions for each Function, Parametric, Polar, and Sequence aplet.
2-2 – For a Function definition, enter an expression to define F(X). The only independent variable in the expression is X. – For a Parametric definition, enter a pair of expressions to define X(T) and Y(T). The only independent variable in the expressions is T. – For a Polar definition, enter an expression to define R(θ). The only independent variable in the expression is θ. – For a Sequence definition, either: Enter the first and second terms for U (U1, or...U9, or U0).
Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specific value. To evaluate a function in Symbolic view, press (9$/_. If a function calls another function, then (9$/_ resolves all references to other functions in terms of their independent variable. 1. Choose the Function aplet. >$3/(7@ Select Function 67$57_ 2. Enter the expressions in the Function aplet’s Symbolic view. >$/3+$@A >;@ _;__ >[ @ __2.__ >$/3+$@B __2.
SYMB view keys The following table details the menu keys that you use to work with the Symbolic view. Key Meaning (',7_ Copies the highlighted expression to the edit line for editing. Press 2._ when done. _ &+._ Checks/unchecks the current expression (or set of expressions). Only checked expression(s) are evaluated in the Plot and Numeric views. __;___ Enters the independent variable in the Function aplet. Or, you can use the >; 7 5@ key on the keyboard.
About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press >3/27@. To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time. Select the expressions you want to be plotted together. Setting up the plot (Plot view setup) Press >6+,)7@SETUP-PLOT to define any of the settings shown in the next two tables. 1. Highlight the field to edit.
Field Meaning (Continued) NRNG Sequence aplet: Specifies the index (N) values for the graph. TSTEP For Parametric plots: the increment for the independent variable. θSTEP For Polar plots: the increment value for the independent variable. SEQPLOT For Sequence aplet: Stairstep or Cobweb types. XTICK Horizontal spacing for tickmarks. YTICK Vertical spacing for tickmarks. Those items with space for a checkmark are settings you can turn on or off. Press 3$*( _ to display the second page.
Exploring the graph Plot view gives you a selection of keys and menu keys to explore a graph further. The options vary from aplet to aplet. PLOT view keys The following table details the keys that you use to work with the graph. Key Meaning >6+,)7@CLEAR Erases the plot and axes. >9,(:6@ Offers additional pre-defined views for splitting the screen and for scaling (“zooming”) the axes. >6+,)7@*>, >6+,)7@*A, Moves cursor to far left or far right. *k, *e, Moves cursor between relations.
Trace a graph You can trace along a function using the *>, or *A, key which moves the cursor along the graph. The display also shows the current coordinate position (x, y) of the cursor. Trace mode and the coordinate display are automatically set when a plot is drawn. Note: Tracing might not appear to exactly follow your plot if the resolution (in Plot Setup view) is set to Faster. This is because RES: FASTER plots in only every other column, whereas tracing always uses every column.
Option Meaning (Continued) In Divides horizontal and vertical scales by the X-factor and Y-factor. For instance, if zoom factors are 4, then zooming in results in 1/4 as many units depicted per pixel. (see Set Factors) Out Multiplies horizontal and vertical scales by the X-factor and Y-factor (see Set Factors). X-Zoom In Divides horizontal scale only, using X–factor. X-Zoom Out Multiplies horizontal scale, using X–factor. Y-Zoom In Divides vertical scale only, using Y–factor.
ZOOM examples Option Meaning (Continued) Integer Rescales horizontal axis only, making each pixel =1 unit. (Not available in Sequence or Statistics aplets.) Trig Rescales horizontal axis so 1 pixel = π/24 radian, 7.58, or 81/3 grads; rescales vertical axis so 1 pixel = 0.1 unit. (Not in Sequence or Statistics aplets.) Un-zoom Returns the display to the previous zoom, or if there has been only one zoom, un-zoom displays the graph with the original plot settings.
X-Zoom In: =220_ X-Zoom In 2._ Now un-zoom. X-Zoom Out: =220_ X-Zoom Out 2._ Now un-zoom. Y-Zoom In: =220_ Y-Zoom In 2._ Now un-zoom. Y-Zoom Out: =220_ Y-Zoom Out 2._ Zoom Square: =220_ Aplets and their views Square 2.
To box zoom The Box Zoom option lets you draw a box around the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle. 1. If necessary, press 0(18_ to turn on the menu-key labels. 2. Press =220_ and select %2;_. 3. Position the cursor on one corner of the rectangle. Press 2._. 4. Use the cursor keys (*e,, etc.) to drag to the opposite corner. 5. Press 2._ to zoom in on the boxed area. To set zoom factors 1. In the Plot view, press 0(18_. 2. Press =220_. 3.
Other views for scaling and splitting the graph The preset viewing options menu (>9,(:6@) contains options for drawing the plot using certain pre-defined configurations. This is a shortcut for changing Plot view settings. For instance, if you have defined a trigonometric function, then you could select Trig to plot your function on a trigonometric scale. It also contains split-screen options.
Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Press >9,(:6@. Select Plot-Detail and press 2._. The graph is plotted twice. You can now zoom in on the right side. 2. Press 0(18_ =220_, select the zoom method and press 2._ or >(17(5@. 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).
Overlay plots If you want to plot over an existing plot without erasing that plot, then use >9,(:6@ Overlay Plot instead of >3/27@. Note that tracing follows only the current functions from the current aplet. Decimal scaling Decimal scaling is the default scaling. If you have changed the scaling to Trig or Integer, you can change it back with Decimal. Integer scaling Integer scaling compresses the axes so that each pixel is 1 × 1 and the origin is near the screen center.
Setting up the table (numeric view setup) Press >6+,)7@NUM to define any of the table settings. Use the Numeric Setup input form to configure the table. 1. Highlight the field to edit. Use the arrow keys to move from field to field. – If there is a number to enter, type it in and press >(17(5@ or 2._. To modify an existing number, press (',7_. – If there is an option to choose, press &+226_, highlight your choice, and press >(17(5@ or 2._.
Exploring the table of numbers NUM view menu keys The following table details the menu keys that you use to work with the table of numbers. Key Meaning =220_ Displays ZOOM menu list. %,*_ Toggles between two character sizes. '()1_ Displays the defining function expression for the highlighted column. To cancel this display, press '() _. Zoom within a table Zooming redraws the table of numbers in greater or lesser detail.
The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4. HINT Automatic recalculation To jump to an independent variable value in the table, use the arrow keys to place the cursor in the independent variable column, then enter the value to jump to. You can enter any new value in the X column. When you press >(17(5@, the values for the dependent variables are recalculated, and the entire table is regenerated with the same interval between X values.
Clear data Press >6+,)7@CLEAR, <(6_ to erase the data from a table. “Build Your Own” menu keys Aplets and their views Key Meaning (',7_ Puts the highlighted independent value (X, T, θ, or N) into the edit line. Pressing >(17(5@ replaces this variable with its current value. ,16_ Inserts a row of zero values at the position of the highlight. Replace a zero by typing the number you want and pressing >(17(5@. 6257_ Sorts the independent variable values into ascending or descending order.
Example: plotting a circle Plot the circle, x2+ y2 = 9. First rearrange it to read 2 y = ± 9–x . To plot both the positive and negative y values, you need to define two equations as follows: y = 2 9 – x and y = – 9 – x 2 1. In the Function aplet, specify the functions. >$3/(7@ Select Function 67$57_ >6+,)7@√ > @ 9 > @>; 7 5@>; @> @>(17(5@ > @ >6+,)7@ √ > @ 9 > @>; 7 5@ >; @> @>(17(5@ 2. Reset the graph setup to the default settings. >6+,)7@SETUP-PLOT >6+,)7@CLEAR 3.
3 Function aplet About the Function aplet The Function aplet enables you to explore up to 10 real–valued, rectangular functions y in terms of x. For example y = 2x + 3 . Once you have defined a function you can: • create graphs to find roots, intercepts, slope, signed area, and extrema • create tables to evaluate functions at particular values. This chapter demonstrates the basic tools of the Function aplet by stepping you through an example.
Define the expressions 2. There are 10 function definition fields on the Function aplet’s Symbolic view screen. They are labeled F1(X) to F0(X). Highlight the function definition field you want to use, and enter an expression. (You can press >'(/@ to delete an existing line, or >6+,)7@CLEAR to clear all lines.) 1> @ >; 7 5@ >(17(5@ > @ >; 7 5@ > @ 3 > @ >; @ > @ 2 >(17(5@ Set up the plot You can change the scales of the x and y axes, graph resolution, and spacing of axis ticks. 3. Display plot settings.
Change the scale 6. You can change the scale to see more or less of your graphs. In this example, choose Auto Scale. (See “VIEWS menu options” on page 2-13 for a description of Auto Scale). >9,(:6@ Select Auto Scale 2.a Trace a graph 7. Trace the linear function. *>, 6 times Note: By default, the tracer is active. 8. Jump from the linear function to the quadratic function. *k, Analyse graph with FCN functions 9. Display the Plot view menu.
To find the greater of the two roots of the quadratic function 10. Find the greater of the two roots of the quadratic function. Note: Move the cursor to the graph of the quadratic equation by pressing the *k, or *e, key. Then move the cursor so that it is near x = – 1 by pressing the *A, or *>, key. Select Root )&1a 2.a The root value is displayed at the bottom of the screen. To find the intersection of the two functions 11. Find the intersection of the two functions. 0(18a )&1a *e, 2.a 12.
To find the slope of the quadratic function 13. Find the slope of the quadratic function at the intersection point. 0(18a )&1a Select Slope 2.a The slope value is displayed at the bottom of the screen. To find the signed area of the two functions 14. To find the area between the two functions in the range –2 ≤ x ≤ –1, first move the cursor to F1 ( x ) = 1 – x and select the signed area option. 0(18a )&1a Select Signed area 2.a 15. Move the cursor to x = – 1 by pressing the *A, or *>, key. 2.a 16.
18. Display the numerical value of the integral. 2.a Note: See “Shading area” on page 3-10 for another method of calculating area. To find the extremum of the quadratic 19. Move the cursor to the quadratic equation and find the extremum of the quadratic. *k, 0(18a )&1a Select Extremum 2.a The coordinates of the extremum are displayed at the bottom of the screen. HINT The Root and Extremum functions return one value only even if the function has more than one root or extremum.
22. Match the table settings to the pixel columns in the graph view. 3/27a 2.a Explore the table 23. Display a table of numeric values. To navigate around a table 24. Move to X = –5.9. To go directly to a value 25. Move directly to X = 10. To access the zoom options 26. Zoom in on X = 10 by a factor of 4. Note: NUMZOOM has a setting of 4. >180@ *e, 6 times 1 0 2.a In =220a 2.
To change font size 27. Display table numbers in large font. To display the symbolic definition of a column 28. Display the symbolic definition for the F1 column. %,*a *A, '()1a The symbolic definition of F1 is displayed at the bottom of the screen. Function aplet interactive analysis From the Plot view (>3/27@), you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Functionbased aplets).
Access FCN variables The FCN variables are contained in the VARS menu. To access FCN variables in HOME: >9$56@ $3/(7a Select Plot FCN *A, *k,or*e, to choose a variable 2.a To access FCN variable in the Function aplet’s Symbolic view: >9$56@ Select Plot FCN *A, *k,or*e, to choose a variable 2.a FCN functions Function aplet The FCN functions are: Function Description Root Select Root to find the root of the current function nearest the cursor.
Shading area Function Description (Continued) Signed area Select Signed area to find the numeric integral. (If there are two or more expressions checkmarked, then you will be asked to choose the second expression from a list that includes the x-axis.) Select a starting point, then move the cursor to selection ending point. The result is saved in a variable named AREA. Intersection Select Intersection to find the intersection of two graphs nearest the cursor.
Plotting a piecewise defined function example Suppose you wanted to graph the following piecewise defined function. x + 2 ;x ≤ – 1 f( x) = x2 ;– 1 < x ≤ 1 4 – x ;x ≥ 1 1. Open the Function aplet. >$3/(7@ Select Function 67$57a 2. Highlight the line you want to use, and enter the expression. (You can press >'(/@ to delete an existing line, or >6+,)7@CLEAR to clear all lines.
4 Parametric aplet About the Parametric aplet The Parametric aplet allows you to explore parametric equations. These are equations in which both x and y are defined as functions of t. They take the forms x = f ( t ) and y = g( t) . Getting started with the Parametric aplet The following example uses the parametric equations x ( t ) = 3 sin t y ( t ) = 3 cos t Note: This example will produce a circle. For this example to work, the angle measure must be set to degrees. Open the Parametric aplet 1.
Set angle measure 3. Set the angle measure to degrees. >6+,)7@ MODES &+226_ Select Degrees 2._ Set up the plot 4. Display the graphing options. >6+,)7@PLOT You can see the Plot Setup input form has two fields not included in the Function aplet, TRNG and TSTEP. TRNG specifies the range of t values. TSTEP specifies the step value between t values. 5. Set the TRNG and TSTEP so that t steps from 0° to 360° in 5° steps. *A, 360 2._ 5 2._ Plot the expression 6. Plot the expression. >3/27@ 7.
Overlay plot 8. Plot a triangle graph over the existing circle graph. >6+,)7@ PLOT *e, 120 2._ >9,(:6@ Select Overlay Plot 2._ 0(18_ 0(18_ A triangle is displayed rather than a circle (without changing the equation) because the changed value of TSTEP ensures that points being plotted are 120° apart instead of nearly continuous. You are able to explore the graph using trace, zoom, split screen, and scaling functionality available in the Function aplet.
5 Polar aplet Getting started with the polar aplet Open the Polar aplet 1. Open the Polar aplet. >$3/(7@ Select Polar 5(6(7a <(6a 67$57a Like the Function aplet, the Polar aplet opens in the Symbolic view. 2 Define the expression 2. Define the polar equation r = 2π cos ( θ ⁄ 2 ) cos ( θ ) . Specify plot settings 3. Specify the plot settings. In this example, we will use the default settings, except for the θRNG fields.
Explore the graph 5. Display the Plot view menu key labels. 0(18a The Plot view options available are the same as those found in the Function aplet. See “Exploring the graph” on page 2-7 for further information. Display the numbers 6. Display the table of values θ for and R1. >180@ The Numeric view options available are the same as those found in the Function aplet. See “Exploring the table of numbers” on page 2-18 for further information.
6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences. You can define a sequence named, for example, U1: • in terms of n • in terms of U1(n-1) • in terms of U1(n-2) • in terms of another sequence, for example, U2(n) • in any combination of the above. Getting started with the Sequence aplet The following example defines and then plots an expression in the Sequence aplet. Open the Sequence aplet 1. Open the Sequence aplet.
Define the expression 2. Define the Fibonacci sequence, in which each term (after the first two) is the sum of the preceding two terms: U 1 = 1 , U2 = 1 , U n = U n – 1 + U n – 2 for n > 3 . In the Symbolic view of the Sequence aplet, highlight the U1(1) field and begin defining your sequence. 1 >(17(5@ 1 >(17(5@ 8 _ >1 @_ > @ 8 _ >1 @_ Note: You can use the 1_, 8 _, and 8 _ menu keys to assist in the entry of equations. >(17(5@ Specify plot settings 3.
Plot the sequence 4. Plot the Fibonacci sequence. >3/27@ 5. In Plot Setup, set the SEQPLOT option to Cobweb. >6+,)7@SETUP-PLOT Select Cobweb &+226_ 2._ >3/27@ Display the table Sequence aplet 6. Display the table of numeric values for this example.
7 Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable. You define an equation or expression in the symbolic view, then supply values for all the variables except one in the numeric view. Solve works only with real numbers. Note the differences between an equation and an expression: • An equation contains an equals sign. Its solution is a value for the unknown variable that makes both sides have the same value.
Getting started with the Solve aplet Suppose you want to find the acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distance of 100 m. The equation to solve is: 2 2 v = u + 2ad Open the Solve aplet 1. Open the Solve aplet. >$3/(7@ Select Solve 67$57a The Solve aplet starts in the Symbolic view. Define the equation 2. Define the equation. >$/3+$@ V>; @ a >$/3+$@ U>; @ > @ 2>[@ >$/3+$@ A>[@ >$/3+$@ D >(17(5@ Note: You can use the equations.
Solve the unknown variable 5. Solve for the unknown variable (A). *e, *e, 62/9(a Therefore, the acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distance of 100 m is approximately 2.47 m/s2. Because the variable A in the equation is linear, once values are substituted into V, U and D, we know that we need not look for any other solutions. Plot the equation The Plot view shows one graph for each member of the selected equation.
7. Trace along the graph representing the left member of the equation until the cursor nears the intersection. *A, ≈20 times Note the value of A displayed near the bottom left corner of the screen. The Plot view provides a convenient way to find an approximation to a solution before using the Numeric view Solve option. See “Plotting to find guesses” on page 7-8 for more information.
Use an initial guess You can usually obtain a faster and more accurate solution if you supply an estimated value for the unknown variable before pressing 62/9(a. Solve starts looking for a solution at the initial guess. Before plotting, make sure the unknown variable is highlighted in the numeric view. Plot the equation to help you select an initial guess when you don’t know the range in which to look for the solution. See “Plotting to find guesses” on page 7-8 for further information.
Interpreting results After Solve has returned a solution, press ,1)2a in the Numeric view for more information. You will see one of the following three messages. Press 2.a to clear the message. 7-6 Message 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.
If Solve could not find a solution, you will see one of the following two messages. Message Condition Bad Guess(es) The initial guess lies outside the domain of the equation. Therefore, the solution was not a real number or it caused an error. Constant? The value of the equation is the same at every point sampled. HINT It is important to check the information relating to the solve process.
Plotting to find guesses The main reason for plotting in the Solve aplet is to help you find initial guesses and solutions for those equations that have difficult-to-find or multiple solutions. Consider the equation of motion for an accelerating body: 2 at x = v 0 t + ------2 where x is distance, v0 is initial velocity, t is time, and a is acceleration. This is actually two equations, y = x and y = v0 t + (at2) / 2.
3. Use the Plot view to find an initial guess for T. First set appropriate X and Y ranges in the Plot Setup. Since we 2 have an equation, X = V × T + A × T ⁄ 2 , the plot will produce two graphs: one for Y = X and one for 2 Y = V × T + A × T ⁄ 2 . Since we have set X = 30 in this example, one of the graphs will be Y = 30 . Therefore, make the YRNG –5 to 35. Keep the XRNG default of –6.5 to 6.5. >6+,)7@SETUP-PLOT *e,> @5 >(17(5@ 35 >(17(5@ 4. Plot the graph. >3/27@ 5.
8. Use this equation to solve for another variable, such as velocity. How fast must a body’s initial velocity be in order for it to travel 50 m within 3 seconds? Assume the same acceleration, 4 m/s2. Leave the last value of V as an initial guess. 3>(17(5@*k,*k,*k, 50 >(17(5@ 62/9(a Using variables in equations You can use any of the real variable names, A to Z and θ. Do not use variable names defined for other types, such as M1 (a matrix variable).
8 Statistics aplet About the Statistics aplet The Statistics aplet can store up to ten separate data sets at one time. It can do one-variable or two-variable statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data. The Symbolic view is used to specify which columns contain data and which column contains frequencies. You can also compute statistics values in HOME and recall the values of specific statistics variables.
Open the Statistics aplet 1. Open the Statistics aplet and clear existing data by pressing 5(6(7_. >$3/(7@ Select Statistics 5(6(7_ <(6_ 67$57_ The Statistics aplet starts in the Numerical view. 1VAR/2VAR menu key label At any time the Statistics aplet is configured for only one of two types of statistical explorations: one-variable ( 9$5 _) or twovariable ( 9$5 _). The 5th menu key label in the Numeric view toggles between these two options and shows the current option. 2. Select 9$5 _.
Choose fit and data columns 4. Select a fit in the Symbolic setup view. >6+,)7@ SETUP-SYMB *e, &+226_ Select Linear 2._ You can define up to five explorations of two-variable data, named S1 to S5. In this example, we will create just one: S1. 5. Specify the columns that hold the data you want to analyze. >6<0%@ You could have entered your data into columns other than C1 and C2. Explore statistics 6. Find the mean advertising time (MEANX) and the mean sales (MEANY). >180@ 67$76_ MEANX is about 3.
Plot the graph 9. Plot the graph. >3/27@ Draw the regression curve 10. Draw the regression curve (a curve to fit the data points). 0(18_ ),7_ This draws the regression line for the best linear fit. Display the equation for best linear fit 11. Return to the Symbolic view. >6<0%@ 12. Display the equation for the best linear fit. *e, to move to the FIT1 field 6+2:_ The full FIT1 expression is shown. The slope (m) is 425.875. The y-intercept (b) is about 376.25.
Predict values 13. To find the predicted sales figure if advertising were to go up to 6 minutes: >+20(@ >0$7+@ S (to highlight Stat-Two) *A,*e, (to highlight PREDY) 2._ 6 >(17(5@ 2._ 14. Return to the Plot view. >3/27@ 15. Jump to the indicated point on the regression line. *e, *272_ 6 2._ Observe the predicted yvalue in the left bottom corner of the screen. Entering and editing statistical data The Numeric view (>180@) is used to enter data into the Statistics aplet.
Statistics aplet’s NUM view keys The Statistics aplet’s Numeric view keys are: Key Meaning (',7_ Copies the highlighted item into the edit line. ,16_ Inserts a zero value above the highlighted cell. 6257_ Sorts the specified independent data column in ascending or descending order, and rearranges a specified dependent (or frequency) data column accordingly. %,*_ Switches between larger and smaller font sizes.
Example You are measuring the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 170cm, 175cm, 180cm. 1. Open the Statistics aplet. >$3/(7@ Select Statistics 5(6(7_ <(6_ 67$57_ 2. Enter the measurement data. 160 >(17(5@ 165 >(17(5@ 170 >(17(5@ 175 >(17(5@ 180 >(17(5@ 3. Find the mean of the sample. Ensure the 9$5_ / 9$5_ menu key label reads 9$5 _. Press 67$76_ to see the statistics calculated from the sample data in C1.
4. Press 2._ to close the statistics window and press >6<0%@ key to see the data set definitions. The first column indicates the associated column of data for each data set definition, and the second column indicates the constant frequency, or the column that holds the frequencies. The keys you can use from this window are: Key Meaning (',7_ Copies the column variable (or variable expression) to the edit line for editing. Press 2._ when done. _ &+._ Checks/unchecks the current data set.
Key Meaning (Continued) >6+,)7@CLEAR Resets default specifications for the data sets or clears the edit line (if it was active). Note: If >6+,)7@CLEAR is used the data sets will need to be selected again before re-use. To continue our example, suppose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded.
8. Display the computed statistics. 67$76_ You can scroll down to the mean. The mean height is approximately 167.63cm. 9. Setup a histogram plot for the data. 2._ >6+,)7@SETUP-PLOT Enter set up information appropriate to your data. 10. Plot a histogram of the data. >3/27@ Angle Setting You can ignore the angle measurement mode unless your Fit definition (in Symbolic view) involves a trigonometric function.
Insert data Highlight the entry following the point of insertion. Press ,16_, then enter a number. It will write over the zero that was inserted. Sort data values 1. In Numeric view, highlight the column you want to sort, and press 6257_. 2. Select the SORT ORDER option. You can choose either Ascending or Descending. 3. Specify the INDEPENDENT and DEPENDENT data columns. Sorting is by the independent column.
Fit models Eight fit models are available: Fit model Meaning Linear (Default.) Fits the data to a straight line, y = mx+b. Uses a least-squares fit. Logarithmic Fits to a logarithmic curve, y = m lnx + b. Exponential Fits to an exponential curve, y = bemx. Power Fits to a power curve, y = bxm. Quadratic Fits to a quadratic curve, y = ax2+bx+c. Needs at least three points. Cubic Fits to a cubic curve, y = ax3+bx2+cx+d. Needs at least four points.
Computed statistics One-variable Statistic Definition NΣ Number of data points. TOTΣ Sum of data values (with their frequencies). MEANΣ Mean value of data set. PVARΣ Population variance of data set. SVARΣ Sample variance of data set. PSDEV Population standard deviation of data set. SSDEV Sample standard deviation of data set. MINΣ Minimum data value in data set. Q1 First quartile: median of ordinals to left of median. MEDIAN Median value of data set.
Two-variable 8-14 Statistic Definition MEANX Mean of x- (independent) values. ΣX Sum of x-values. ΣX2 Sum of x2-values. MEANY Mean of y- (dependent) values. ΣY Sum of y-values. ΣY2 Sum of y2-values. ΣXY Sum of each xy. SCOV Sample covariance of independent and dependent data columns. PCOV Population covariance of independent and dependent data columns CORR Correlation coefficient of the independent and dependent data columns for a linear fit only (regardless of the Fit chosen).
Plotting You can plot: • histograms ( 9$5 _) • box-and-whisker plots ( 9$5 _) • scatter plots of data ( 9$5 _). Once you have entered your data (>180@), defined your data set (>6<0%@), and defined your Fit model for two-variable statistics (>6+,)7@SETUP-SYMB), you can plot your data. You can select up to five scatter or box-and-whisker plots at a time. You can plot only one histogram at a time. To plot statistical data 1. In Symbolic view (>6<0%@), select (_ &+._) the data sets you want to plot. 2.
Plot types Histogram One-variable statistics. The numbers below the plot mean that the current bar (where the cursor is) starts at 0 and ends at 2 (not including 2), and the frequency for this column, (that is, the number of data elements that fall between 0 and 2) is 1. You can see information about the next bar by pressing the *A, key. Box and Whisker Plot One-variable statistics. The left whisker marks the minimum data value. The box marks the first quartile, the median, and the third quartile.
Fitting a curve to 2VAR data In the Plot view, press ),7_. This draws a curve to fit the checked two-variable data set(s). See “To choose the fit” on page 8-11. >3/27@ 0(18_ ),7_ >6<0%@ 6+2:_ The expression in Fit2 shows that the slope=1.98082191781 and the y-intercept=2.2657. Correlation coefficient The correlation coefficient is stored in the CORR variable. It is a measure of fit to a linear curve only. Regardless of the Fit model you have chosen, CORR relates to the linear model.
Setting up the plot (Plot setup view) The Plot Setup view (>6+,)7@SETUP-PLOT) sets most of the same plotting parameters as it does for the other built-in aplets. See “Setting up the plot (Plot view setup)” on page 2-5. Settings unique to the Statistics aplet are as follows: Plot type (1VAR) STATPLOT enables you to specify either a histogram or a box-and-whisker plot for one-variable statistics (when 9$5 is set).
Trouble-shooting a plot If you have problems plotting, check that you have the following: Statistics aplet • The correct 9$5 _ or 9$5 _ menu label on (Numeric view). • The correct fit (regression model), if the data set is twovariable. • Only the data sets to compute or plot are checkmarked (Symbolic view). • The correct plotting range.
Exploring the graph The Plot view has menu keys for zooming, tracing, and coordinate display. There are also scaling options under >9,(:6@. These options are described in“Exploring the graph” on page 2-7. Statistics aplet’s PLOT view keys 8-20 Key Meaning >6+,)7@CLEAR Erases the plot. >9,(:6@ Offers additional pre-defined views for splitting the screen, overlaying plots, and autoscaling the axes. >6+,)7@*>, >6+,)7@*A, Moves cursor to far left or far right. =220_ Displays ZOOM menu.
Calculating predicted values The functions PREDX and PREDY 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. Find predicted values 1. In Plot view, draw the regression curve for the data set. 2. Press *e, to move to the regression curve. 3. Press *272_ and enter the value of X.
9 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hypothesis tests based on the Normal Z–distribution or Student’s t–distribution.
Getting started with the Inference aplet This example describes the Inference aplet’s options and functionality by stepping you through an example using the example data for the Z–Test on 1 mean. Open the Inference aplet 1. Open the Inference aplet. >$3/(7@ Select Inferential 67$57a. The Inference aplet opens in the Symbolic view. Inference aplet’s SYMB view keys The table below summarizes the options available in Symbolic view.
If you choose one of the hypothesis tests, you can choose the alternative hypothesis to test against the null hypothesis. For each test, there are three possible choices for an alternative hypothesis based on a quantitative comparison of two quantities. The null hypothesis is always that the two quantities are equal.Thus, the alternative hypotheses cover the various cases for the two quantities being unequal: <, >, and ≠.
Enter data 4. Enter the sample statistics and population parameters that define the chosen test or interval. >6+,)7@SETUP-NUM The table below lists the fields in this view for our current Z–Test: 1 µ example. Field name Definition µ0 Assumed population mean σ Population standard deviation x Sample mean n Sample size α Alpha level for the test By default, each field already contains a value. These values constitute the example database and are explained in the +(/3a feature of this aplet.
Plot test results 8. Display a graphic view of the test results. >3/27@ Horizontal axes are presented for both the distribution variable and the test statistic. A generic bell curve represents the probability distribution function. Vertical lines mark the critical value(s) of the test, as well as the value of the test statistic. The rejection region is marked R and the test numeric results are displayed between the horizontal axes.
Enter data 2. In the C1 column, enter the random numbers produced by the calculator. > @529 >(17(5@ > @295 >(17(5@ > @952 >(17(5@ > @259 >(17(5@ > @925 >(17(5@ > @592 >(17(5@ HINT If the Decimal Mark setting in the Modes input form (>6+,)7@MODES) is set to Comma, use > @ instead of > @. 3. If necessary, select 1–variable statistics. Do this by pressing the fifth menu key until 9$5a a is displayed as its menu label. Calculate statistics 4. Calculate statistics. 67$76a The mean of 0.
Choose inference method and type 7. Choose an inference method. &+226a Select CONF INTERVAL 2.a 8. Choose a distribution statistic type. *e, &+226a Select T-Int: 1 µ 2.a Set up the interval calculation 9. Set up the interval calculation. Note: The default values are sample data from the on-line help example. Import the data 10. Import the data from the Statistics aplet. Note: The data from C1 is displayed by default.
11. Specify a 90% confidence interval in the C: field. *e,*e,*e, to move to the C: field 0.9 >(17(5@ Display Numeric view 12. Display the confidence interval in the Numeric view. Note: The interval setting is 0.5. >180@ Display Plot view 13. Display the confidence interval in the Plot view. >3/27@ You can see, from the second text row, that the mean is contained within the 90% confidence interval (CI) of 0.3469814 to 0.8370186. Note: The graph is a simple, generic bell-curve.
Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are based on statistics of samples of the populations. The HP 39G/40G hypothesis tests use the Normal Z–distribution or Student’s t-distribution to calculate probabilities.
Results The results are: Result Description Test Z Z–test statistic. Prob Probability associated with the Z–Test statistic. Critical Z Boundary values of Z associated with the α level that you supplied. Critical x Boundary values of x required by the α value that you supplied. Two–Sample Z–Test Menu name Z–Test: µ1–µ2 On the basis of two samples, each from a separate population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Results The results are: Result Description Test Z Z–Test statistic Prob Probability associated with the Z–Test statistic. Critical Z Boundary value of Z associated with the α level that you supplied. One–Proportion Z–Test Menu name Z–Test: 1P On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the proportion of successes in the two populations is equal.
Results The results are: Result Description Test P Proportion of successes in the sample. Test Z Z–Test statistic. Prob Probability associated with the Z–Test statistic. Critical Z Boundary value of Z associated with the level you supplied. Two–Proportion Z–Test Menu name Z–Test: P1–P2 On the basis of statistics from two samples, each from a different population, the 2 proportion Z–Test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Results The results are: Result Description Test P1–P2 Difference between the proportions of successes in the two samples. Test Z Z–Test statistic. Prob Probability associated with the Z–Test statistic. Critical Z Boundary values of Z associated with the α level that you supplied. One–Sample T–Test Menu name T–Test: 1 µ The One–sample T–Test is used when the population standard deviation is not known.
Results The results are: Result Description Test T T–Test statistic. Prob Probability associated with the T–Test statistic. Critical T Boundary value of T associated with the α level that you supplied. Critical x Boundary value of x required by the α value that you supplied. Two–Sample T–Test Menu name T–Test: µ1 – µ2 The Two–sample T–Test is used when the population standard deviation is not known.
Inputs Results Inference aplet The inputs are: Field name Definition x1 Sample 1 mean. x2 Sample 2 mean. S1 Sample 1 standard deviation. S2 Sample 2 standard deviation. n1 Sample 1 size. n2 Sample 2 size. α Significance level. _Pooled? Check this option to pool samples based on their standard deviations. The results are: Result Description Test T T–Test statistic. Prob Probability associated with the T–Test statistic.
Confidence intervals The confidence interval calculations that the HP 39G/40G can perform are based on the Normal Z–distribution or Student’s t–distribution. One–Sample Z–Interval Menu name Z–INT: 1 µ This option uses the Normal Z–distribution to calculate a confidence interval for µ, the true mean of a population, when the true population standard deviation, σ, is known. Inputs Results 9-16 The inputs are: Field name Definition x Sample mean. σ Population standard deviation. n Sample size.
Two–Sample Z–Interval Menu name Z–INT: µ1– µ2 This option uses the Normal Z–distribution to calculate a confidence interval for the difference between the means of two populations, µ1 – µ2, when the population standard deviations, σ1 and σ2, are known. Inputs Results Inference aplet The inputs are: Field name Definition x1 Sample 1 mean. x2 Sample 2 mean. n1 Sample 1 size. n2 Sample 2 size. σ1 Population 1 standard deviation. σ2 Population 2 standard deviation. C Confidence level.
One–Proportion Z–Interval Menu name Z–INT: 1 P This option uses the Normal Z–distribution to calculate a confidence interval for the proportion of successes in a population for the case in which a sample of size, n, has a number of successes, x. Inputs Results 9-18 The inputs are: Field name Definition x Sample success count. n Sample size. C Confidence level. The results are: Result Description Critical Z Critical value for Z. π Min Lower bound for π. π Max Upper bound for π.
Two–Proportion Z–Interval Menu name Z–INT: P1 – P2 This option uses the Normal Z–distribution to calculate a confidence interval for the difference between the proportions of successes in two populations. Inputs Results Inference aplet The inputs are: Field name Definition x1 Sample 1 success count. x2 Sample 2 success count. n1 Sample 1 size. n2 Sample 2 size. C Confidence level. The results are: Result Description Critical Z Critical value for Z.
One–Sample T–Interval Menu name T–INT: 1 µ This option uses the Student’s t–distribution to calculate a confidence interval for µ, the true mean of a population, for the case in which the true population standard deviation, σ, is unknown. Inputs Results 9-20 The inputs are: Field name Definition x Sample mean. Sx Sample standard deviation. n Sample size. C Confidence level. The results are: Result Description Critical T Critical value for T. µ Min Lower bound for µ.
Two–Sample T–Interval Menu name T–INT: µ1 – µ2 This option uses the Student’s t–distribution to calculate a confidence interval for the difference between the means of two populations, µ1 − µ2, when the population standard deviations, σ1and σ2, are unknown. Inputs Results Inference aplet The inputs are: Field name Definition x1 Sample 1 mean. x2 Sample 2 mean. s1 Sample 1 standard deviation. s2 Sample 2 standard deviation. n1 Sample 1 size. n2 Sample 2 size. C Confidence level.
10 Using mathematical functions Math functions The HP 39G/40G contains many math functions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob. on the MATH menu) contains functions for working with probability. To use a math function, you enter the function onto the command line, and include the arguments in parentheses after the function. You can also select a math function from the MATH menu.
To select a function 1. Press >0$7+@ to display the MATH menu. The categories appear in alphabetical order. Press *e, or *k, to scroll through the categories. To skip directly to a category, press the first letter of the category’s name. Note: You do not need to press >$/3+$@ first. 2. The list of functions (on the right) applies to the currently highlighted category (on the left). Use *A, and *>, to switch between the category list and the function list. 3.
Math functions by category Following are definitions for all categories of functions except List, Matrix, and Statistics, each of which appears in its own chapter. Except for the keyboard operations, which do not appear in the MATH menu, all other functions are listed by their category in the MATH menu. Syntax Each function’s definition includes its syntax, that is, the exact order and spelling of a function’s name, its delimiters (punctuation), and its arguments.
Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. > @,> @,>[@,> @ Add, Subtract, Multiply, Divide. Also accepts complex numbers, lists and matrices. value1+ value2, etc. >6+,)7@ex Natural exponential. Also accepts complex numbers. e^value Example e^5 returns 148.413159103 >OQ@ Natural logarithm. Also accepts complex numbers.
>6+,)7@ASIN Arc sine: sin–1x. Output range is from –90° to 90°, –π/2 to π/2, or –100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. ASIN(value) Example ASIN(1) returns 90 (Degrees mode). >6+,)7@ACOS Arc cosine: cos–1x. Output range is from 0° to 180°, 0 to π, or 0 to 200 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. Output will be complex for values outside the normal COS domain of –1 ≤ x ≤ 1 .
*;N, Power (x raised to y). Also accepts complex numbers. value^power Example 2^8 returns 256 >6+,)7@ABS Absolute value. For a complex number, this is 2 2 x +y . ABS(value) ABS((x,y)) Example ABS(–1) returns 1 ABS((1,2)) returns 2.2360679775 >6+,)7@ n Takes the nth root of x.
Calculus functions The symbols for differentiation and integration are available directly form the keyboard—>G G[@ and ) respectively—as well as from the MATH menu. % Differentiates expression with respect to the variable of differentiation. From the command line, use a formal name (S1, etc.) for a non-numeric result. See “Finding derivatives” on page 10-23.
Complex number functions 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. ARG Argument. Finds the angle defined by a complex number. Inputs and outputs use the current angle format set in Modes. ARG((x,y)) Example ARG((3,3)) returns 45 (Degrees mode) CONJ Complex conjugate.
Constants The HP 39G/40G has an internal numeric representation for these constants. e Natural logarithm base. Internally represented as 2.71828182846. e i Imaginary value for √−1 , the complex number (0,1). i MAXREAL Maximum real number. Internally represented as 9.99999999999 x 10499. MAXREAL MINREAL Minimum real number. Internally represented as 1 × 10 – 499 . MINREAL π Internally represented as 3.14159265359.
ALOG Antilogarithm (exponential). This is more accurate than 10^x due to limitations of the power function. ALOG(value) EXP x Natural exponential. This is more accurate than e due to limitations of the power function. EXP(value) EXPM1 Exponent minus 1 : ex–1. This is more accurate than EXP when x is close to zero. EXPM1(value) LNP1 Natural log plus 1 : ln(x+1). This is more accurate than the natural logarithm function when x is close to zero.
Loop functions The loop functions display a result after evaluating an expression a given number of times. ITERATE Repeatedly for #times evaluates an expression in terms of variable. The value for variable is updated each time, starting with initialvalue. ITERATE(expression,variable,initialvalue, #times) Example ITERATE(X2,X,2,3) returns 256 RECURSE Provides a method of defining a sequence without using the Symbolic view of the Sequence aplet.
Polynomial functions Polynomials are products of constants (coefficients) and variables raised to powers (terms). POLYCOEF Polynomial coefficients. Returns the coefficients of the polynomial with the specified roots. POLYCOEF ([roots]) Example To find the polynomial with roots 2, –3, 4, –5: POLYCOEF([2,-3,4,-5]) returns[1,2,-25, -26,120], representing x4+2x3–25x2–26x+120. POLYEVAL Polynomial evaluation. Evaluates a polynomial with the specified coefficients for the value of x.
HINT The results of POLYROOT will often not be easily seen in HOME due to the number of decimal places, especially if they are complex numbers. It is better to store the results of POLYROOT to a matrix. For example, POLYROOT([1,0,0,-8] 672?_ M1 will store the three complex cube roots of 8 to matrix M1 as a complex vector. Then you can see them easily by going to the Matrix Catalog. and access them individually in calculations by referring to M1(1), M1(2) etc.
HINT UTPC The setting of Time will be different for each calculator, so using RANDSEED(Time) is guaranteed to produce a set of numbers which are as close to random as possible. You can set the seed using the command RANDSEED. Upper-Tail Chi-Squared Probability given degrees of freedom, evaluated at value. Returns the probability that a χ2 random variable is greater than value.
Real-number functions Some real-number functions can also take complex arguments. CEILING Smallest integer greater than or equal to value. CEILING(value) Examples CEILING(3.2) returns 4 CEILING(-3.2) returns -3 DEG→RAD Degrees to radians. Converts value from Degrees angle format to Radians angle format. DEG→RAD(value) Example DEG→RAD(180) returns 3.14159265359, the value of π. FLOOR Greatest integer less than or equal to value. FLOOR(value) Example FLOOR(-3.
HMS→ Hours-minutes-seconds to decimal. Converts a number or expression in H.MMSSs format (time or angle that can include fractions of a second) to x.x format (number of hours or degrees with a decimal fraction). HMS→(H.MMSSs) Example HMS→(8.30) returns 8.5 →HMS Decimal to hours-minutes-seconds. Converts a number or expression in x.x format (number of hours or degrees with a decimal fraction) to H.MMSSs format (time or angle up to fractions of a second). →HMS(x.x) Example →HMS(8.5) returns 8.
MOD Modulo. The remainder of value1/value2. value1 MOD value2 Example 9 MOD 4 returns 1 % x percent of y; that is, x/100*y. %(x,y) Example %(20,50) returns 10 %CHANGE Percent change from x to y, that is, 100(y–x)/x. %CHANGE(x,y) Example %CHANGE(20,50) returns 150 %TOTAL Percent total : (100)y/x. What percentage of x is y. %TOTAL(x,y) Example %TOTAL(20,50) returns 250 RAD→DEG Radians to degrees. Converts value from radians to degrees.
SIGN Sign of value. If positive, the result is 1. If negative, –1. If zero, result is zero. For a complex number, this is the unit vector in the direction of the number. SIGN(value) SIGN((x,y)) Examples SIGN (–2) returns –1 SIGN((3,4)) returns (.6,.8) TRUNCATE Truncates value to decimal places. Accepts complex numbers. TRUNCATE(value,places) Example TRUNCATE(2.3678,2) returns 2.36 XPON Exponent of value. XPON(value) Example XPON(123.
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 | (where) in the CHARS menu (>6+,)7@CHARS) as well as the MATH menu. = (equals) Sets an equality for an equation. This is not a logical operator and does not store values. (See “Test functions” on page 1020.
QUOTE Encloses an expression that should not be evaluated numerically. QUOTE(expression) Examples QUOTE(SIN(45)) 672?_ F1(X) stores the expression SIN(45) rather than the value of SIN(45). Another method is to enclose the expression in single quotes. For example, X^3+2*X 672?_ F1(X) puts the expression X^3_2*X into F1(X) in the Function aplet. | (where) Evaluates expression where each given variable is set to the given value. Defines numeric evaluation of a symbolic expression.
AND Compares value1 and value2. Returns 1 if they are both nonzero, otherwise returns 0. value1 AND value2 IFTE If expression is true, do the trueclause; if not, do the falseclause. IFTE(expression,trueclause,falseclause) Example IFTE(X>0,X2,X3) NOT Returns 1 if value is zero, otherwise returns 0. NOT value OR Returns 1 if either value1 or value2 is non-zero, otherwise returns 0. value1 OR value2 XOR Exclusive OR.
Symbolic calculations The HP 39G/40G has the ability to perform symbolic calculations, for example, symbolic integration and differentiation. You can perform symbolic calculations in HOME and in the Function aplet. In HOME When you perform calculations that contain normal variables, the calculator substitutes values for any variables. For example, if you enter A+B on the command line and press >(17(5@, the calculator retrieves the values for A and B from memory and substitutes them in the calculation.
Finding derivatives The HP 39G/40G can perform symbolic differentiation on some functions. There are two ways of using the HP 39G/40G to find derivatives. To find derivatives in HOME • You can perform differentiations in HOME by using the formal variables, S1 to S5. • You can perform differentiations of functions of X in the Function aplet. To find the derivative of the function in HOME, use a formal variable in place of X.
To find derivatives in the Function aplet’s Symbolic view To find the derivative of the function in the Function aplet’s Symbolic view, you define two functions and define the second function as a derivative of the first function. For 2 example, to differentiate sin ( x ) + 2 cos x : 1. Access the Function aplet’s Symbolic view and define F1. >6<0%@>6,1@;_>[ @> @ > @2>;@ >&26@;_> @2._ 2. Define F2(X) as the derivative of F(1). >G G[@ ;_ > @>$/3+$@ F1> @ ;_ > @> @ 2._ 3. Select F2(X) and evaluate it.
To find the indefinite integral using formal variables For example, to find the indefinite integral of ∫ 3x 2 – 5 dx use: ∫ ( 0, S1, 3X 2 – 5, X ) 1. Enter the function. >6+,)7@>G G[@0> @ >$/3+$@S1 > @ 3 >[@ >$/3+$@X >[ @ > @ 5 > @ >$/3+$@X > @ >(17(5@ HINT If the Decimal Mark setting in the Modes input form (>6+,)7@MODES)is set to Comma, use > @ instead of > @. 2. Show the result format. *k, 6+2:_ 3. Press 2._ to close the show window. 4. Copy the result and evaluate.
The ‘extra’ constant of 6.4 results from the substitution of x = 0 into (x – 2)5/5, and should be disregarded if an indefinite integral is required.
11 Variables and memory management Introduction The HP 39G/40G has approximately 232K of user memory. The calculator uses this memory to store variables, perform computation, and store history. A variable is an object that you create in memory to hold data. The HP 39G/40G has two types of variables, home variables and aplet variables. • Home variables are available in all aplets. For example, you can store real numbers in variables A to Z and complex numbers in variables Z0 to Z9.
Storing and recalling variables You can store numbers or expressions from a previous input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12-digit mantissa with a 3-digit exponent. Numeric precision in the display, however, depends on the display mode (Standard, Fixed, Scientific, Engineering, or Fraction). A displayed number has only the precision that is displayed.
To store the results of a calculation If the value you want to store is in the HOME view display history, for example the results of a previous calculation, you need to copy it to the command line, then store it. 1. Perform the calculation for the result you want to store. 3>;@> @8>[@6> @>[8@3 >(17(5@ 2. Move the highlight to the result you wish to store. 3. Press &23$/3+$@ A 6.
To use variables in calculations You can use variables in calculations. The calculator substitutes the variable’s value in the calculation: 65 > @>$/3+$@A >(17(5@ The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organised by category. For each variable category in the left column, there is a list of variables in the right column. You select a variable category and then select a variable in the category. 1. Open the VARS menu. >9$56@ 2.
5. Choose whether to place the variable name or the variable value on the command line. – Press 9$/8(a to indicate that you want the variable’s contents to appear on the command line. – Press 1$0(a to indicate that you want the variable’s name to appear on the command line. 6. Press 2.a to place the value or name on the command line. The selected object appears on the command line. 2.a Note: The VARS menu can also be used to enter the names or values of variables into programs.
4. Enter data for L2. 55 2.a 48 2.a 86 2.a 90 2.a 77 2.a 5. Press >+20(@ to access HOME. 6. Open the variable menu and select L1. >9$56@ *e,*e,*e,*A, 7. Copy it to the command line. Note: Because the 1$0(a option is highlighted, the variable’s name, rather than its contents, is copied to the command line. 2.a 8. Insert the + operator and select the L2 variable from the List variables. > @>9$56@ *e,*e,*e,*A,*e,2.a 9. Store the answer in the List catalog L3 variable.
Home variables It is not possible to store data of one type in a variable of another type. For example, you use the Matrix catalog to create matrices. You can create up to ten matrices, and you can store these in variables M0 to M9. You cannot store matrices in variables other than M0 to M9. Category Available names Complex Z0 to Z9 For example, (1,2) 672?a Z0 or 2+3i 672?a Z1. You can enter a complex number by typing (r,i), where r represents the real part, and i represents the imaginary part.
Aplet variables To access an aplet variable Aplet variables store values that are unique to a particular aplet. These include symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections. See the Reference Information chapter for more information about aplet variables. Category Available names Function F0 to F9 (Symbolic view). See “Function aplet variables” on page R-9.
Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the Memory Manager to determine which aplets or variables consume large amounts of memory. You can make deletions to free up memory. Example 1. Start the Memory Manager. A list of variable categories is displayed.
12 Matrices Introduction You can perform 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. For example, the following matrix: 1 23 4 56 is displayed in the history as: [[1,2,3],[4,5,6]] (If the Decimal Mark in MODES is set to Comma, then the row separators are periods.) You can enter matrices directly in the command line, or create them in the matrix editor. Vectors Vectors are one-dimensional arrays.
Creating and storing matrices You can create, edit, delete, send, and receive matrices in the Matrix catalog. To open the Matrix catalog, press >6+,)7@ MATRIX. You can also create and store matrices—named or unnamed—-in HOME. For example, the command: POLYROOT([1,0,–1,0])&M1 stores the root of the complex vector of length 3 into the M1 variable.
To create a matrix in the matrix catalog 1. Press >6+,)7@MATRIX to open the Matrix catalog. The Matrix catalog lists the 10 available matrix variables, M0 to M9. 2. Highlight the matrix variable name you want to use and press 1(:_. 3. Select the type of matrix to create. – For a vector (one-dimensional array), select Real vector or Complex vector. Certain operations (+, -, CROSS) do not recognize a one-dimensional matrix as a vector, so this selection is important.
To transmit a matrix You can send matrices between calculators just as you can send aplets, programs, lists, and notes. 1. Align the HP 39G calculators’ infrared ports. 2. Open the Matrix catalogs on both calculators. 3. Highlight the matrix to send. 4. Press 6(1'_. 5. Press 5(&9_ on the receiving calculator. Matrices can also be transmitted to or from a computer a cable and Connectivity Kit.
To display a matrix • In the Matrix catalog (>6+,)7@MATRIX), highlight the matrix name and press (',7_. • In HOME, enter the name of the matrix variable and press >(17(5@. To display one element In HOME, enter matrixname(row,column). For example, if M2 is [[3,4],[5,6]], then M2(1,2) >(17(5@ returns 4. To create a matrix in HOME 1. Enter the matrix in the edit line. Start and end the matrix and each row with square brackets (the shifted > @ and > @ keys). 2.
Matrix arithmetic You can use the arithmetic functions (+, –, ×, / ) with matrix arguments. Division left–multiplies by the inverse of the divisor. 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 M1 and [[5,6],[7,8]] into M2. Example 1. Create the first matrix. >6+,)7@MATRIX 1(:_ 2._ 1 >(17(5@ 2 >(17(5@ *e, 3 >(17(5@ 4 >(17(5@ 2. Create the second matrix.
To multiply two matrices To multiply the two matrices M1 and M2 that you created for the previous example, use the following keystrokes: >$/3+$@M1>[@ >$/3+$@M2 >(17(5@ To multiply a matrix by a vector, enter the matrix first, then the vector. The number of elements in the vector must equal the number of columns in the matrix.
Solving systems of linear equations Example Solve the following linear system: 2x + 3y + 4z = 5 x+y–z = 7 4x – y + 2z = 1 1. Open the Matrix catalog and choose to create a vector in the M1 variable. >6+,)7@MATRIX 1(:_ *e,>(17(5@ 2. Create the vector of the constants in the linear system. 5 >(17(5@ 7 >(17(5@ 1 >(17(5@ 3. Return to the Matrix catalog. The vector you created is listed as M1. >6+,)7@MATRIX 4. Select the M2 variable and create a new matrix. *e,1(:_ Select Real matrix 2._ 5.
6. Return to HOME and enter the calculation to left multiply the constants vector by the inverse of the coefficients matrix. >+20(@>$/3+$@M2 >6+,)7@x –1 >[@ >$/3+$@M1 7. Evaluate the calculation. >(17(5@ The result is a vector of the solutions: • x = 2 • y = 3 • z = –2 An alternative method, is to use the RREF function. See “RREF” on page 12-12. Matrix functions and commands About functions Matrices • Functions can be used in any aplet or in HOME.
About commands Matrix commands are listed in the CMDS menu (>6+,)7@ CMDS), in the matrix category. See “Matrix commands” on page 15-23 for details of the matrix commands available for use in programming. Functions differ from commands in that a function can be used in an expression. Commands cannot be used in an expression.
EIGENVAL Displays the eigenvalues in vector form for matrix. EIGENVAL(matrix) EIGENVV Eigenvectors and Eigenvalues for a square matrix. Displays a list of two arrays. The first contains the eigenvectors and the second contains the eigenvalues. EIGENVV(matrix) IDENMAT Identity matrix. Creates a square matrix of dimension size × size whose diagonal elements are 1 and off-diagonal elements are zero. IDENMAT(size) INVERSE Inverts a square matrix (real or complex). INVERSE(matrix) LQ LQ Factorization.
QR QR Factorization. Factors an m×n matrix into three matrices: {[[m×m orthogonal]],[[m×n uppertrapezoidal]],[[n×n permutation]]}. QR(matrix) RANK Rank of a rectangular matrix. RANK(matrix) ROWNORM Row Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row. ROWNORM(matrix) RREF Reduced Row Echelon Form. Changes a rectangular matrix to its reduced row-echelon form. RREF(matrix) SCHUR Schur Decomposition. Factors a square matrix into two matrices.
TRACE Finds the trace of a square matrix. The trace is equal to the sum of the diagonal elements. (It is also equal to the sum of the eigenvalues.) TRACE(matrix) TRN Transposes matrix. For a complex matrix, TRN finds the conjugate transpose. TRN(matrix) Examples Identity Matrix You can create an identity matrix with the IDENMAT function. For example, IDENMAT(2) creates the 2×2 identity matrix [[1,0],[0,1]]. You can also create an identity matrix using the MAKEMAT (make matrix) function.
Reduced-Row Echelon Form The following set of equations x – 2y + 3z = 14 2x + y – z = – 3 4x – 2y + 2z = 14 1 – 2 3 14 can be written as the augmented matrix 2 1 – 1 – 3 4 – 2 2 14 which can then stored as a 3 × 4 real matrix in M1. You can use the RREF function to change this to reduced row echelon form, storing it as M2 for convenience. The reduced row echelon matrix gives the solution to the linear equation in the forth column.
13 Lists You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matrices, all enclosed in braces. A list may, for example, contain a sequence of real numbers such as {1,2,3}. (If the Decimal Mark in MODES is set to Comma, then the separators are periods.) Lists represent a convenient way to group related objects. There are ten list variables available, named L0 to L9.
3. Enter the values you want in the list, pressing >(17(5@ after each one. Values can be real or complex numbers (or an expression). If you enter a calculation, it is evaluated and the result is inserted in the list. 4. When done, press >6+,)7@LIST to see the List catalog, or press >+20(@ to return to HOME. List catalog keys 13-2 The list catalog keys are: Key Meaning (',7a Opens the highlighted list for editing. 6(1'a Transmits the highlighted list to another HP 39G/40G or a PC.
List edit keys Create a list in HOME When you press edit to create or change a list, the following keys are available to you: Key Meaning (',7a Copies the highlighted list item into the edit line. ,16a Inserts a new value before the highlighted item. >'(/@ Deletes the highlighted item from the list. >6+,)7@CLEAR Clears all elements from the list. >6+,)7@*e, or *k, Moves to the end or the beginning of the list. 1. Enter the list in the edit line.
Displaying and editing lists To display a list • In the List catalog, highlight the list name and press (',7a. • In HOME, enter the name of the list and press>(17(5@. To display one element In HOME, enter listname(element#). For example, if L2 is {3,4,5,6}, then L2(2) >(17(5@ returns 4. To edit a list 1. Open the List catalog. >6+,)7@LIST. 2. Press *k, or *e, to highlight the name of the list you want to edit (L1, etc.) and press (',7a to display the list contents. (',7a 3.
To insert an element in a list 1. Open the List catalog. >6+,)7@LIST. 2. Press *k, or *e, to highlight the name of the list you want to edit (L1, etc.) and press (',7a to display the list contents. (',7a 3. Press *k, or *e, to the insertion position. New elements are inserted above the highlighted position. In this example, an element, with the value of 9, is inserted between the first and second elements in the list. *e, ,16a 9 4. Press 2.a.
Deleting lists To delete a list In the List catalog, highlight the list name and press >'(/@. You are prompted if you want to delete the contents of the highlighted list variable. Press >(17(5@ to delete the contents. To delete all lists In the List catalog, press >6+,)7@CLEAR. Transmitting lists You can send lists to calculators or PCs just as you can aplets, programs, matrices, and notes. 1. Align the HP 39G calculators’ infrared ports. 2. Open the List catalogs on both calculators. 3.
List functions Following are details of list functions. You can 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 >0$7+@> @ (the alpha L character key). This displays the List category. Press *A,, select a function, and press 2.a. List functions have the following syntax: • Functions have arguments that are enclosed in parentheses and separated by commas. Example: CONCAT(L1,L2).
CONCAT Concatenates two lists into a new list. CONCAT(list1,list2) Example CONCAT({1,2,3},{4}) returns {1,2,3,4}. ∆LIST Creates a new list composed of the differences between the sequential elements in list1. The new list has one fewer elements than list1. The first differences for {x1 x2 ... xn} are {x2–x1 ... xn–xn–1}. ∆LIST(list1) Example In HOME, store {3,5,8,12,17,23} in L5 and find the first differences for the list.
ΠLIST Calculates the product of all elements in list. ΠLIST(list) Example ΠLIST({2,3,4}) returns 24. POS Returns the position of an element within a list. The element can be a value, a variable, or an expression. If there is more than one instance of the element, the position of the first occurrence is returned. A value of 0 is returned if there is no occurrence of the specified element.
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. Example In this example, use the Statistics aplet to find the mean, median, maximum and minimum values of the elements in the list, L1. 1. Create L1 with values 88, 90, 89, 65, 70, and 89.
4. In the Symbolic view, define H1 (for example) as C1 (sample) and 1 (frequency). Make sure that H1 is checkmarked. >6<0%@ 5. Go to the Numeric view to display calculated statistics. >180@67$76a See “One-variable” on page 8-13 for the meaning of each computed statistic.
14 Notes and sketches Introduction The HP 39G/40G has text and picture editors for entering notes and sketches. • Each aplet has its own independent Note view and Sketch view. Notes and sketches that you create in these views are associated with the aplet. When you save the aplet, or send it to another calculator, the notes and sketches are saved or sent as well. • The Notepad is a collection of notes independent of all aplets. These notes can also be sent to another calculator via the Notepad Catalog.
Note edit keys Key Meaning 63$&(_ Space key for text entry. 3$*( _ $ =_ Alpha-lock for letter entry. >6+,)7@$ =_ Lower-case Alpha-lock. %.63_ 14-2 Displays next page of a multi-page note. Backspaces cursor and deletes character. >'(/@ Deletes current character. >(17(5@ Starts a new line. >6+,)7@CLEAR Erases the entire note. >9$56@ Menu for entering variable names, and contents of variables. >0$7+@ Menu for entering math operations, and constants.
Aplet sketch view You can attach pictures to an aplet in its Sketch view (>6+,)7@SKETCH). Your work is automatically saved with the aplet. Press any other view key or >+20(@ to exit the Sketch view Sketch keys Key 672 Meaning Stores the specified portion of the current sketch to a graphics variable (G1 through G0). _ Adds a new, blank page to the current sketch set. 1(:3_ 3$*( To draw a line _ Displays next sketch in the sketch set. Animates if held down.
To draw a box 1. In Sketch view, press '5$:_ and move the cursor to where you want any corner of the box to be. 2. Press %2;_. This turns on box-drawing. 3. Move the cursor to mark the opposite corner for the box. You can adjust the size of the box by moving the cursor. 4. Press 2._ to finish the box. To draw a circle 1. In Sketch view, press '5$:_ and move the cursor to where you want the center of the circle to be. 2. Press &,5&/_. This turns on circle drawing. 3.
To label parts of a sketch 1. Press 7(;7_ and type the text in the edit line. To lock the Alpha shift on, press $ =_ (for uppercase) or >6+,)7@$ =_ (for lowercase). To make the label a smaller character size, turn off %,* _ before pressing $ =_. (%,*_ is a toggle between small and large font size). The smaller character size cannot display lowercase letters. 2. Press 2._. 3. Position the label where you want it by pressing the *k,, *e,,*A,,*>, keys. 4. Press 2._ again to affix the label. 5.
To import a graphics variable You can copy the contents of a graphics variable into the Sketch view of an aplet. 1. Open the Sketch view of the aplet (>6+,)7@SKETCH). The graphic will be copied here. 2. Press >9$56@, +20(_. Highlight Graphic, then press *A, and highlight the name of the variable (G1, etc.). 3. Press 9$/8(_ 2._ to recall the contents of the graphics variable. 4. Move the box to where you would like to copy the graphic, then press 2._.
4. Write your note. See “Note edit keys” on page 14-2 for more information on the entry and editing of notes. 5. When you are finished, press >+20(@ or an aplet key to exit Notepad. Your work is automatically saved. Notepad Catalog keys Notes and sketches Key Meaning (',7_ Opens the selected note for editing. 1(:_ Begins a new note, and asks for a name. 6(1'_ Transmits the selected note to another HP 39G/40G or PC. 5(&9_ Receives a note being transmitted from another HP 39G/40G or PC.
To import a note You can import a note from the Notepad into an aplet’s Note view, and vice-versa. Suppose you want to copy a note named “Assignments” from the Notepad into the Function Note view: 1. In the Function aplet, display the Note view (>6+,)7@NOTE). 2. Press >9$56@ +20(_, highlight Notepad in the left-hand list, then highlight the name “Assignments” in the righthand list. 3. Press 9$/8(_ 2._ to copy the contents of “Assignments” to the Function Note view.
15 Programming Introduction This chapter describes how to program using the HP 39G/ 40G. In this chapter you’ll learn about: HINT The Contents of a Program • using the Program catalog to create and edit programs • programming commands • storing and retrieving variables in programs • programming variables. More information on programming, including examples and special tools, can be found at HP’s calculators web site: www.hp.
Program catalog The Program catalog is where you create, edit, delete, send, receive, or run programs. This section describes how to Open Program catalog • open the Program catalog • create a new program • enter commands from the program commands menu • enter functions from the MATH menu • edit a program • run and debug a program • stop a program • copy a program • send and receive a program • delete a program or its contents • customize an aplet. 1. Press >6+,)7@PROGRM.
Program catalog keys The program catalog keys are: Programming Key Meaning (',7a Opens the highlighted program for editing. 1(:a Prompts for a new program name, then opens an empty program. 6(1'a Transmits the highlighted program to another HP 39G/40G or to a disk drive. 5(&9a Receives the highlighted program from another HP 39G/40G or from a disk drive. 581a Runs the highlighted program. >6+,)7@*k, or *e, Moves to the beginning or end of the Program catalog.
Creating and editing programs Create a new program 1. Press >6+,)7@PROGRM to open the Program catalog. 2. Press 1(:a. The HP 39G/40G prompts you for a name. A program name can contain special characters, such as a space. However, if you use special characters and then run the program by typing it in HOME, you must enclose the program name in double quotes (" "). Don’t use the " symbol within your program name. 3. Type your program name, then press 2.a. When you press 2.a, the Program Editor opens. 4.
Enter commands Until you become familiar with the HP 39G/40G commands, the easiest way to enter commands is to use the Commands menu from the Program editor. You can always type in commands using alpha characters. 1. From the Program editor, press >6+,)7@CMDS to open the Program Commands menu. >6+,)7@CMDS 2. On the left, use *e, or *k, to highlight a command category, then press *A, to access the commands in the category. Select the command that you want. *e,*e,*A,*e, 3. Press 2.
Editing keys The editing keys are: Key Meaning Inserts the 672?a character at the editing point. 672?a 63$&(a Inserts space into text. A3$*(a Displays previous page of the program. 3$*( Displays next page of the program. a *k,*e, Moves up or down one line. *A,*>, Moves right or left one character. $ =a %.63a Alpha-lock for letter entry. Press >6+,)7@ A...Z to lock lower case. Backspaces cursor and deletes character. >'(/@ Deletes current character. >(17(5@ Starts a new line.
Using programs Run a program From HOME, type RUN program_name. or From the Program catalog, highlight the program you want to run and press 581a. Regardless of where you start the program, all programs run in HOME. What you see will differ slightly depending on where you started the program. If you start the program from HOME, the HP 39G/40G displays the contents of Ans (Home variable containing the last result), when the program has finished.
Working with programs Copy a program You can use the following procedure if you want to make a copy of your work before editing—or if you want to use one program as a template for another. 1. Press >6+,)7@PROGRM to open the Program catalog. 2. Press 1(:a. 3. Type a new file name, then choose 2.a. The Program Editor opens with a new program. 4. Press >9$56@ to open the Variable menu. 5. Press > @ to quickly scroll to Program. 6. Press *A,, then highlight the program you want to copy. 7.
Delete all programs You can delete all programs at once. 1. In the Program catalog, press >6+,)7@CLEAR. 2. Press <(6a. Delete the contents of a program You can clear the contents of a program without deleting the program name. 1. Press >6+,)7@PROGRM to open the Program catalog. 2. Highlight a program, then press (',7a. 3. Press >6+,)7@CLEAR, then press <(6a. 4. The contents of the program are deleted, but the program name remains.
Aplet naming convention To assist users in keeping track of aplets and associated programs, use the following naming convention when setting up an aplet’s programs: • Start all program names with an abbreviation of the aplet name. We will use APL in this example. • Name programs called by menu entries in the VIEWS menu number, after the entry, for example: • – APL.ME1 for the program called by menu option 1 – APL.
3. Create a program called EXP.ME2 with contents as shown. This program sets the numeric view options for the aplet, and runs the program that you can use to configure the angle mode. 4. Create a program called EXP.ANG which the previous two programs call. 5. Create a program called EXP.S which runs when you start the aplet, as shown. This program sets the angle mode to degrees, and sets up the initial function that the aplet plots.
SETVIEWS ’’’’;;’’’’;18; Sets the first menu option to be "Auto scale". This is the fourth standard Function aplet view menu option and the 18 "Auto scale", specifies that it is to be included in the new menu. The empty quotes will ensure that the old name of "Auto scale" appears on the new menu. See “SETVIEWS” on page 15-14. ’’My Entry1’’;’’EXP.ME1’’;1; Sets the second menu option. This option runs program EXP.ME1, then returns to view 1, Plot view. ’’My Entry2’’;’’EXP.ME2’’;3; Sets the third menu option.
You only need to run this program once to configure your aplet’s VIEWS menu. Once the aplet’s VIEWS menu is configured, it remains that way until you run SETVIEWS again. You do not need to include this program for your aplet to work, but it is useful to specify that the program is attached to the aplet, and transmitted when the aplet is transmitted. 7. Return to the program catalog. The programs that you created should appear as follows: 8. You must now RUN the program EXP.
Programming commands This section describes the commands for programming with HP 39G/40G. You can enter these commands in your program by typing them or by accessing them from the 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.
• All the programs that are called from the VIEWS menu are transferred when the aplet is transferred, for example to another calculator or to a PC. • As part of the VIEWS menu configuration, you can specify programs that you want transferred with the aplet, but are not called as menu options. For example, these can be sub-programs that menu options use, or the program that defines the aplet’s VIEWS menu.
Auto-run programs If the Prompt item is “Start”, then the ProgramName program runs whenever you start the aplet. This is useful for setting up a program to configure the aplet. Users can select the Start item from the Views menu to reset the aplet if they change configurations. You can also define a menu item called “Reset” which is autorun if the user chooses the RESET button in the APLET view. ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected.
View numbers The views are numbered as follows: UNCHECK 0 HOME 11 List Catalog 1 Plot 12 Matrix Catalog 2 Symbolic 13 Notepad Catalog 3 Numeric 14 Programs Catalog 4 Plot-Setup 15 Plot-Detail 5 Symbolic-Setup 16 Plot-Table 6 Numeric-Setup 17 Overlay Plot 7 Views 18 Auto scale 8 Note 19 Decimal 9 Sketch view 20 Integer 10 Aplet Catalog 21 Trig Unchecks (unselects) the corresponding function in the current aplet.
IF... THEN... ELSE... END Executes the true-clause sequence of commands if the testclause is true, or the false-clause sequence of commands if the test-clause is false. IF test–clause THEN true-clause ELSE false-clause END Example 1&A : IF A==1 THEN MSGBOX A " EQUALS 1" : ELSE MSGBOX A " IS NOT EQUAL TO 1" : END CASE...END Executes a series of test-clause commands that execute the appropriate true-clause sequence of commands.
RUN Runs the named program. If your program name contains special characters, such as a space, then you must enclose the file name in double quotes (" "). RUN "program name" or RUN programname STOP Stops the current program. STOP 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 39G/40G default settings with the Function aplet as the current aplet.
FREEZE Halts the program, freezing the current display. Execution resumes when any key is pressed. LINE Draws a line from (x1, y1) to (x2, y2). LINE x1;y1;x2;y2 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 TLINE Toggles the pixels along the line from (x1, y1) to (x2, y2) on and off. Any pixel that was turned off, is turned on; any pixel that was turned on, is turned off.
→GROB Creates a graphic from expression, using font_size, and stores the resulting graphic in graphicname. Font sizes are 1, 2, or 3. If the fontsize argument is 0, the HP 39G/40G creates a graphic display like that created by the SHOW operation. →GROB graphicname;expression;fontsize GROBNOT Replaces graphic in graphicname with bitwise-inverted graphic. GROBNOT graphicname GROBOR Using the logical OR, superimposes graphicname2 onto graphicname1.
REPLACE Replaces portion of graphic in graphicname1 with graphicname2, starting at position. REPLACE also works for lists and matrices. REPLACE graphicname1;(position);graphicname2: SUB Extracts a portion of the named graphic (or list or matrix), and stores it in a new variable, name. The portion is specified by position and positions. SUB name;graphicname;(position);(positions): ZEROGROB Creates a blank graphic with given width and height, and stores it in graphicname.
FOR…TO…STEP ...END FOR name=start-expression TO end-expression [STEP increment]; loop-clause END FOR A=1 TO 12 STEP 1; DISP 3;A: END Note that the STEP parameter is optional. If it is omitted, a step value of 1 is assumed. BREAK Terminates loop. BREAK Matrix commands The matrix commands take variables M0–M9 as arguments. ADDCOL Add Column. Inserts values into a column before column_number in the specified matrix. You enter the values as a vector.
RANDMAT Creates random matrix with a specified number of rows and columns and stores the result in name (name must be M0...M9). The entries will be integers ranging from –9 to 9. RANDMAT name;rows;columns REDIM Redimensions the specified matrix or vector to size. For a matrix, size is a list of two integers {n1,n2}. For a vector, size is a list containing one integer {n}. REDIM name;size REPLACE Replaces portion of a matrix or vector stored in name with an object starting at position start.
Print commands These commands print to an HP infrared printer, for example the HP 82240B printer. Note: The HP 40G does not have an infrared port and will not print to an infrared printer. PRDISPLAY Prints the contents of the display. PRDISPLAY PRHISTORY Prints all objects in the history. PRHISTORY PRVAR Prints name and contents of variablename. PRVAR variablename You can also use the PRVAR command to print the contents of a program or a note.
Example 3 & A:CHOOSE A; "COMIC STRIPS"; "DILBERT"; "CALVIN&HOBBES"; "BLONDIE"; DISP Displays textitem in a row of the display at the line_number. A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings. Lines are numbered from the top of the screen, 1 being the top and 7 being the bottom. DISP line_number;textitem Example DISP 3;"A is" 2+2 Result: A is 4 (displayed on line 3) DISPTIME Displays the current date and time.
FREEZE This command prevents the display from being updated after the program runs. This allows you to view the graphics created by the program. Cancel FREEZE by pressing any key. FREEZE GETKEY Waits for a key, then stores the keycode rc.p in name, where r is row number, c is column number, and p is key-plane number. The key-planes numbers are: 1 for unshifted; 2 for shifted; 4 for alpha-shifted; and 5 for both alpha-shifted and shifted.
MSGBOX Displays a message box containing textitem. A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings of text. For example, "AREA IS:" 2+2 becomes AREA IS: 4. Use >6+,)7@CHARS to type the quote marks " ". MSGBOX textitem: Example 1 & A: MSGBOX "AREA IS: "π*A^2: You can also use the NoteText variable to provide text arguments. This can be used to insert line breaks. For example, press >6+,)7@NOTE and type AREA IS >(17(5@.
Stat-One and Stat-Two commands The following commands are used for analysis of onevariable and two-variable statistical data. Stat-One commands DO1VSTATS Calculates STATS using datasetname and stores the results in the corresponding variables: NΣ, TotΣ, MeanΣ, PVarΣ, SVarΣ, PSDev, SSDev, MinΣ, Q1, Median, Q3, and MaxΣ. Datasetname can be H1, H2, ..., or H5. Datasetname must define at least two data points. DO1VSTATS datasetname SETFREQ Defines datasetname frequency according to column or value.
Storing and retrieving variables in programs The HP 39G/40G 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 and 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.
Coord )XQFWLRQ 3DUDPHWULF 3RODU 6HTXHQFH 6ROYH 6WDWLVWLFV Extremum )XQFWLRQ FastRes )XQFWLRQ 6ROYH Turns the coordinate-display mode in Plot view on or off. From Plot view, use the Menu mean key to toggle coordinate display on an off. In a program, type 1 & Coord—to turn coordinate display on (default). 0 & Coord—to turn coordinate display off. Contains the last value found by the Extremum operation in the Plot-FCN menu.
Hwidth Sets the width of histogram bars. 6WDWLVWLFV From Plot Setup in 1VAR stats set a value for Hwidth or In a program, type n & Hwidth Indep $OO $SOHWV Defines the value of the independent variable used in tracing mode. In a program, type n & Indep InvCross $OO $SOHWV Toggles between solid crosshairs or inverted crosshairs. (Inverted is useful if the background is solid). From Plot Setup, check (or uncheck) InvCross or In a program, type: 1 & InvCross—to invert the crosshairs.
Nmin / Nmax 6HTXHQFH Defines the minimum and maximum independent variable values. Appears as the NRNG fields in the Plot Setup input form. From Plot Setup, enter values for NRNG. or In a program, type n 1 &Nmin n 2 &Nmax where n 2 > n 1 Recenter $OO $SOHWV Recenters at the crosshairs locations when zooming. From Plot-Zoom-Set Factors, check (or uncheck) Recenter or In a program, type 1 & Recenter— to turn recenter on (default). 0 & Recenter—to turn recenter off.
Simult )XQFWLRQ 3DUDPHWULF 3RODU 6HTXHQFH Toggles between simultaneous and sequential graphing of all selected expressions. From Plot Setup, check (or uncheck) _SIMULT or In a program, type 1 & Simult—for simultaneous graphing. 0 & Simult—for sequential graphing. Slope )XQFWLRQ StatPlot 6WDWLVWLFV Contains the last value found by the Slope function in the Plot–FCN menu. Toggles type of 1–variable statistics plot between Histogram or Box–and–Whisker.
Tmin / Tmax 3DUDPHWULF Defines the minimum and maximum independent variable values. Appears as the TRNG field in the Plot Setup input form. From Plot Setup, enter values for TRNG. or In a program, type n 1 & Tmin n 2 & Tmax where n 2 > n 1 Tracing Turns tracing mode on or off in Plot view. $OO $SOHWV In a program, type 1 & Tracing—to turn Tracing mode on (default). 0 & Tracing—to turn Tracing mode off. Tstep Defines the step size for an independent variable.
Xtick $OO $SOHWV Defines the distance between tick marks for the horizontal axis. From the Plot Setup input form, enter a value for Xtick. or In a program, type n & Xtick where n > 0 Ytick Defines the distance between tick marks for the vertical axis. $OO $SOHWV From the Plot Setup input form, enter a value for Ytick. or In a program, type n & Ytick where n > 0 Xmin / Xmax $OO $SOHWV Defines the minimum and maximum horizontal values of the plot screen.
Xzoom Sets the horizontal zoom factor. $OO $SOHWV From Plot-ZOOM-Set Factors, enter the value for XZOOM. or In a program, type n & XZOOM where n > 0 Yzoom Sets the vertical zoom factor. $OO $SOHWV From Plot-ZOOM-Set Factors, enter the value for YZOOM. or In a program, type n & YZOOM Symbolic-view variables The following aplet variables available in the Symbolic view. Angle $OO $SOHWV Sets the angle mode. From Symbolic Setup, choose Degrees, Radians, or Grads for angle measure.
X1, Y1...X9,Y9 X0,Y0 3DUDPHWULF Can contain any expression. Independent variable is T. Example ’SIN(4*T)’ & Y1(T):’2*SIN(6*T)’ STO& X1(T) R1...R9, R0 Can contain any expression. Independent variable is θ. 3RODU Example ’2*SIN(2*θ)’ & R1(θ) U1...U9, U0 Can contain any expression. Independent variable is N. 6HTXHQFH Example RECURSE (U,U(N-1)*N,1,2) & U1(N) E1...E9, E0 6ROYH Can contain any equation or expression. Independent variable is selected by highlighting it in Numeric View.
Numeric-view variables The following aplet variables control the Numeric view. The value of the variable applies to the current aplet only. C1...C9, C0 C0 through C9, for columns of data. Can contain lists. 6WDWLVWLFV Enter data in the Numeric view or In a program, type LIST &Cn where n = 0, 1, 2, 3 ... 9 Digits $OO $SOHWV Number of decimal places to use for Number format. From Solve’s Numeric Setup view, enter a value in the second field of Number Format.
Format $OO $SOHWV Defines the number display format. From Solve’s Numeric Setup view, choose Standard, Fixed, Scientific, or Engineering in the Number Format field. or In a program, store the constant name (or its number) into the variable Format. 1. Standard 2. Fixed 3. Scientific 4. Engineering Note: Fraction is not a valid mode in aplets. Except in Solve, the value of Format takes effect only after the current aplet is saved with a new name. Until then, HFormat is in effect.
NumRow Defines the highlighted row in Numeric view. $OO $SOHWV H[FHSW 6WDWLVWLFV DSOHW In a program, type n & NumRow where n > 0 NumStart )XQFWLRQ 3DUDPHWULF 3RODU 6HTXHQFH Defines the starting value for a table in Numeric view. From Num Setup, enter a value for NUMSTART. or In a program, type n & NumStart NumStep )XQFWLRQ 3DUDPHWULF 3RODU 6HTXHQFH Defines the step size (increment value) for an independent variable in Numeric view. From Num Setup, enter a value for NUMSTEP.
StatMode 6WDWLVWLFV Toggles between 1–variable and 2–variable statistics in the Statistics aplet. Does not appear in the Plot Setup input form. Corresponds to the 9$5 a and 9$5 a menu keys in Numeric View. In a program, store the constant name (or its number) into the variable StatMode. 1VAR =1, 2VAR=2. Example 1VAR & StatMode or 1 & StatMode Note variables The following aplet variable is available in Note view. NoteText Use NoteText to recall text previously entered in Note view.
16 Extending aplets Aplets are the application environments where you explore different classes of mathematical operations. You can extend the capability of the HP 39G/40G in the following ways: • Create new aplets, based on existing aplets, with specific configurations such as angle measure, graphical or tabular settings, and annotations. • Transmit aplets between HP 39G calculators via an infra red link. • Download e-lessons (teaching aplets) from the HewlettPackard’s Calculator web site.
Aplet Keys Key Meaning 6$9(_ Saves the highlighted aplet with a name. 5(6(7_ Resets the default values and settings in the highlighted aplet. This erases any stored data or functions. 6257_ Alphabetically or chronologically sorts the items in the Aplet Library menu list. 6(1'_ Transmits the highlighted aplet to another HP 39G/40G or a storage device. 5(&9_ (receive) Receives the aplet sent from another HP 39G/40G or storage device. 67$57_ Opens the selected aplet.
3. Decide whether you want the aplet to operate in Degrees, Radians, or Grads. >6+,)7@ MODES &+226_ Select Degrees 2._ 4. Ensure the TRIANGLES aplet is saved in the Aplet Library. >$3/(7@ The Solve aplet can now be reset and used for other problems. Example: To use the customized aplet To use the aplet, simply select the appropriate formula, change to the Numeric view and solve for the missing variable.
4. Solve for the missing value. 62/9(_ The length of the ladder is approximately 8.72 metres Resetting an aplet Resetting an aplet clears all data and resets all default settings. To reset an aplet, open the Library, select the aplet and press 5(6(7_. You can only reset an aplet that is based on a built-in aplet if the programmer who created it has provided a Reset option. Annotating an aplet with notes The Note view (>6+,)7@NOTE) attaches a note to the current aplet. See Chapter 14, “Notes and Sketches.
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 39G to another. This takes place via the infrared port. You can also send aplets to, and receive aplets from, a remote storage device (aplet disk drive or computer). This takes place via a cable connection and requires an aplet disk drive or special software running on a PC (such as the PC Connectivity Kit).
Sorting items in the aplet library menu list 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 advantage of storing an aplet is to allow you to keep a copy of a working environment for later use. The aplet library is where you go to manage your aplets. Press >$3/(7@.
R Reference information Regulatory information This section contains information that shows how the HP 39G/40G graphing calculator complies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the HP 39G/40G in these regions. USA This calculator generates, uses, and can radiate radio frequency energy and may interfere with radio and television reception.
LED safety The infrared port located on the top of the calculator is classified as a Class 1 LED (light emitting diode) device according to International Standard IEC 825-1 (EN 60825-1. This device is not considered harmful, but the following precautions are recommended: • Do not attempt to make any adjustments to the unit. • Avoid direct eye exposure to the infrared LED beam. Be aware that the beam is invisible light and cannot be seen.
3. HP does not warrant that the operation of HP products will be uninterrupted or error free. If HP is unable, within a reasonable time, to repair or replace any product to a condition as warranted, you will be entitled to a refund of the purchase price upon prompt return of the product. 4. HP products may contain re manufactured parts equivalent to new in performance or may have been subject to incidental use. 5.
8. FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU. CAS The HP 40G is packaged with a computerized algebra system (CAS). Refer to the CAS User Manual for further information. Resetting the HP 39G/40G If the calculator “locks up” and seems to be stuck, you must reset it.
To erase all memory and reset defaults If the calculator does not respond to the above resetting procedures, you might need to restart it by erasing all of memory. You will lose everything you have stored. All factory-default settings are restored. 1. Press and hold the >21@ key, the first menu key, and the last menu key simultaneously. 2. Release all keys. Note: To cancel this process, release only the top-row keys, then press the third menu key.
Glossary R-6 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.
menu A choice of options given in the display. It can appear as a list or as a set of menukey labels across the bottom of the display. menu keys The top row of keys. Their operations depend on the current context. The labels along the bottom of the display 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.
message that appears when the calculator is on: Warning: Low Bat. The HP 39G/40G 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 replace batteries: 1. Turn the calculator off and place the slide cover over the keyboard to prevent keys from being pressed. CAUTION Your calculator can lose memory if it is turned on while the batteries are being removed.
Category Available name (Continued) Graphic G1...G9, G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1...L9, L0 Matrix M1...M9, M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User-named Program Editline User-named Real A...
Category Available name (Continued) Plot-FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum Parametric aplet variables The parametric aplet variables are: R-10 Category Available name Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Referen
Category Available name (Continued) Symbolic Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum Polar aplet variables The polar aplet variables are: Category Available names Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Tracing Symbolic Reference information Angle R1
Category Available names (Continued) Numeric Digits Format NumCol NumFont NumIndep Note NoteText Sketch Page NumRow NumStart NumStep NumType NumZoom PageNum Sequence aplet variables The sequence aplet variables are: R-12 Category Available name Plot Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumS
Solve aplet variables The solve aplet variables are: Reference information Category Available name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Numeric Digits Format NumCol NumRow Note NoteText Sketch Page PageNum R-13
Statistics aplet variables The statistics aplet variables are: R-14 Category Available name Plot Axes Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S2mark S3mark S4mark S5mark StatPlot Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle S1fit S2fit S3fit S4fit S5fit Numeric C0,...
Menu maps of the MATH menu Math functions The math functions are: Reference information Category Available name Calculus % ) TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL π Hyperb.
R-16 Category Available name (Continued) Polynom. POLYCOEF POLYEVAL POLYFORM POLYROOT Prob.
Program constants The program constants are: Reference information Category Available name Angle Degrees Grads Radians Format Standard Fixed SeqPlot Cobweb Stairstep S1...
Program commands The program commands are: R-18 Category Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Graphic DISPLAYR RDISPLAY RGROB GROBNOT GROBOR GROBXOR MAKEGROB PLOTR RPLOT REPLACE SUB ZEROGROB Loop FOR = TO STEP END DO UNTIL END WHILE REPEAT END BREAK Matrix ADDCOL ADDROW DELCOL DELROW EDITMAT RANDMAT REDIM REPLACE SCALE SCALEADD SUB SWAPCOL SWAPROW Print PRDISPLAY PRHISTORY PRVAR Pro
Selected status messages The status messages are: Reference information Message Meaning 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 >6+,)7@MEMORY).
R-20 Message Meaning (Continued) (OFF SCREEN) Function value, root, extremum, or intersection is not visible in the current screen. Receive Error Problem with data reception from another calculator. Re-send the data. 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).
Index A absolute value 10-6 add 10-4 algebraic entry 1-18 alpha characters typing 1-6 alphabetical sorting 16-6 angle measure 1-9 in statistics 8-10 setting 1-11 animation 14-5 creating 14-5 annunciators 1-3 Ans (last answer) 1-22 antilogarithm 10-4, 10-10 aplet attaching notes 16-4 clearing 16-4 copying 16-5 definition of R-6 deleting 16-6 Function 10-22 Inference 9-2 key 1-4 library 16-6 Note view 14-1 opening 1-15 Parametric 4-1 Polar 5-1 receiving 16-5 resetting 16-4 sending 16-5 Sketch view 14-1 Solve
C calculus operations 10-8 catalogs 1-28 chronological sorting 16-6 circle drawing 14-4 clearing aplet 16-4 characters 1-21 display 1-21 display history 1-24 edit line 1-21 lists 13-6 plot 2-6 cobweb graph 6-2 coefficients polynomial 10-12 columns changing position 15-24 combinations 10-13 comma mode with matrices 13-7 commands aplet 15-14 Branch 15-17 definition of R-6 Drawing 15-19 Graphic 15-20 Loop 15-22 Print 15-25 Program 15-5, R-18 Prompt 15-25 Stat-One 15-29 Stat-Two 15-29 with matrices 12-10 comple
deleting aplet 16-6 lists 13-6 matrices 12-4 programs 15-9 statistical data 8-10 delimiters, programming 15-1 derivatives definition of 10-7 in Function aplet 10-24 in Home 10-23 determinant square matrix 12-10 differentiation 10-7 display 15-20 adjusting contrast 1-2 annunciator line 1-2 capture 15-20 clearing 1-2 date and time 15-26 element 12-5 engineering 1-10 fixed 1-10 fraction 1-10 history 1-21 line 1-21 list elements 13-4 matrices 12-5 parts of 1-2 printing contents 15-25 rescaling 2-14 scientific 1
fixed number format 1-10 font size change 3-8, 14-5 forecasting 8-21 fraction number format 1-10 full-precision display 1-10 function analyse graph with FCN tools 3-3 definition 2-2 definition of R-6 entering 1-18 gamma 10-13 intersection point 3-4 math menu R-15 quadratic 3-4 slope 3-5 syntax 10-3 tracing 2-8 Function aplet 2-21, 3-1 function variables Area 15-30 Axes 15-30 Connect 15-30 FastRes 15-31 Grid 15-31 in menu map R-9 Indep 15-32 Isect 15-32 Labels 15-33 Recenter 15-33 Root 15-33 Ycross 15-36 G
hyperbolic trigonometry ACOSH 10-9 ALOG 10-10 ASINH 10-9 ATANH 10-9 COSH 10-9 EXP 10-10 EXPM1 10-10 LNP1 10-10 SINH 10-9 TANH 10-9 hypothesis alternative 9-3 inference tests 9-9 null 9-3 tests 9-3 I i 10-9 implied multiplication 1-19 importing graphics 14-6 notes 14-8 increasing display contrast 1-2 indefinite integral using symbolic variables 10-25 independent values adding to table 2-19 independent variable defined for Tracing mode 15-32 inference confidence intervals 9-16 hypothesis tests 9-9 One-Propor
list arithmetic with 13-7 calculate sequence of elements 13-8 calculating product of 13-9 composed from differences 13-8 concatenating 13-8 counting elements in 13-9 creating 13-1, 13-3, 13-4, 13-5 deleting 13-6 deleting list items 13-3 displaying 13-4 displaying list elements 13-4 editing 13-3 finding statistical values in list elements 13-10 generate a series 13-8 generating series 13-8 list function syntax 13-7 list variables 13-1 returning position of element in 13-9 reversing order in 13-9 sending and
multiplying and dividing by scalar 12-6 multiplying by vector 12-7 multiplying row by value and adding result to second row 15-24 multiplying row number by value 15-24 negating elements 12-7 opening Matrix Editor 15-26 redimension 15-24 replacing portion of matrix or vector 15-24 sending or receiving 12-4 singular value decomposition 12-12 singular values 12-12 size 12-12 spectral norm 12-12 spectral radius 12-12 start Matrix Editor 15-23 storing elements 12-3, 12-5 storing matrix elements 12-5 swap column
in Solve aplet 7-5 scientific 1-10 Standard 1-10 numeric precision 11-9 Numeric view adding X values 2-19 automatic 2-17 build your own table 2-19 display defining function for column 2-18 recalculating 2-19 setup 2-17, 2-19 O off automatic 1-1 power 1-1 On/Cancel 1-1 One-Proportion Z-Interval 9-18 One-Sample T-Interval 9-20 One-Sample T-Test 9-13 One-Sample Z-Interval 9-16 One-Sample Z-Test 9-9 order of precedence 1-20 overlaying plots 2-16, 4-3 P π 10-9 paired columns 8-11 Parametric aplet 4-1 paramet
polar variables Axes 15-30 Connect 15-30 Grid 15-31 in menu map R-11 Indep 15-32 Labels 15-33 Recenter 15-33 Ycross 15-36 polynomial coefficients 10-12 evaluation 10-12 form 10-12 roots 10-12 Taylor 10-7 polynomial functions POLYCOEF 10-12 POLYEVAL 10-12 POLYFORM 10-12 POLYROOT 10-12 position argument 15-20 power (x raised to y) 10-6 precedence 1-20 predicted values statistical 8-21 print contents of display 15-25 name and contents of variable 15-25 object in history 15-25 variables 15-25 probability functi
TRUNCATE 10-18 XPON 10-18 recalculation for table 2-19 receive error R-20 receiving aplet 16-5 lists 13-6 matrices 12-4 programs 15-8 redrawing table of numbers 2-18 reduced row echelon 12-12 regression analysis 8-17 fit models 8-12 formula 8-12 user-defined fit 8-12 regulatory information Canada R-1 USA R-1 relative error statistical 8-17 resetting aplet 16-4 calculator R-4 If calculator does not turn on R-5 memory R-5 result copying to edit line 1-21 reusing 1-21 root interactive 3-9 nth 10-6 variable 15-
sketches creating 14-5 creating a blank graphic 15-22 creating a set of 14-5 erasing a line 15-20 labeling 14-5 opening view 14-3 sets 14-5 storing in graphics variable 14-5 slope interactive 3-9 soft key labels 1-2 solve error messages 7-7 initial guesses 7-5 interpreting intermediate guesses 7-7 interpreting results 7-6 plotting to find guesses 7-8 setting number format 7-5 solve variables Axes 15-30 Connect 15-30 FastRes 15-31 Grid 15-31 in menu map R-13 Indep 15-32 Labels 15-33 Recenter 15-33 Ycross 15-
displaying definitions 3-8 evaluating variables in view 2-3 setup view for statistics 8-10 symbolic functions | (where) 10-20 equals 10-19 ISOLATE 10-19 LINEAR? 10-19 QUAD 10-19 QUOTE 10-20 Symbolic view defining expressions 3-2 syntax 10-3 syntax errors 15-7 T table navigate around 3-7 numeric values 3-7 numeric view setup 2-17 tangent 10-4 inverse hyperbolic 10-9 Taylor polynomial 10-7 tickmarks for plotting 2-6 time 10-16 setting 15-26 time, converting 10-16 times sign 1-19 tmax 15-35 tmin 15-35 too few
V W value go directly to 3-7 recall 11-3 storing 11-2 variables aplet 11-1 categories 11-7 definition 11-1, 11-7, R-7 in equations 7-10 in Symbolic view 2-3 independent 15-35 local 11-1 previous result (Ans) 1-22 printing 15-25 root 15-33 root-finding 3-9 step size of independent 15-35 types 11-1, 11-7 use in calculations 11-4 VARS menu 11-4, 11-5 map R-8 vectors column 12-1 cross product 12-10 definition of R-7 views 1-17 configuration 1-17 definition of R-7 warning symbol 1-7 warranty R-2 where command
