HP (Hewlett-Packard) 49g+ manual

hp 49g+ graphing calculator user’s manual H Edition 2 HP part number F2228-90001[...]

Notice REGISTER YOUR PR ODUCT AT: www. register.hp.com THIS MANUAL AND ANY EX AMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” A ND ARE SUBJEC T TO CHANGE WITHOU T NOTICE. HEW LETT-PACKAR D COMPANY MAKES NO WARRANTY O F A N Y K I N D W I T H RE G AR D T O TH I S MA N U AL , I N CL U DI N G , BU T NOT LIMITED TO , THE IMPLIED WARRANTIE S OF MERCHANT[...]

Preface You have in your hands a compact symbolic and numerical computer that will facilitate calculation and mathematical analysis of problems in a variety of disciplines, from elementary mathematics to advanced engineering and science subjects. This manual contains examples that illustrate the use of the basic calculator functions and operations.[...]

Page TOC-1 Table of Contents Chapter 1 – Getting Started , 1-1 Basic Operations , 1-1 Batteries, 1-1 Turning the calculator on and off, 1-2 Adjusting the display contrast, 1-2 Contents of the calculator’s display, 1-2 Menus, 1-3 The TOOL menu, 1-3 Setting time and date, 1-4 Introducing the calculator’s keyboard , 1-4 Selecting calculator mode[...]

Page TOC-2 Creating algebraic expressions, 2-4 Using the Equation Writer (EQW) to create expressions , 2-5 Creating arithmetic expressions, 2-5 Creating algebraic expressions, 2-8 Organizing data in the calculator , 2-9 The HOME directory, 2-9 Subdirectories, 2-9 Variables , 2-10 Typing variable names, 2-10 Creating variables, 2-11 Algebraic mode, [...]

Page TOC-3 Unit conversions, 3-14 Physical constants in the calculator , 3-14 Defining and using functions , 3-16 Reference , 3-18 Chapter 4 – Calculations with complex numbers , 4-1 Definitions , 4-1 Setting the calculator to COMPLEX mode , 4-1 Entering complex numbers, 4-2 Polar representation of a complex number, 4-2 Simple operations with com[...]

Page TOC-4 The PARTFRAC function, 5-11 The FCOEF function, 5-11 The FROOTS function, 5-12 Step-by-step operations with polynomials and fractions , 5-12 Reference , 5-13 Chapter 6 – Solution to equations , 6-1 Symbolic solution of algebraic equations , 6-1 Function ISOL, 6-1 Function SOLVE, 6-2 Function SOLVEVX, 6-4 Function ZEROS, 6-4 Numerical s[...]

Page TOC-5 Chapter 8 – Vectors , 8-1 Entering vectors , 8-1 Typing vectors in the stack, 8-1 Storing vectors into variables in the stack, 8-2 Using the Matrix Writer (MTRW) to enter vectors, 8-2 Simple operations with vectors , 8-5 Changing sign, 8-5 Addition, subtraction, 8-5 Multiplication by a scalar, and division by a scalar, 8-6 Absolute val[...]

Page TOC-6 Solution with the inverse matrix, 9-10 Solution by “division” of matrices, 9-10 References , 9-10 Chapter 10 – Graphics , 10-1 Graphs options in the calculator , 10-1 Plotting an expression of the form y = f(x) , 10-2 Generating a table of values for a function , 10-3 Fast 3D plots , 10-5 Reference , 10-8 Chapter 11 – Calculus Ap[...]

Page TOC-7 Chapter 14 – Differential Equations , 14-1 The CALC/DIFF menu , 14-1 Solution to linear and non-linear equations , 14-1 Function LDEC, 14-2 Function DESOLVE, 14-3 The variable ODETYPE, 14-4 Laplace Transforms , 14-5 Laplace transform and inverses in the calculator, 14-5 Fourier series , 14-6 Function FOURIER, 14-6 Fourier series for a [...]

Page TOC-8 Chapter 17 – Numbers in Different Bases , 17-1 The BASE menu , 17-1 Writing non-decimal numbers , 17-1 Reference , 17-2 Chapter 18 – Using SD cards , 18-1 Storing objects in the SD card , 18-1 Recalling an object from the SD card , 18-2 Purging an object from the SD card , 18-2 Limited Warranty – W-1 Service , W-2 Regulatory inform[...]

Page 1-1 Chapter 1 Getting started This chapter is aimed at providing basic information in the operation of your calculator. The exercises are aimed at familiarizing yourself with the basic operations and settings before actually performing a calculation. Basic Operations The following exercises are aimed at getting you acquainted with the hardware[...]

Page 1-2 b. Insert a new CR2032 lithium battery. Make sure its positive (+) side is facing up. c. Replace the plate and push it to the original place. After installing the batteries, press [ON] to turn the power on. Warning: When the low battery icon is displayed, you need to replace the batteries as soon as possible. However, avoid removing the ba[...]

Page 1-3 For details on the meaning of these specifications see Chapter 2 in the calculator’s user’s guide. The second line shows the characters { HOME } indicating that the HOME directory is the current file directory in the calculator’s memory. At the bottom of the display you will find a number of labels, namely, @EDIT @VIEW @@ RCL @@ @@ST[...]

Page 1-4 and Chapter 2 and Appendix L in the user’s guide for more information on editing) @VIEW B VIEW the contents of a variable @@ RCL @@ C ReCaLl the contents of a variable @@STO@ D STOre the contents of a variable ! PURGE E PURGE a variable CLEAR F CLEAR the display or stack These six functions form the first page of the TOOL menu. This menu[...]

Page 1-5 the blue ALPHA key, key (7,1) , can be combined with some of the other keys to activate the alternative functions shown in the keyboard. For example, the P key, key(4,4) , has the following six functions associated with it: P Main function, to activate the SYMBolic menu „´ Left-shift function, to activate the MTH (Math) menu … N Right[...]

Page 1-6 ~p ALPHA function, to enter the upper-case letter P ~„p ALPHA-Left-Shift function, to enter the lower-case letter p ~…p ALPHA-Right-Shift function, to enter the symbol π Of the six functions associated with a key only the first four are shown in the keyboard itself. The figure in next page shows these four labels for the P key. Notice[...]

Page 1-7 Press the !!@@OK#@ ( F ) soft menu key to return to normal display. Examples of selecting different calculator modes are shown next. Operating Mode The calculator offers two operating modes: the Algebraic mode, and the Reverse Polish Notation ( RPN ) mode. The default mode is the Algebraic mode (as indicated in the figure above), however, [...]

Page 1-8 1./3.*3. ————— /23.Q3™™+!¸2.5` After pressing ` the calculator displays the expression: √ (3.*(5.-1/(3.*3.))/23.^3+EXP(2.5)) Pressing ` again will provide the following value (accept Approx mode on, if asked, by pressing !!@@OK#@ ): You could also type the expression directly into the display without using the equation wri[...]

Page 1-9 different levels are referred to as the stack levels , i.e., stack level 1, stack level 2, etc. Basically, what RPN means is that, instea d of writing an operation such as 3 + 2, in the calculator by using 3+2` we write first the operands, in the proper order, and then the operator, i.e., 3`2`+ As you enter the operands, they occupy differ[...]

Page 1-10 5 . 2 3 23 3 3 1 5 3 e + ⋅ − ⋅       3` Enter 3 in level 1 5` Enter 5 in level 1, 3 moves to level 2 3` Enter 3 in level 1, 5 moves to level 2, 3 to level 3 3* Place 3 and multiply, 9 appears in level 1 Y 1/(3 × 3), last value in lev. 1; 5 in level 2; 3 in level 3 - 5 - 1/(3 × 3) , occupies level 1 now; 3 in leve[...]

Page 1-11 (12 significant digits).”To learn more abo ut reals, see Chapter 2 in this guide. To illustrate this and other number formats try the following exercises: • Standard format : This mode is the most used mode as it shows numbers in the most familiar notation. Press the !!@@OK#@ soft menu key, with the Number format set to Std , to retur[...]

Page 1-12 Press the !!@@OK#@ soft menu key to complete the selection: Press the !!@@OK#@ soft menu key return to the calculator display. The number now is shown as: Notice how the number is rounded, not truncated. Thus, the number 123.4567890123456, for this setting, is displayed as 123.457, and not as 123.456 because the digit after 6 is > 5. ?[...]

Page 1-13 This result, 1.23E2, is the calculator’s version of powers-of-ten notation, i.e., 1.235 × 10 2 . In this, so-called, scientific notation, the number 3 in front of the Sci number format (shown earlier) represents the number of significant figures after the decimal point. Scientific notation always includes one integer figure as shown ab[...]

Page 1-14 • Decimal comma vs. decimal point Decimal points in floating-point numbers can be replaced by commas, if the user is more familiar with such notation. To replace decimal points for commas, change the FM option in the CALCULATOR MODES input form to commas, as follows (Notice that we have changed the Number Format to Std ): • Press the [...]

Page 1-15 • Grades : There are 400 grades ( 400 g ) in a complete circumference. The angle measure affects the trig functions like SIN, COS, TAN and associated functions. To change the angle measure mode, use the following procedure: • Press the H button. Next, use the down arrow key, ˜ , twice. Select the Angle Measure mode by either using th[...]

Page 1-16 Selecting CAS settings CAS stands for C omputer A lgebraic S ystem. This is the mathematical core of the calculator where the symbolic mathematical operations and functions are programmed. The CAS offers a number of settings can be adjusted according to the type of operation of interest. To see the optional CAS settings use the following:[...]

Page 1-17 options above). Unselected options will show no check mark in the underline preceding the option of interest (e.g., the _Numeric, _Approx, _Complex, _Verbose, _Step/Step, _Incr Pow options above). • After having selected and unselected all the options that you want in the CAS MODES input form, press the @@@OK@@@ soft menu key. This will[...]

Page 1-18 The calculator display can be customized to your preference by selecting different display modes. To see the opti onal display settings use the following: • First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key ( D ) to display the DISPLAY MODES inp[...]

Page 1-19 ( D ) to display the DISPLAY MODES input form. The Font: field is highlighted, and the option Ft8_0:system 8 is selected. This is the default value of the display font. Pressing the @CHOOS soft menu key ( B ), will provide a list of available system fonts, as shown below: The options available are three standard System Fonts (sizes 8, 7, [...]

Page 1-20 Selecting properties of the Stack First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key ( D ) to display the DISPLAY MODES input form. Press the down arrow key, ˜ , twice, to get to the Stack line. This line shows two properties that can be modified.[...]

Page 1-21 Selecting properties of the equation writer (EQW) First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key ( D ) to display the DISPLAY MODES input form. Press the down arrow key, ˜ , three times, to get to the EQW (Equation Writer) line. This line show[...]

Page 2-1 Chapter 2 Introducing the calculator In this chapter we present a number of basic operations of the calculator including the use of the Equation Writer and the manipulation of data objects in the calculator. Study the examples in this chapter to get a good grasp of the capabilities of the calculator for future applications. Calculator obje[...]

Page 2-2 Notice that, if your CAS is set to EXACT (see Appendix C in user’s guide) and you enter your expression using integer numbers for integer values, the result is a symbolic quantity, e.g., 5*„Ü1+1/7.5™/ „ÜR3-2Q3 Before producing a result, you will be asked to change to Approximate mode. Accept the change to get the following result[...]

Page 2-3 To evaluate the expression we can use th e EVAL function, as follows: µ„î` If the CAS is set to Exact , you will be ask ed to approve changing the CAS setting to Approx . Once this is done, you will get the same re sult as before. An alternative way to evaluate the expression entered e arlier between quotes is by using the option …ï[...]

Page 2-4 This expression is semi-symbolic in the sense that there are floating-point components to the result, as well as a √ 3. Next, we switch stack locations [using ™ ] and evaluate using function  NUM, i.e., ™…ï . This latter result is purely numerical, so that the two results in the stack, although representing the same expression,[...]

Page 2-5 Entering this expression when the calculator is set in the RPN mode is exactly the same as this Algebraic mode exercise. For additional information on editing algebraic expressions in the calculator’s display or stack see Chapter 2 in the calculator’s user’s guide. Using the Equation Writer (EQW) to create expressions The equation wr[...]

Page 2-6 The cursor is shown as a left-facing key. The cursor indicates the current edition location. For example, for the cursor in the location indicated above, type now: *„Ü5+1/3 The edited expression looks as follows: Suppose that you want to replace the quantity between parentheses in the denominator (i.e., 5+1/3) with (5+ π 2 /2). First, [...]

Page 2-7 The expression now looks as follows: Suppose that now you want to add the fraction 1/3 to this entire expression, i.e., you want to enter the expression: 3 1 ) 2 5 ( 2 5 5 2 + + ⋅ + π First, we need to highlight the entire first term by using either the right arrow ( ™ ) or the upper arrow ( — ) keys, repeatedly, until the entire ex[...]

Page 2-8 Creating algebraic expressions An algebraic expression is very similar to an arithmetic expression, except that English and Greek letters may be included. The process of creating an algebraic expression, therefore, follows the same idea as that of creating an arithmetic expression, except that use of the alphabetic keyboard is included. To[...]

Page 2-9 Also, you can always copy special characters by using the CHARS menu ( …± ) if you don’t want to memorize the keystroke combination that produces it. A listing of commonly used ~‚ keystroke combinations is listed in Appendix D of the user’s guide. For additional information on editing, evaluating, factoring, and simplifying algebr[...]

Page 2-10 Variables Variables are similar to files on a computer hard drive. One variable can store one object (numerical values, algebraic expressions, lists, vectors, matrices, programs, etc). Variables are referred to by their names, which can be any combination of alphabetic and numerical characters, starting with a letter (either English or Gr[...]

Page 2-11 To unlock the upper-case locked keyboard, press ~ Try the following exercises: ³~~math` ³~~m„a„t„h` ³~~m„~at„h` The calculator display will show the following (left-hand side is Algebraic mode, right-hand side is RPN mode): Creating variables The simplest way to create a variable is by using the K . The following examples are[...]

Page 2-12 Press ` to create the variable. The variable is now shown in the soft menu key labels: The following are the keystrokes required to enter the remaining variables: A12: 3V5K~a12` Q: ³~„r/„Ü ~„m+~„r™™ K~q` R: „Ô3‚í2‚í1™ K~r` z1: 3+5*„¥ K~„z1` (Accept change to Complex mode if asked). p1: ‚å‚é~„r³„ì*[...]

Page 2-13 • RPN mode (Use H @@OK@@ to change to RPN mode). Use the following keystrokes to store the value of –0.25 into variable α : 0.25` ~‚a` . At this point, the screen will look as follows: This expression means that the value –0.25 is ready to be stored into α . Press K to create the variable. The variable is now shown in the soft[...]

Page 2-14 p1: ‚å‚é~„r³„ì* ~„rQ2™™™ ³ ~„p1™` K . The screen, at this point, will look as follows: You will see six of the seven variables listed at the bottom of the screen: p1, z1, R, Q, A12, α . Checking variables contents The simplest way to check a variable content is by pressing the soft menu key label for the variable[...]

Page 2-15 Using the right-shift key followed by soft menu key labels This approach for viewing the contents of a variable works the same in both Algebraic and RPN modes. Try the following examples in either mode: J‚ @@p1@@ ‚ @@z1@@ ‚ @@@R@@ ‚ @@@Q@@ ‚ @@A12@@ This produces the following screen (Algebraic mode in the left, RPN in the right[...]

Page 2-16 Deleting variables The simplest way of deleting variables is by using function PURGE. This function can be accessed directly by using the TOOLS menu ( I ), or by using the FILES menu „¡ @@OK@@ . Using function PURGE in the stack in Algebraic mode Our variable list contains variables p1, z1, Q, R, and α . We will use command PURGE to d[...]

Page 2-17 Using function PURGE in the stack in RPN mode Assuming that our variable list contains the variables p1, z1, Q, R, and α . We will use command PURGE to delete variable p1 . Press ³ @@p1@@ ` I @PURGE@ . The screen will now show variable p1 removed: To delete two variables simultaneously, say variables R and Q , first create a list (in RP[...]

Page 2-18 this exercise, we use the ORDER command to reorder variables in a directory, we use, in ALG mode: „°˜ Show PROG menu list and select MEMORY @@OK@@ ˜˜˜˜ Show the MEMORY menu list and select DIRECTORY @@OK@@ —— Show the DIRECTORY menu list and select ORDER @@OK@@ activate the ORDER command There is an alternative way to access t[...]

Page 2-19 Press the @CHECK! soft menu key to set flag 117 to soft MENU . The screen will reflect that change: Press @@OK@@ twice to return to normal calculator display. Now, we’ll try to find the ORDER command using similar keystrokes to those used above, i.e., we start with „° . Notice that instead of a menu list, we get soft menu labels with[...]

Page 2-20 The ORDER command is not shown in this screen. To find it we use the L key to find it: To activate the ORDER command we press the C ( @ORDER ) soft menu key. References For additional information on entering and manipulating expressions in the display or in the Equation Writer see Chapter 2 of the calculator’s user’s guide. For CAS (C[...]

Page 3-1 Chapter 3 Calculations with real numbers This chapter demonstrates the use of the calculator for operations and functions related to real numbers. The user should be acquainted with the keyboard to identify certain functions available in the keyboard (e.g., SIN, COS, TAN, etc.). Also, it is assumed that the reader knows how to change the c[...]

Page 3-2 6.3` 8.5 - 4.2` 2.5 * 2.3` 4.5 / Alternatively, in RPN mode, you can separate the operands with a space ( # ) before pressing the operator key. Examples: 3.7#5.2 + 6.3#8.5 - 4.2#2.5 * 2.3#4.5 / • Parentheses ( „Ü ) can be used to group operations, as well as to enclose arguments of functions. In ALG mode: „Ü5+3.2™/„Ü7- 2.2` In[...]

Page 3-3 „Ê 2.32` Example in RPN mode: 2.32„Ê • The square function, SQ, is available through „º . Example in ALG mode: „º2.3` Example in RPN mode: 2.3„º The square root function, √ , is available through the R key. When calculating in the stack in ALG mode, enter the function before the argument, e.g., R123.4` In RPN mode, e[...]

Page 3-4 enter the function XROOT followed by the arguments ( y,x ), separated by commas, e.g., ‚»3‚í 27` In RPN mode, enter the argument y , first, then, x , and finally the function call, e.g., 27`3‚» • Logarithms of base 10 are calculated by the keystroke combination ‚Ã (function LOG) while its inverse function (ALOG, or antilogari[...]

Page 3-5 2.45` ‚¹ 2.3` „¸ • Three trigonometric functions are readily available in the keyboard: sine ( S ), cosine ( T ), and tangent ( U ). Arguments of these functions are angles in either degrees, radians, grades. The following examples use angles in degrees (DEG): In ALG mode: S30` T45` U135` In RPN mode: 30S 45T 135U • The inverse [...]

Page 3-6 Real number functions in the MTH menu The MTH ( „´ ) menu include a number of mathematical functions mostly applicable to real numbers. With the default setting of CHOOSE boxes for system flag 117 (see Chapter 2), the M TH menu shows the following functions: The functions are grouped by the type of argument (1. vectors, 2. matrices, 3. [...]

Page 3-7 For example, in ALG mode, the keystroke sequence to calculate, say, tanh(2.5), is the following: „´4 @@OK@@ 5 @@OK@@ 2.5` In the RPN mode, the keystrokes to perform this calculation are the following: 2.5`„´4 @@OK@@ 5 @@OK@@ The operations shown above assume that you are using the default setting for system flag 117 ( CHOOSE boxes ).[...]

Page 3-8 Finally, in order to select, for example, the hyperbolic tangent (tanh) function, simply press @@TANH@ . Note: To see additional options in these soft menus, press the L key or the „« keystroke sequence. For example, to calculate tanh(2.5), in the ALG mode, when using SOFT menus over CHOOSE boxes , follow this procedure: „´ @@HYP@ @@[...]

Page 3-9 Option 1. Tools.. contains functions used to operate on units (discussed later). Options 2. Length.. through 17.Viscosity .. contain menus with a number of units for each of the quantities described. For example, selecting option 8. Force.. shows the following units menu: The user will recognize most of these units (some, e.g., dyne, are n[...]

Page 3-10 Pressing on the appropriate soft menu key will open the sub-menu of units for that particular selection. For example, for the @) SPEED sub-menu, the following units are available: Pressing the soft menu key @) UNITS will take you back to the UNITS menu. Recall that you can always list the full menu labels in the screen by using ‚˜ , e.[...]

Page 3-11 Attaching units to numbers To attach a unit object to a number, the number must be followed by an underscore ( ‚Ý , key(8,5)). Thus, a force of 5 N will be entered as 5_N. Here is the sequence of steps to enter this number in ALG mode, system flag 117 set to CHOOSE boxes : 5‚Ý ‚Û 8 @@OK@@ @@OK@@ ` Note : If you forget the undersc[...]

Page 3-12 ____________________________________________________ Prefix Name x Prefix Name x ____________________________________________________ Y yotta +24 d deci -1 Z zetta +21 c centi -2 E exa +18 m milli -3 P peta +15 µ micro -6 T tera +12 n nano -9 G giga +9 p pico -12 M mega +6 f femto -15 k,K kilo +3 a atto -18 h,H hecto +2 z zepto -21 D(*) [...]

Page 3-13 which shows as 65_(m ⋅ yd). To convert to units of the SI system, use function UBASE (find it using the command catalog, ‚N ): Note: Recall that the ANS(1) variable is available through the keystroke combination „î (associated with the ` key). To calculate a division, say, 3250 mi / 50 h, enter it as (3250_mi)/(50_h) ` which transf[...]

Page 3-14 These operations produce the following output: Unit conversions The UNITS menu contains a TOOLS sub-menu, which provides the following functions: CONVERT(x,y): convert unit object x to units of object y UBASE(x): convert unit object x to SI units UVAL(x): extract the value from unit object x UFACT(x,y): factors a unit y from unit object x[...]

Page 3-15 The soft menu keys corresponding to this CONSTANTS LIBRARY screen include the following functions: SI when selected, constants values are shown in SI units (*) ENGL when selected, constants values are shown in English units (*) UNIT when selected, constants are shown with units attached (*) VALUE when selected, constants are shown without[...]

Page 3-16 To copy the value of Vm to the stack, select the variable name, and press ! ²STK , then, press @QUIT@ . For the calculator set to the ALG, the screen will look like this: The display shows what is called a tagged value , Vm:359.0394 . In here, Vm, is the tag of this result. Any arithmetic operation with this number will ignore the tag. T[...]

Page 3-17 and get the result you want without having to type the expression in the right- hand side for each separate value. In the following example, we assume you have set your calculator to ALG mode. Enter the following sequence of keystrokes: „à³~h„Ü~„x™‚Å ‚¹~„x+1™+„¸~„x` The screen will look like this: Press the J key[...]

Page 3-18 between quotes that contain that local variable, and show the evaluated expression. To activate the function in ALG mode, type the name of the function followed by the argument between parentheses, e.g., @@@H@@@ „Ü2` . Some examples are shown below: In the RPN mode, to activate the function enter the argument first, then press the soft[...]

Page 4-1 Chapter 4 Calculations with complex numbers This chapter shows examples of calculations and application of functions to complex numbers. Definitions A complex number z is written as z = x + iy , (Cartesian form) where x and y are real numbers, and i is the imaginary unit defined by i 2 = - 1. The number has a real par t, x = Re(z), and an [...]

Page 4-2 Entering complex numbers Complex numbers in the calculator can be entered in either of the two Cartesian representations, namely, x+iy , or (x,y) . The results in the calculator will be shown in the ordered-pair format, i.e., (x,y) . For example, with the calculator in ALG mode, the complex number (3.5,-1.2), is entered as: „Ü3.5‚í1[...]

Page 4-3 The result shown above represents a magnitude, 3.7, and an angle 0.33029…. The angle symbol ( ∠ ) is shown in front of the angle measure. Return to Cartesian or rectangular coordinates by using function RECT (available in the catalog, ‚N ). A complex number in polar representation is written as z = r ⋅ e i θ . You can enter this c[...]

Page 4-4 (3+5i) + (6-3i) = (9,2); (5-2i) - (3+4i) = (2,-6) (3-i)(2-4i) = (2,-14); (5-2i)/(3+4i) = (0.28,-1.04) 1/(3+4i) = (0.12, -0.16) ; -(5-3i) = -5 + 3i The CMPLX menus There are two CMPLX (CoMPLeX numbers) menus available in the calculator. One is available through the MTH menu (introduced in Chapter 3) and one directly into the keyboard ( ?[...]

Page 4-5 Examples of applications of these functions are shown next in RECT coordinates. Recall that, for ALG mode, the function must precede the argument, while in RPN mode, you enter the argument first, and then select the function. Also, recall that you can get these functions as soft menu labels by changing the setting of system flag 117 (See C[...]

Page 4-6 Functions applied to complex numbers Many of the keyboard-based functions and MTH menu functions defined in Chapter 3 for real numbers (e.g., SQ, ,LN, e x , etc.), can be applied to complex numbers. The result is another complex number, as illustrated in the following examples. Note: When using trigonometric functions and their inverses wi[...]

Page 4-7 Function DROITE is found in the command catalog ( ‚N ). If the calculator is in APPROX mode, the result will be Y = 5.*(X-5.)-3. Reference Additional information on complex number operations is presented in Chapter 4 of the calculator’s user’s guide.[...]

Page 5-1 Chapter 5 Algebraic and arithmetic operations An algebraic object, or simply, algebraic, is any number, variable name or algebraic expression that can be operated upon, manipulated, and combined according to the rules of algebra. Examples of algebraic objects are the following: • A number: 12.3, 15.2_m, ‘ π ’, ‘e’, ‘i’ • A[...]

Page 5-2 After building the object, press ` to show it in the stack (ALG and RPN modes shown below): Simple operations with algebraic objects Algebraic objects can be added, subtracted, multiplied, divided (except by zero), raised to a power, used as arguments for a variety of standard functions (exponential, logarithmic, trigonometry, hyperbolic, [...]

Page 5-3 In ALG mode, the following keystrokes will show a number of operations with the algebraics contained in variables @@A1@@ and @@A2@@ (press J to recover variable menu): @@A1@@ + @@A2@@ ` @@A1@@ - @@A2@@ ` @@A1@@ * @@A2@@ ` @@A1@@ / @@A2@@ ` ‚¹ @@A1@@ „¸ @@A2@@ The same results are obtained in RPN mode if using the following keystrokes[...]

Page 5-4 Functions in the ALG menu The ALG (Algebraic) menu is available by using the keystroke sequence ‚× (associated with the 4 key). With system flag 117 set to CHOOSE boxes , the ALG menu shows the following functions: Rather than listing the description of each function in this manual, the user is invited to look up the description using t[...]

Page 5-5 Copy the examples provided onto your stack by pressing @ECHO! . For example, for the EXPAND entry shown above, press the @ECHO! soft menu key to get the following example copied to the stack (press ` to execute the command): Thus, we leave for the user to explore the applications of the functions in the ALG menu. This is a list of the comm[...]

Page 5-6 Operations with transcendental functions The calculator offers a number of functions that can be used to replace expressions containing logarithmic and exponential functions ( „Ð ), as well as trigonometric functions ( ‚Ñ ). Expansion and factoring using log-exp functions The „Ð produces the following menu: Information and example[...]

Page 5-7 These functions allow to simplify expressions by replacing some category of trigonometric functions for another one. For example, the function ACOS2S allows to replace the function arccosine (acos(x)) with its expression in terms of arcsine (asin(x)). Description of these commands and examples of their applications are available in the cal[...]

Page 5-8 FACTORS: SIMP2: The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are presented in detail in Chapter 5 in the calculator’s user’s guide. The following sections show some applications to polynomials and fractions. Polynomials Polynomials are algebraic expressions consisting of one or mo[...]

Page 5-9 The variable VX Most polynomial examples above were written using variable X. This is because a variable called VX exists in the calculator’s {HOME CASDIR} directory that takes, by default, the value of ‘X’. This is the name of the preferred independent variable for al gebraic and calculus applications. Avoid using the variable VX in[...]

Page 5-10 Note : you could get the latter result by using PARTFRAC: PARTFRAC(‘(X^3-2*X+2)/(X-1)’) = ‘X^2+X-1 + 1/(X-1)’. The PEVAL function The function PEVAL (Polynomial EVALuation) can be used to evaluate a polynomial p(x) = a n ⋅ x n +a n-1 ⋅ x n-1 + …+ a 2 ⋅ x 2 +a 1 ⋅ x+ a 0 , given an array of coefficients [ a n , a n-1 , ?[...]

Page 5-11 The PROPFRAC function The function PROPFRAC converts a rational fraction into a “proper” fraction, i.e., an integer part added to a fract ional part, if such decomposition is possible. For example: PROPFRAC(‘5/4’) = ‘1+1/4’ PROPFRAC(‘(x^2+1)/x^2’) = ‘1+1/x^2’ The PARTFRAC function The function PARTFRAC decomposes a rat[...]

Page 5-12 The FROOTS function The function FROOTS, in the ARITHMETIC/POLYNOMIAL menu, obtains the roots and poles of a fraction. As an example, applying function FROOTS to the result produced above, will result in: [1 –2. –3 –5. 0 3. 2 1. –5 2.]. The result shows poles followed by their multiplicity as a negative number, and roots followed [...]

Page 5-13 Reference Additional information, definitions, and examples of algebraic and arithmetic operations are presented in Chapter 5 of the calculator’s user’s guide.[...]

Page 6-1 Chapter 6 Solution to equations Associated with the 7 key there are two menus of equation-solving functions, the Symbolic SOLVer ( „Î ), and the NUMerical SoLVer ( ‚Ï ). Following, we present some of the functions contained in these menus. Symbolic solution of algebraic equations Here we describe some of the functions from the Symbol[...]

Page 6-2 Using the RPN mode, the solution is accomplished by entering the equation in the stack, followed by the variable, before entering function ISOL. Right before the execution of ISOL, the RPN stack should look as in the figure to the left. After applying ISOL, the result is shown in the figure to the right: The first argument in ISOL can be a[...]

Page 6-3 The following examples show the use of function SOLVE in ALG and RPN modes (Use Complex mode in the CAS): The screen shot shown above displays two solutions. In the first one, β 4 -5 β =125, SOLVE produces no solutions { }. In the second one, β 4 - 5 β = 6, SOLVE produces four solutions, shown in the last output line. The very last sol[...]

Page 6-4 Function SOLVEVX The function SOLVEVX solves an equation for the default CAS variable contained in the reserved variable name VX. By default, this variable is set to ‘X’. Examples, using the ALG mode with VX = ‘X’, are shown below: In the first case SOLVEVX could not find a solution. In the second case, SOLVEVX found a single solut[...]

Page 6-5 To use function ZEROS in RPN mode, enter first the polynomial expression, then the variable to solve for, and then function ZEROS. The following screen shots show the RPN stack before and after the application of ZEROS to the two examples above (Use Complex mode in the CAS):: The Symbolic Solver functions presented above produce solutions [...]

Page 6-6 Following, we present applications of items 3. Solve poly.. , 5. Solve finance , and 1. Solve equation.. , in that order. Appendix 1-A, in the calculator’s user’s guide, contains instructions on how to use input forms with examples for the numerical solver applications. Item 6. MSLV (Multiple equation SoLVer) will be presented later in[...]

Page 6-7 Press ` to return to stack. The stack will show the following results in ALG mode (the same result would be shown in RPN mode): All the solutions are complex numbers: (0.432,-0.389), (0.432,0.389), (- 0.766, 0.632), (-0.766, -0.632). Generating polynomial coefficients given the polynomial's roots Suppose you want to generate the polyn[...]

Page 6-8 Generating an algebraic expression for the polynomial You can use the calculator to generate an algebraic expression for a polynomial given the coefficients or the roots of the polynomial. The resulting expression will be given in terms of the default CAS variable X. To generate the algebraic expression using the coefficients, try the foll[...]

Page 6-9 Financial calculations The calculations in item 5. Solve finance.. in the Numerical Solver ( NUM.SLV ) are used for calculations of time value of money of interest in the discipline of engineering economics and other financial applications. This application can also be started by using the keystroke combination „Ò (associated with the 9[...]

Page 6-10 Then, enter the SOLVE environment and select Solve equation… , by using: ‚Ï @@OK@@ . The corresponding screen will be shown as: The equation we stored in variable EQ is already loaded in the Eq field in the SOLVE EQUATION input form. Also, a field labeled x is provided. To solve the equation all you need to do is hig hlight the field[...]

Page 6-11 Notice that function MSLV requires three arguments: 1. A vector containing the equations, i.e., ‘[SIN(X)+Y,X+SIN(Y)=1]’ 2. A vector containing the variables to solve for, i.e., ‘[X,Y]’ 3. A vector containing initial values for the solution, i.e., the initial values of both X and Y are zero for this example. In ALG mode, press @ECH[...]

Page 6-12 by MSLV is numerical, the information in the upper left corner shows the results of the iterative process used to obtain a solution. The final solution is X = 1.8238, Y = -0.9681 . Reference Additional information on solving single and multiple equations is provided in Chapters 6 and 7 of the calculator’s user’s guide.[...]

Page 7-1 Chapter 7 Operations with lists Lists are a type of calculator’s object that can be useful for data processing. This chapter presents examples of operations with lists. To get started with the examples in this Chapter, we use the Approximate mode (See Chapter 1). Creating and storing lists To create a list in ALG mode, first enter the br[...]

Page 7-2 Addition, subtraction, multiplication, division Multiplication and division of a list by a single number is distributed across the list, for example: Subtraction of a single number from a list will subtract the same number from each element in the list, for example: Addition of a single number to a list produces a list augmented by the num[...]

Page 7-3 Note : If we had entered the elements in lists L4 and L3 as integers, the infinite symbol would be shown whenever a division by zero occurs. To produce the following result you need to re-enter the lists as integer (remove decimal points) using Exact mode: If the lists involved in the operation have different lengths, an error message (Inv[...]

Page 7-4 ABS INVERSE (1/x) Lists of complex numbers You can create a complex number list, say, L5 = L1 ADD i*L2 (type the instruction as indicated before), as follows: Functions such as LN, EXP, SQ, etc., can also be applied to a list of complex numbers, e.g., Lists of algebraic objects The following are examples of lists of algebraic objects with [...]

Page 7-5 With system flag 117 set to SOFT menus, the MTH/LIST menu shows the following functions: The operation of the MTH/LIST menu is as follows: ∆ LIST : Calculate increment among consecutive elements in list Σ LIST : Calculate summation of elements in the list Π LIST : Calculate product of elements in the list SORT : Sorts elements in incre[...]

Page 7-6 The SEQ function The SEQ function, available through the command catalog ( ‚N ), takes as arguments an expression in terms of an index, the name of the index, and starting, ending, and increment values for the index, and returns a list consisting of the evaluation of the expression for all possible values of the index. The general form o[...]

Page 8-1 Chapter 8 Vectors This Chapter provides examples of entering and operating with vectors, both mathematical vectors of many elements, as well as physical vectors of 2 and 3 components. Entering vectors In the calculator, vectors are represented by a sequence of numbers enclosed between brackets, and typically entered as row vectors. The bra[...]

Page 8-2 ( ‚í ) or spaces ( # ). Notice that after pressing ` , in either mode, the calculator shows the vector elements separated by spaces. Storing vectors into variables in the stack Vectors can be stored into variables. The screen shots below show the vectors u 2 = [1, 2] , u 3 = [-3, 2, -2] , v 2 = [3,-1] , v 3 = [1, -5, 2] Stored into vari[...]

Page 8-3 The @EDIT key is used to edit the contents of a selected cell in the Matrix Writer. The @VEC@@ key, when selected, will produce a vector, as opposed to a matrix of one row and many columns. The ← WID key is used to decrease the width of the columns in the spreadsheet. Press this key a couple of times to see the column width decrease in y[...]

Page 8-4 The @+ROW@ key will add a row full of zeros at the location of the selected cell of the spreadsheet. The @-ROW key will delete the row corresponding to the selected cell of the spreadsheet. The @+COL@ key will add a column full of zeros at the location of the selected cell of the spreadsheet. The @-COL@ key will delete the column correspon[...]

Page 8-5 (3) Move the cursor up two positions by using —— . Then press @-ROW . The second row will disappear. (4) Press @+ROW@ . A row of three zeroes appears in the second row. (5) Press @-COL@ . The first column will disappear. (6) Press @+COL@ . A column of two zeroes appears in the first column. (7) Press @GOTO@ 3 @@OK@@ 3 @@OK@@ @@OK@@ to [...]

Page 8-6 Attempting to add or subtract vectors of different length produces an error message: Multiplication by a scalar, and division by a scalar Multiplication by a scalar or division by a scalar is straightforward: Absolute value function The absolute value function (ABS), when applied to a vector, produces the magnitude of the vector. For examp[...]

Page 8-7 The MTH/VECTOR menu The MTH menu ( „´ ) contains a menu of functions that specifically to vector objects: The VECTOR menu contains the following functions (system flag 117 set to CHOOSE boxes): Magnitude The magnitude of a vector, as discussed earlier, can be found with function ABS. This function is also available from the keyboard ( ?[...]

Page 8-8 Cross product Function CROSS (option 3 in the MTH/VECTOR menu) is used to calculate the cross product of two 2-D vectors, of two 3-D vectors, or of one 2-D and one 3- D vector. For the purpose of calculating a cross product, a 2-D vector of the form [A x , A y ], is treated as the 3-D vector [A x , A y ,0]. Examples in ALG mode are shown n[...]

Page 9-1 Chapter 9 Matrices and linear algebra This chapter shows examples of creating matrices and operations with matrices, including linear algebra applications. Entering matrices in the stack In this section we present two different methods to enter matrices in the calculator stack: (1) using the Matrix Writer, and (2) typing the matrix directl[...]

Page 9-2 Press ` once more to place the matrix on the stack. The ALG mode stack is shown next, before and after pressing , once more: If you have selected the textbook display option (using H @) DISP! and checking off  Textbook ), the matrix will look like the one shown above. Otherwise, the display will show: The display in RPN mode will look v[...]

Page 9-3 Operations with matrices Matrices, like other mathematical objects, can be added and subtracted. They can be multiplied by a scalar, or among themselves. An important operation for linear algebra applications is the inverse of a matrix. Details of these operations are presented next. To illustrate the operations we will create a number of [...]

Page 9-4 In RPN mode, try the following eight examples: A22 ` B22 `+ A22 ` B22 `- A23 ` B23 `+ A23 ` B23 `- A32 ` B32 `+ A32 ` B32 `- A33 ` B33 `+ A33 ` B33 `- Multiplication There are different multiplication operations that involve matrices. These are described next. The examples are shown in algebraic mode. Multiplication by a scalar Some exampl[...]

Page 9-5 Matrix multiplication Matrix multiplication is defined by C m × n = A m × p ⋅ B p × n . Notice that matrix multiplication is only possible if the number of columns in the first operand is equal to the number of rows of the second operand. The general term in the product, c ij , is defined as . , , 2 , 1 ; , , 2 , 1 , 1 n j m i for b a[...]

Page 9-6 The identity matrix The identity matrix has the property that A ⋅ I = I ⋅ A = A . To verify this property we present the following examples using the matrices stored earlier on. Use function IDN (find it in the MTH/MATRIX/MAKE menu) to generate the identity matrix as shown here: The inverse matrix The inverse of a square matrix A is th[...]

Page 9-7 Characterizing a matrix (The matrix NORM menu) The matrix NORM (NORMALIZE) menu is accessed through the keystroke sequence „´ . This menu is described in detail in Chapter 10 of the calculator’s user’s guide. Some of these functions are described next. Function DET Function DET calculates the determinant of a square matrix. For exam[...]

Page 9-8 This system of linear equations can be written as a matrix equation, A n × m ⋅ x m × 1 = b n × 1 , if we define the following matrix and vectors: m n nm n n m m a a a a a a a a a A ×             = L M O M M L L 2 1 2 22 21 1 12 11 , 1 2 1 ×             = m m x x[...]

Page 9-9 . 6 13 13 , , 4 2 2 8 3 1 5 3 2 3 2 1           − − =           =           − − − = b x A and x x x This system has the same number of equations as of unknowns, and will be referred to as a square system. In general, there should be a unique[...]

Page 9-10 Solution with the inverse matrix The solution to the system A ⋅ x = b , where A is a square matrix is x = A -1 ⋅ b . For the example used earlier, we can find the solution in the calculator as follows (First enter matrix A and vector b once more): Solution by “division” of matrices While the operation of division is not defined fo[...]

Page 10-1 Chapter 10 Graphics In this chapter we introduce some of the graphics capabilities of the calculator. We will present graphics of functions in Cartesian coordinates and polar coordinates, parametric plots, graphics of conics, bar plots, scatterplots, and fast 3D plots. Graphs options in the calculator To access the list of graphic formats[...]

Page 10-2 Plotting an expression of the form y = f(x) As an example, let's plot the function, ) 2 exp( 2 1 ) ( 2 x x f − = π • First, enter the PLOT SETUP environment by pressing, „ô . Make sure that the option Function is selected as the TYPE , and that ‘X’ is selected as the independent variable ( INDEP ). Press L @@@OK@@@ to ret[...]

Page 10-3 VIEW, then press @AUTO to generate the V-VIEW automatically. The PLOT WINDOW screen looks as follows: • Plot the graph: @ERASE @DRAW (wait till the calculator finishes the graphs) • To see labels: @EDIT L @LABEL @MENU • To recover the first graphics menu: LL @) PICT • To trace the curve: @TRACE @@X,Y@@ . Then use the right- and le[...]

Page 10-4 • We will generate values of the function f(x), defined above, for values of x from –5 to 5, in increments of 0.5. First, we need to ensure that the graph type is set to FUNCTION in the PLOT SETUP screen ( „ô , press them simultaneously, if in RPN mode). The field in front of the Type option will be highlighted. If this field is no[...]

Page 10-5 • • The @ZOOM key, when pressed, produces a menu with the options: In , Out , Decimal, Integer , and Trig . Try the following exercises: • • With the option In highlighted, press @@@OK@@@ . The table is expanded so that the x-increment is now 0.25 rather than 0.5. Simply, what the calculator does is to multiply the original increm[...]

Page 10-6 • Press „ô , simultaneously if in RPN mode, to access to the PLOT SETUP window. • Change TYPE to Fast3D. ( @CHOOS! , find Fast3D , @@OK@@ ). • Press ˜ and type ‘X^2+Y^2’ @@@OK@@@ . • Make sure that ‘X’ is selected as the Indep: and ‘Y’ as the Depnd: variables. • Press L @@@OK@@@ to return to normal calculator dis[...]

Page 10-7 • When done, press @EXIT . • Press @CANCL to return to the PLOT WINDOW environment. • Change the Step data to read: Step Indep: 20 Depnd: 16 • Press @ERASE @DRAW to see the surface plot. Sample views: • When done, press @EXIT . • Press @CANCL to return to PLOT WINDOW. • Press $ , or L @@@OK@@@ , to return to normal calculato[...]

Page 10-8 • Press LL @) PICT to leave the EDIT environment. • Press @CANCL to return to the PLOT WINDOW environment. Then, press $ , or L @@@OK@@@ , to return to normal calculator display. Reference Additional information on graphics is available in Chapters 12 and 22 in the calculator’s user’s guide.[...]

Page 11-1 Chapter 11 Calculus Applications In this Chapter we discuss applications of the calculator’s functions to operations related to Calculus, e.g., limits, derivatives, integrals, power series, etc. The CALC (Calculus) menu Many of the functions presented in this Chapter are contained in the calculator’s CALC menu, available through the k[...]

Page 11-2 where the limit is to be calculated. Function lim is available through the command catalog ( ‚N~„l ) or through option 2. LIMITS & SERIES… of the CALC menu (see above). Function lim is entered in ALG mode as lim(f(x),x=a) to calculate the limit ) ( lim x f a x → . In RPN mode, enter the function first, then the expression ‘x[...]

Page 11-3 Anti-derivatives and integrals An anti-derivative of a function f(x) is a function F(x) such that f(x) = dF/dx. One way to represent an anti-derivative is as a indefinite integral , i.e., C x F dx x f + = ∫ ) ( ) ( if and only if, f(x) = dF/dx, and C = constant. Functions INT, INTVX, RISCH, SIGMA and SIGMAVX The calculator provides func[...]

Page 11-4 Please notice that functions SIGMAVX and SIGMA are designed for integrands that involve some sort of integer f unction like the factorial (!) function shown above. Their result i s the so-called discrete derivative, i.e., one defined for integer numbers only. Definite integrals In a definite integral of a function, the resulting anti -der[...]

Page 11-5 where f (n) (x) represents the n-th derivative of f(x) with respect to x, f (0) (x) = f(x). If the value x 0 = 0, the series is referred to as a Maclaurin’s series. Functions TAYLR, TAYLR0, and SERIES Functions TAYLR, TAYLR0, and SERIES are used to generate Taylor polynomials, as well as Taylor series with residuals. These functions are[...]

Page 11-6 expression for h = x - a, if the second argument in the function call is ‘x=a’, i.e., an expression for the increment h. The list returned as the first output object includes the following items: 1 - Bi-directional limit of the function at point of expansion, i.e., ) ( lim x f a x → 2 - An equivalent value of the function near x = a[...]

Page 12-1 Chapter 12 Multi-variate Calculus Applications Multi-variate calculus refers to functions of two or more variables. In this Chapter we discuss basic concepts of mu lti-variate calculus: partial derivatives and multiple integrals. Partial derivatives To quickly calculate partial derivatives of multi-variate functions, use the rules of ordi[...]

Page 12-2 To define the functions f(x,y) and g(x,y,z), in ALG mode, use: DEF(f(x,y)=x*COS(y)) ` DEF(g(x,y,z)= √ (x^2+y^2)*SIN(z) ` To type the derivative symbol use ‚ ¿ . The derivative )) , ( ( y x f x ∂ ∂ , for example, will be entered as ∂ x(f(x,y)) ` in ALG mode in the screen. Multiple integrals A physical interpretation of the doubl[...]

Page 13-1 Chapter 13 Vector Analysis Applications This chapter describes the use of functions HESS, DIV, and CURL, for calculating operations of vector analysis. The del operator The following operator, referred to as the ‘del’ or ‘nabla’ operator, is a vector- based operator that can be applied to a scalar or vector function: [] [] [] [] z[...]

Page 13-2 Alternatively, use function DERIV as follows: Divergence The divergence of a vector function, F (x,y,z) = f(x,y,z) i +g(x,y,z) j +h(x,y,z) k , is defined by taking a “dot-product” of the del operator with the function, i.e., F divF • ∇ = . Function DIV can be used to calculate the divergence of a vector field. For example, for F ([...]

Page 14-1 Chapter 14 Differential Equations In this Chapter we present examples of solving ordinary differential equations (ODE) using calculator functions. A differential equation is an equation involving derivatives of the independent variable. In most cases, we seek the dependent function that satisfies the differential equation. The CALC/DIFF m[...]

Page 14-2 Function LDEC The calculator provides function LDEC (Linear Differential Equation Command) to find the general solution to a linear ODE of any order with constant coefficients, whether it is homogeneous or not. This function requires you to provide two pieces of input: • the right-hand side of the ODE • the characteristic equation of [...]

Page 14-3 The solution is: which is equivalent to y = K 1 ⋅ e –3x + K 2 ⋅ e 5x + K 3 ⋅ e 2x + (450 ⋅ x 2 +330 ⋅ x+241)/13500. Function DESOLVE The calculator provides function DESOLVE (Differential Equation SOLVEr) to solve certain types of differential equation s. The function requires as input the differential equation and the unknown[...]

Page 14-4 The variable ODETYPE You will notice in the soft-menu key labels a new variable called @ODETY (ODETYPE). This variable is produced with the call to the DESOL function and holds a string showing the type of ODE used as input for DESOLVE. Press @ODETY to obtain the string “ 1st order linear ”. Example 2 – Solving an equation with init[...]

Page 14-5 Laplace Transforms The Laplace transform of a function f(t) produces a function F(s) in the image domain that can be utilized to find the solution of a linear differential equation involving f(t) through algebraic methods. The steps involved in this application are three: 1. Use of the Laplace transform converts the linear ODE involving f[...]

Page 14-6 and you will notice that the CAS default variable X in the equation writer screen replaces the variable s in this definition. Therefore, when using the function LAP you get back a function of X, which is the Laplace transform of f(X). Example 2 – Determine the inverse Laplace transform of F(s) = sin(s). Use: ‘1/(X+1)^2’ ` ILAP The c[...]

Page 14-7 Using the calculator in ALG mode, first we define functions f(t) and g(t): Next, we move to the CASDIR sub-directory under HOME to change the value of variable PERIOD, e.g., „ (hold) §`J @) CASDI `2 K @PERIOD ` Return to the sub-directory where you defined functions f and g, and calculate the coefficients. Set CAS to Complex mode (see [...]

Page 14-8 Thus, c 0 = 1/3, c 1 = ( π⋅ i+2)/ π 2 , c 2 = ( π⋅ i+1)/(2 π 2 ). The Fourier series with three elements will be written as g(t) ≈ Re[(1/3) + ( π⋅ i+2)/ π 2 ⋅ exp(i ⋅π⋅ t)+ ( π⋅ i+1)/(2 π 2 ) ⋅ exp(2 ⋅ i ⋅π⋅ t)]. Reference For additional definitions, applications, and exercises on solving differential equ[...]

Page 15-1 Chapter 15 Probability Distributions In this Chapter we provide examples of applications of the pre-defined probability distributions in the calculator. The MTH/PROBABILITY.. sub-menu - part 1 The MTH/PROBABILITY.. sub-menu is accessible through the keystroke sequence „´ . With system flag 117 set to CHOOSE boxes, the following functio[...]

Page 15-2 We can calculate combinations, permutations, and factorials with functions COMB, PERM, and ! from the MTH/PROBABILITY.. sub-menu. The operation of those functions is described next: • COMB(n,r): Calculates the number of combinations of n items taken r at a time • PERM(n,r): Calculates the number of permutations of n items taken r at a[...]

Page 15-3 The MTH/PROB menu - part 2 In this section we discuss four continuous probability distributions that are commonly used for problems related to statistical inference: the normal distribution, the Student’s t distribution, the Chi-square ( χ 2 ) distribution, and the F-distribution. The functions provided by the calculator to evaluate pr[...]

Page 15-4 UTPT, given the parameter ν and the value of t, i.e., UTPT( ν ,t) = P(T>t) = 1- P(T<t). For example, UTPT(5,2.5) = 2.7245…E-2. The Chi-square distribution The Chi-square ( χ 2 ) distribution has one parameter ν , known as the degrees of freedom. The calculator provides for values of the upper-tail (cumulative) distribution fun[...]

Page 16-1 Chapter 16 Statistical Applications The calculator provides the following pre-programmed statistical features accessible through the keystroke combination ‚Ù (the 5 key): Entering data Applications number 1, 2, and 4 from the list above require that the data be available as columns of the matrix Σ DAT. This can be accomplished by ente[...]

Page 16-2 The form lists the data in Σ DAT, shows that column 1 is selected (there is only one column in the current Σ DAT). Move about the form with the arrow keys, and press the @  CHK@ soft menu key to select those measures (Mean, Standard Deviation, Variance, Total number of data points, Maximum and Minimum values) that you want as output [...]

Page 16-3 Obtaining frequency distributions The application 2. Frequencies.. in the STAT menu can be used to obtain frequency distributions for a set of data. The data must be present in the form of a column vector stored in variable Σ DAT. To get started, press ‚Ù˜ @@@OK@@@ . The resulting input form contains the following fields: Σ DAT : th[...]

Page 16-4 This information indicates that our data ranges from -9 to 9. To produce a frequency distribution we will use the interval (-8,8) dividing it into 8 bins of width 2 each. • Select the program 2. Frequencies.. by using ‚Ù˜ @@@OK@@@ . The data is already loaded in Σ DAT, and the option Col should hold the value 1 since we have only o[...]

Page 16-5 data sets (x,y), stored in columns of the Σ DAT matrix. For this application, you need to have at least two columns in your Σ DAT variable. For example, to fit a linear relationship to the data shown in the table below: x y 0 0.5 1 2.3 2 3.6 3 6.7 4 7.2 5 11 • First, enter the two columns of data into variable Σ DAT by using the matr[...]

Page 16-6 Level 3 shows the form of the equation. Level 2 shows the sample correlation coefficient, and level 1 shows the covariance of x-y. For definitions of these parameters see Chapter 18 in the user’s guide. For additional information on the data-fit feature of the calculator see Chapter 18 in the user’s guide. Obtaining additional summary[...]

Page 16-7 • Press @@@OK@@@ to obtain the following results: Confidence intervals The application 6. Conf Interval can be accessed by using ‚Ù— @@@OK@@@ . The application offers the following options: These options are to be interpreted as follows: 1. Z-INT: 1 µ .: Single sample confidence interval for the population mean, µ , with known po[...]

Page 16-8 4. Z-INT: p 1− p 2 .: Confidence interval for the difference of two proportions, p 1 -p 2 , for large samples with unknown population variances. 5. T-INT: 1 µ .: Single sample confidence interval for the population mean, µ , for small samples with unknown population variance. 6. T-INT: µ1−µ2 .: Confidence interval for the differen[...]

Page 16-9 The graph shows the standard normal distribution pdf (probability density function), the location of the critical points ± z α/2 , the mean value (23.2) and the corresponding interval limits (2 1.88424 and 24.51576). Press @TEXT to return to the previous results screen, and/or press @@@OK@@@ to exit the confidence interval environment. [...]

Page 16-10 1. Z-Test: 1 µ .: Single sample hypothesis testing for the population mean, µ , with known population variance, or for large samples with unknown population variance. 2. Z-Test: µ1−µ2 .: Hypothesis testing for the difference of the population means, µ 1 - µ 2 , with either known population variances, or for large samples with unk[...]

Page 16-11 Select µ ≠ 150 . Then, press @@@OK@@@ . The result is: Then, we reject H 0 : µ = 150 , against H 1 : µ ≠ 150 . The test z value is z 0 = 5.656854. The P-value is 1.54 × 10 -8 . The critical values of ± z α /2 = ± 1.959964, corresponding to critical  x range of {147.2 152.8}. This information can be observed graphically by p[...]

Page 17-1 Chapter 17 Numbers in Different Bases Besides our decimal (base 10, digits = 0-9) number system, you can work with a binary system (base 2, digits = 0,1), an octal system (base 8, digits = 0-7), or a hexadecimal system (base 16, digits=0-9,A-F), among others. The same way that the decimal integer 321 means 3x10 2 +2x10 1 +1x10 0 , the num[...]

Page 17-2 base to be used for binary integers, choose either HEX(adecimal), DEC(imal), OCT(al), or BIN(ary) in the BASE menu. For example, if @HEX  ! is selected, binary integers will be a hexadecimal numbers, e.g., #53, #A5B, etc. As different systems are selected, the numbers will be automatically converted to the new current base. To write a [...]

Page 18-1 Chapter 18 Using SD cards The calculator provides a memory card port where you can insert an SD flash card for backing up calculator objects, or for downloading objects from other sources. The SD card in the calculator will appear as port number 3. Accessing an object from the SD card is performed similarly as if the object were located i[...]

Page 18-2 Enter object, type the name of the stored object using port 3 (e.g., :3:VAR1 ), press K . Recalling an object from the SD card To recall an object from the SD card onto the screen, use function RCL, as follows: • In algebraic mode: Press „© , type the name of the stored object using port 3 (e.g., :3:VAR1 ), press ` . • In RPN mode:[...]

P a ge W - 1 Li m i t e d W a r r a n t y hp 49 g + g r aph i n g c a l c u l a t o r; W a r r an t y p e r i o d : 12 m o n t h s 1. H P w a rr an t s t o y o u , t h e e nd - u s e r c u s t o m e r, t ha t H P ha r d w a r e , a cc es s o r i es and s u pp l i es wi l l b e f r e e f r o m d e f e c t s i n ma t e ri a l s an d w o r k ma n s h [...]

P a ge W - 2 7 . T O T H E E X T E N T A LL O W ED BY L O C A L L A W , T H E R E M ED I ES IN T HI S W A RR A N T Y S T A T E M E N T A R E Y O UR S O L E A N D E X C LU S I V E R E M ED I ES . E X C E P T A S IN D I C A T ED A B OV E , IN N O E V E N T W I L L H P O R I T S S U P P L I E R S B E L I A B L E F O R L O SS O F D A T A O R F O R D I [...]

P a ge W - 3 +39 - 02 - 75 4 19 7 82 (It a l i an ) T u r ke y +42 0 - 5 - 41 4 22 5 23 U K +44 - 20 7 - 4 5 80 1 61 C ze c h Re p u b l ic +42 0 - 5 - 41 4 22 5 23 S o u t h A f ric a +27 - 11 - 23 7 62 0 0 L u x e mb o u r g +32 - 2 - 7 12 6 219 O t h e r E u r o p e an c o u n t r i es +42 0 - 5 - 41 4 22 5 23 A s i a P a ci f ic C o u n t r y :[...]

P a ge W - 4 R e g u l a t o r y i n f o r m a t i o n T h i s se c t i o n c o n t a i n s i n f o r m at i o n t h at s h o w s h o w t h e h p 4 9 g + g r ap h i n g c a l c u l at o r c o m p l i es w i t h r eg u l at i o n s i n c e rta i n r e g i o n s . A ny m o d i f ic at i o n s t o t h e c a l c u l at o r n o t e x pr e s s l y a ppr [...]