HP 48gII - Manuals

Page TOC-3 Operations with units, 3-12 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, ...

Page TOC-4 The PROPFRAC function, 5-11 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...

Page TOC-5 The SEQ function , 7-6 The MAP function , 7-6 Reference , 7-6 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 Changi...

Page TOC-6 Function TRACE, 9-7 Solution of linear systems , 9-7 Using the numerical solver for linear systems, 9-8 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 expres...

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 Warranty – W-1 Service , W-2 Regulatory information , W-4

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

Page 1-3 RAD XYZ HEX R= 'X' 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 w...

Page 1-4 @EDIT A EDIT the contents of a variable (see Chapter 2 in this Guide and Chapter 2 and Appendix L in the user's guide for more information on editing) @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 PU...

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

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...

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

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) , o...

Page 1-11 more about reals, see Chapter 2 in this Guide. To illustrate this and other number formats try the following exercises: • Standard format : This mode is the most used mode as it shows numbers in the most familiar notation. Press the !!@@OK#@ soft menu key, with the Number format set to Std...

Page 1-12 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): • Scientif...

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...

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 ch...

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. T...

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 f...

Page 1-18 The calculator display can be customized to your preference by selecting different display modes. To see the optional display settings use the following: • First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft ...

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 @CHOOSE soft menu key ( B ), will provide a list of available system fonts, as shown below: The options avai...

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. Thi...

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 ...

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 c...

Page 2-3 To evaluate the expression we can use the EVAL function, as follows: µ„î If the CAS is set to Exact , you will be asked to approve changing the CAS setting to Approx . Once this is done, you will get the same result as before. An alternative way to evaluate the expression entered earlier be...

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 and evaluate using function Æ NUM: ™…ï . This latter result is purely numerical, so that the two results in the stack, although representin...

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...

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 ...

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 t...

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 was listed in an earlier section. For additional information on editing, evaluating, fac...

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 charac...

Page 2-11 To unlock the upper-case locked keyboard, press ~ Try the following exercises: ³~~math1~` 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...

Page 2-13 • RPN mode (Use I\ @@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 variabl...

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 ke...

Page 2-17 To delete two variables simultaneously, say variables R and Q , first create a list (in RPN mode, the elements of the list need not be separated by commas as in Algebraic mode): J „ä³ @@@R!@@ ™ ³ @@@ !@@ ` Then, press I @PURGE@ use to purge the variables. Additional information on variable...

Page 2-19 Press the @CHECK! soft menu key to set flag 117 to soft MENU . The screen will reflect that change: Press 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 m...

Page 2-20 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 (Computer Algebraic System) settings, see A...

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...

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 i...

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 MTH menu shows the following functions: The functions are grouped by the ...

Page 3-8 Finally, in order to select, for example, the hyperbolic tangent (tanh) function, simply press @@TA H@ . 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...

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 @)U ITS will take you back to the UNITS menu. Recall that you can always list the fu...

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@@ ...

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 ...

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...

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

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 functio...

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...

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 writte...

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 C...

Page 4-5 CONJ(z): Produces the complex conjugate of z Examples of applications of these functions are shown next. 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 func...

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 : not...

Page 4-7 Function DROITE is found in the command catalog ( ‚N ). 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: ...

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 (expo...

Page 5-4 Functions in the ALG menu The ALG (Algebraic) menu is available by using the keystroke sequence ‚× (associated with the ‚ 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 use...

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 th...

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 examp...

Page 5-8 FACTORS: SIMP2: The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are the following: Additional information on applications of the ARITHMETIC menu functions are presented in Chapter 5 in the calculator’s user's guide. Polynomials Polynomial...

Page 5-9 The variable VX 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 algebraic and calculus applications. Avoid using the variable VX in your programs or equations, so as ...

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 functions 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 o...

Page 5-12 The FROOTS function The function FROOTS 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 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 de...

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...

Page 6-3 The following examples show the use of function SOLVE in ALG and RPN modes. [ Note : not all lines will be visible when done with the exercises in the following figures.] The screen shot shown above displays two solutions. In the first one, β 4 -5 β =125, SOLVE produces no solutions { }. In...

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: The Symbolic Solver functions presented above...

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 (Multip...

Page 6-9 ' (X-1)*(X-3)*(X+2)*(X-1) '. To expand the products, you can use the EXPAND command. The resulting expression is: ' X^4+-3*X^3+ -3*X^2+11*X-6' . Financial calculations The calculations in item 5. Solve finance.. in the Numerical Solver ( NUM.SLV ) are used for calculations of time value of ...

Page 6-11 Solution to simultaneous equations with MSLV Function MSLV is available in the ‚Ï menu. The help-facility entry for function MSLV is shown next: 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 th...

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 ...

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 opera...

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 here), 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 followin...

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 ...

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 brack...

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 = , u 3 = , v 2 = , v 3 = Stored...

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 coupl...

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....

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 f...

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...

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 th...

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 3 Textbook ), the matrix will look like the one shown above. Otherwise, the display...

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 ill...

Page 9-4 In RPN mode, you can try a few more exercises: A ` `+ A ` `- A ` `+ A ` `- A ` `+ A ` `- A ` `+ A ` `- 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 exam...

Page 9-5 Vector-matrix multiplication, on the other hand, is not defined. This multiplication can be performed, however, as a special case of matrix multiplication as defined next. Matrix multiplication Matrix multiplication is defined by C m × n = A m × p ⋅ B p × n . Notice that matrix multiplicati...

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 t...

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 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 solution to the sys...

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 th...

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 (...

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 @LA EL @ME U • To recover the first graphics menu: LL @)PICT • To trace the curve: @T...

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 opti...

Page 10-5 • • The @@ IG@ key simply changes the font in the table from small to big, and vice versa. Try it. • • The @ OOM 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@@@ . T...

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 c...

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

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,...

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

Page 11-5 Infinite series A function f(x) can be expanded into an infinite series around a point x=x 0 by using a Taylor’s series, namely, ∑ ∞ = − ⋅ = 0 ) ( ) ( ! ) ( ) ( n n o o n x x n x f x f , where f (n) (x) represents the n-th derivative of f(x) with respect to x, f (0) (x) = f(x). If the valu...

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 multi-variate calculus: partial derivatives and multiple integrals. Partial derivatives To quickly calculate partial derivatives ...

Page 12-2 Multiple integrals A physical interpretation of the double integral of a function f(x,y) over a region R on the x-y plane is the volume of the solid body contained under the surface f(x,y) above the region R. The region R can be described as R = {a<x<b, f(x)<y<g(x)} or as R = {...

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...

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 divergen...

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 sa...

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 sid...

Page 14-3 'X ' ` 'X X X ' ` DE The solution is: which can be simplified 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 equations. The functi...

Page 14-4 The variable ODETYPE You will notice in the soft-menu key labels a new variable called @ODET (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 @ODET to obtain the string “ 1st order linear ”....

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 Lap...

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 ...

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...

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 ...

Page 15-3 start lists of random numbers is presented in detail in Chapter 17 of the user's guide. 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...

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 fo...

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 ...

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 (21.88424 and 24.51576). Press @TE T to return to the previous results screen, and/or press @@@OK@@...

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 ...

Page W-1 Warranty hp 48gII Graphing Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice...

Page W-2 7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), ...

Page W-4 Regulatory information This section contains information that shows how the hp 48gII 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 48gII in these regions...