Hp 48g Graphing Calculator Manual do Utilizador

mHEWLETTPACKARDHP 48G SeriesUser’s Guide

17. lists and SequencesCreating Lists ... 17-1List Processing...

Operations in the EquationWriter Application (continued)KeyDescriptioni^iCLEAR)Erases the display without leaving the EquationWriter application.Inser

8The HatrixWriterThe HP 48’s MatrixWriter application provides you with extensive capabilities for entering and manipulating arrays (both one-dimensio

Entering ArraysThe MatrixWriter application provides a special environment for entering, viewing, and editing arrays. You can access the Matrix Writer

Step 1: Select the MatrixWriter application, and key in the firstelement (cell 1-1):(i^iMATRIXl 2Step 2: Enter the hrst element and the rest of the

If the displayed number is wider than the cell width, an ellipsis indicates “more to the right” (as in 1 = 2,,.). The default cell width is four chara

Editing ArraysMatrixWriter provides functions that make it simple t.o edit the arrays you've entered.To edit an array you’re wiewing wi

To insert a column:1. Move the cursor to the column where you want the new column inserted.2. Press +CijL . A column of zeros is inserted.Example:

Step Jfi Set top-to-bottom entry mode. Fill in the new column.fNWI G 0 +4 1 (SPC) 3 fENTER)Step 5: Restore left-to-right entry mode, then enter the

Summary of MatrixWriter OperationsKeyDescriptionPlaces contents of the current cell in the data entry line for editing. (Press fi^fEDITjto get the EDI

Graphic ObjectsGraphic objects (or grabs) encode the data for HP 48 ‘‘pictures,’’ including plots of mathematical data, custom graphical images, and r

Getting General and PrincipEil Solutions... 20-16Showing Hidden Variables...

The PICTURE EnvironmentTo enter the PICTURE environment directly:m From the stack, press pi^fPICTURE).The Default PICTURE DisplayTo exit the PICTURE e

Turning Pixels On and OffTwo operations, DOT+ and DÛT- . allow you to selectively turn pixels on and off. If one of these keys is active, it displays

To draw a circle on the current grob:1. From within the Picture Editor, move the cursor to where you want the center of the circle,2. Press Q (or MA

2. Open the Picture Editor (f^nlfPICTURE) iEDI T ) and move the cursor to the upper left corner of the rectangular region where you want to superimpo

Step 4-' Draw a circle using the existing mark and the current cursor position.Step 5: Delete the lower semicircle.a (move to left of circle)(mo

view aI::’!* [i, ''.rineiiiiy rSirpiy^'ey;1. Save the currently displayed grob (see above) if you want to keep it.2. Recall the desir

Graphic Object CommandsThe PRG command menus contain two submenus, GROB and PICT , that contain programmable commands useful for manipulating pictures

Graphics Object Commands (continued)KeyProgrammableCommandDescription.1FIX?Returns 1 if the pixel specified by the coordinate in level 1 is on, or 0 i

Graphics Object Commands (continued)Key P r ogr ammable CommandDescriptionSUBRE PL,.CDREPL>LCDiNIMLCD-SIZEANIMATE(Subset.) Extracts and returns to

10Unit ObjectsThe Units application contains a catalog of 147 units that you can combine with real numbers to create unii objects. The Units applicati

Bar Plots ... 23-19Scatter Plots...

10For example, in (inch) is defined as .0254 n, and Fdy (Faraday) is defined as 96487 H*s. (See appendix E for a complete listing of the built-in unit

A left-shifted menu key converts the unit object in the command line or level i to the corresponding unit.A right-shifted menu key divides by the corr

By spelling unit names, you can create a unit object without switching betw'een submenus in the UNITS Catalog menu. However, the menu keys elimin

Unit PrefixesPrefix NameExponentÍ yotta -f24zetta4-21E exa+ 18F=peta+ 15Ttera+ 12Ggiga+9himega+6k or l<kilo+3h or H hecto+2Pideka+ 1PrefixName Expo

Using the UNITS Catalog MenuThe UNITS Catalog menu lets you convert the unit object in stack level 1 to any dimensionally consistent unit in the menu.

Converting Angular UnitsPlanar and solid angles are associated with actual units. However, although this distinguishes them from scalars {dimensionles

units. Such operations convert results with units to the units from the object in level 1.Temperature units require special note: see “Working with Te

Step 2: Now find t.he square root of the result.1: 8_ft^3^s''3Step 3: Find the cube root of the result.3®®1: 2_ft^SExample: Percentage.

10Working with Temperature UnitsThe HP 48 lets you work with temperature units the same ways you work with other units—except you mus

Example: Convert 25_,,.“Cv'min to °in.Step 1: First, create the unit object 25..C’C rMin.fr^ (units 1 (NXTl T E M F'1:25_“C/nin25 “Fi

27. Transmitting and Printing DataTransferring Data Between Two HP 48s... 27-1Printing...

Determine if 12 °C is greater than 52 °F. (The > operatorinterprets temperatures as levels.)1:1li^fUNITSlfNXTl TEM-F'12 = C52 “ FÌPRGÌ TEST

Step 1: First, enter the temperature.1: 150_“C(i^iUNITS)(N^ TEMP 150 “ CStep 2: Convert the units to kelvins. This conversion works correctlyat th

Creating User-Defined UnitsIf you use a unit that’s not contained in the UNITS Catalog menu, you can create a user-defined unit that behaves just like

11y^S^ig iflaiherdiaticaP F^mcJionsBuilt-In Functions and CommandsBuilt-in functions and built-in commands are subsets of HP 48 operations. An operati

Expressing Functions: Algebraic SyntaxThe difference between functions and other commands is that functions can be included in algebraic expressions.

Algebraic objects use algebraic syntax and thus use the normal rules of algebraic precedence to determine the order in which the functions are execute

11Remember: Unless you surround functions in single-quotes (the ' ‘ tick-mark delimiters), the HP 48 assumes that you are using postfix syntax wh

Press o® to obtain 7T.m Press @S) ^ obtain e. Press @(5) I to obtain t.The HP 48 also provides 40 physical constants (with their units) through

Finding Mathematical Functions on the HP 48Topic or Group AccessReferenceArithmetic Keyboard Chapter 12Exponential Functions Keyboard Chapter 12Logari

The DEFINE command lets you create a user-defined function directly from an equation. The equation must have the form ' name< . arguments&apo

Exploring the Programs in the EXAMPLES Directory . 29-19Using HP 48S/SX programs with the HP 48G/GX . . 29-20Where to Find More Information...

To execute a user-defined function:11 To use the stack, put the arguments on the stack in the same order they appear in the left side of the functio

Example: Write a user-defined function to calculate the ratio ofsurface area to volume of a box. The formula for this calculation isA 2{hw + hi + wl)

Step 5: Use BOXR to calculate the ratio of surface area to volumefor a box 9 inches high, 18 inches wide, and 21 inches long. Enter the height, width

Functions of Real and Complex Numbers12Math Functions on the Main KeyboardThe following tables describe built-in commands that appear on keyboard. 12A

Exponential and Logarithmic FunctionsKeyProgranmiableCommandDescriptionALOG Prefix. Common (base 10) antilogarithm.LOGPrefix. Base 10 logarithm.SI©EXP

Hyperbolic FunctionsHyperbolic functions are found in the MTH HYP menu ((MTH) HYP ).KeyPrograiniiiable DescriptionCommand(MTH) H Y P ;SINKSINH Prefix.

Probability and Test StatisticsUse the commands in the PROB (probability) menu (pvffFT) (TtorT) F-'ROB ) to calculate combinations, permutations,

Test Statistics CommandsKeysProgrammableCommandDescription[MTHlfNXTl PROB (NXTl:UTPCUTPCUpper-tail chi-square distribution.Prefix. Takes the degrees o

Example: The scores on a final exam approximate a normal curvewuth a mean of 71 and standard deviation of 11. What percentage of the students scored

Real Number FunctionsSome functions can only use real numbers as arguments. Among these are angle conversions, percentages, and several functions that

1The Keyboard' and DisplayOrganization of the DisplayFor most operations, the display is divided into three sections, as shown below. This config

The following illustrates the conversion to and from HMS format:12Decimal Format Hours (or degrees)1.42673Hours-Minutes-Seconds FormatHours (or degree

Percent FunctionsPercent FunctionsKey ProgrammableCommandDescription(MTHl RE%Prefix. A percent of B, ox B percent of T (A is in level 2, B is in level

12Command/DescriptionExampleInput OutputIP Prefix. Integer part of the argument.1 = “5 1« 5MANT Prefix. Mantissa of the argument.1 = 1 = 23E12 U 1.2

Complex NumbersMost functions that work with real numbers also work with complex numbers. So, the way you use complex numbers is similar to the way yo

instead.) In polar form, the magnitude and phase angle are separated by a comma and angle sign (¿). (The angle is based on the current angle mode: Deg

Real Calculations with Complex ResultsThe coinpiex-number capabilities of the HP 48 can affect the results of real-number operations. Certain calculat

12Command/DescriptionExampleInput OutputC^R Command. Complex to real; separates a complex number into two real numbers, the rectangular coordinates x

13¥eet®cs andAll vectors are array objects. The general case of n-dimensional vectors is covered in chapter 14, “Matrices and Linear Algebra”—this cha

Three-Dimensional Display ModesRectangular Cylindrical Spherical[a b c][rxy c][rz:eztt)]13x' b3D Vector ComponentsPolar mode is actually two mode

of how vectors are displayed, the HP 48 stores them internally in rectangular form.If you enter one type of coordinates, you can simply change the coo

annunciators and directory path; when you clear the message, the directory path and annunciators reappear.Annunciator areaCurrent directory path/lessa

Press (MTH1 V E U T R V . The returned values are the same as the displayed components.13Vector Math CommandsA vector, like a real number, is a single

Additional commands for manipulating vectors and elements of vectors are covered in chapter 14.Examples: Calculating with 2D and 3D VectorsTo calculat

Example: Finding the Component in One Direction. The followingdiagram represents three 2D vectors. Find their sum, and then use DOT to resolve them a

Fast Fourier TransformsA physical process can be described in two distinct ways: The change of a quantity, h, as a function of time, i (k(t)). m The

13To prepare an array for fast Fourier transforms:1. Put the array of data on the stack.2. If necessary, add zeros to the array so that all dimensio

14and Lni#ar Algeb'TjThe HP 48 has extensive capabilities for entering and manipulating arrays. Array objects represent both vectors and matrices

145. After you’ve entered all of the numl)ers in the matrix, press f ENTER) to put the matrix on the stack.For more details about using the Matrix Wr

To create an array filled with random integers:1. Enter one of the following onto the stack: A list containing the dimensions of the desired rando

elements are discarded. If the vector does not contain enough elements to complete the matrix, the undefined diagonal elements are set to zero.14Disas

contains a real number representing the number of columns in the original matrix.To extract the vector of diagonals from a matrix:1. Enter the matrix

Annunciators (continued)SymbolMeaningFiflDRadians angle mode is active.nPHDCra.ds angle mode is active.R.iZPolar/CylindricaJ coordinates mode is activ

Extracting Rows and ColumnsTo extract a particular row from an array:1. Enter the array onto the stack.2. Enter the row number (or element number if

Extracting and Replacing Elements of MatricesTo extract the array element at a specified position:1. Enter the array onto the stack.2. Enter one of

Commands for Characterizing MatricesKeyPrograrnmableCommandDescriptionfMTHl lifti K h' H ! . b. ;SIZE SIZE Command. Returns the dimensions of t

Commands for Characterizing Matrices (continued)Key ProgrammableCommandDescriptionSRRD SRADCommand. Returns the spectral radius of a square matrix. Th

Transforming MatricesTo transpose a matrix:1. Enter the matrix onto the stack.2. Press (MTH1 MhTR MFiKE TRH to transpose the matrix. The first row o

Calculating with Matrix ElementsTo add or subtract two matrices:1. Enter the two matrices onto the stack in the same order as you would to add or sub

To “divide” an array by a square matrix:1. Enter the array onto the stack.2. Enter the square matrix. The number of rows in the matrix must equal th

Step 2: Enter the name of the matrix and tlie subscripts.(a)- (hold) MAT R (release)OdD ©O J S30 ® o K o2 5ZZmTR(J,k)Dj=lk=lCTwaa iBraia iiHi i

14To conjugate each element of a complex matrix:1. Enter the complex matrix onto the stack.2. Press (MTH 1 (NXT 1 CMPL fNXT) CuNJ to conjugate each

To calculate the “best” solution to any system of linear equations:B1. Press CTfsoivrimm OK to open the SOLVE SYS i EM fl input form.2. Enter the ma

The Command LineThe command line appears whenever you start keying in or editing text. The stack lines move up to make room. If you type more than 21

14Ill-Conditioned and Singular MatricesA singular matrix is a square matrix that doesn’t have an inverse.You normally get an error if you use [llx) to

Determining the Accuracy of a Matrix SolutionThere are two approaches to evaluating the accuracy of a computedmatrix solution when you suspect that yo

Gaussian Elimination and Elementary Row OperationsThe systematic process, known as Gaussian elimination is one of the most common approaches to solvin

Gaussian elimination uses elementary row operations to convert the augmented matrix to the equivalent row-reduced echelon matrix, from which the solut

To compute the row-reduced echelon form of a matrix:1.2,14Enter the matrix onto the stack. If you are attempting to solve a system of linear equations

1. Enter the square (n x n) matrix onto the stack,2, Press f MTH ] MfiTR (IMXT) EGV . An n x n matrix of eigenvectors is returned to level 2 and an

sc hi UR Schur Decomposition. This procedure factors asquare matrix A into an orthogonal matrix Q (returned to level 2) and an upper-triangular matri

15The HP 48 lets you to do binary arithmetic—operations that work with binary integers.Binary Integers and BasesOn the HP 48, binary integer objects c

HEX, DEC, OCT, and BIN are programmable. The settings for flags --11 and —12 correspond to the current base. (For more information on flags -11 a

1. Enter the binary integer objects.2. Press ED or 0-1. Enter the binary integer onto the stack.2. Press es to find the “negative” of a binary num

right of their associated primary keys. To execute LN, for example, press the o key followed by the iW) key, Alpha keyboard. Activated by pressing

Using Boolean OperatorsThe following table contains commands from the MTH BASE LOGIC menu (fMTH) i3i-lSE (NXtI LOGIC) that perform Boolean operations

Coimiiand/DescriptionExampleInputOutputASR Arithmetic Shift Right. Performs 1 bit arithmetic right shift. The most significant bit is regenerated.1# 8

16Date, Time and Fiactian AritlimeticThe HP 48 has a sophisticated built-in clock and calendar. The HP 48 uses the Gregorian calendar which reformed t

i 16To put the current date on the stack (in number form):B Press i^rnMEl Dfl i E .To add or subtract a given number of days from a given date:1. Ent

Calculating with TimesTo set or change the current time format:1. Press OK .2. Press to highlight the time format field.3. Press \*/- \ one or mo

1. Enter the two time numbers in HMS format.2. Press f^fTIME) [NXTjin HMS format.The time number returned is also1. Enter the two time numbers in HMS

Calculating with FractionsA fraction is an algebraic representation of an arithmetic operation that hasn’t yet been evaluated. For example, the fracti

16To convert a fraction into a decimal: Put the fraction on level 1 of the stack. Press i EVAL j.To convert a decimal into a fraction involving

17Lists and SequencesCreating ListsTo enter a 1st from the keyboard:1. Use to indicate the beginning and end of a list.2. Enter the elements of the

Regulatory InformationU.S.A.I’he HI' 48 geiitTciles and useb radio iVe<iiieiicy • m iu,v and niay intorirre with radio and leievisi<)n recc

When you press (left-shift) or ®( right-shift), the d or annunciator appears in the displa)'.To cancel a shift key: To clear the shift key, pr

To append a new element to the end of a list:1. Enter the list.2. Enter the new element.3. Press Q-17List ProcessingThe way the calculator performs

Step 1: Enter a list that contains the objects, and enter the numberof objects taken at a time on level 1.(3(11) 4 (SPCl 5 (SPCl 6 (ENTER)3 (ENT

Example: Concatenate {321} and { 4 5 6 }.Step 1: Enter the two lists.OSD 3 GD2C1ED1(ENTER) I5DSD 4 fs^ 5 fSKT) 6(ENTER)Step 2: Concatenate the

Step Enter the function and execute it.0 (±3 iENlWI ft^;ST PROC1.- £ £9 4£ 5? }To apply a procedyre seqyentiaiy to elements of a list:1. Enter the li

173. Execute STREAM. STREAM is designed to take the first two elements, excute the operation, then take the result and the next element and execute a

CEM3 LIST EL.EM GET I similar to GET, but it also increments a position index. The new index is put on level 2. The original list is put on level 3

5. Enter the step size of the increment. The number of elementsgenerated is the integer portion of(final —initial) step+ 1.176. Execute SEQ .Example:

18Solving EquationsSolving an Equation for an Unknown VariableTo solve an equation for numeric answers bj' hand, you might use the following gene

value of the unknown variable for which the expression has a value of 0.Program. A program to be solved must return one real number. A solution is a v

and B contains the expression D, E, and C.;E) ' , you will see labels for el,Note For equations that use a placeholder variable—such as an integ

(f^fSYMBOLIC 1 Accesses the symbolic algebra and calculus capabilities of the HP 48 (see chapter 20).@(TIMF) Accesses the HP 48’s Alarm Browser and cl

The message is based on the value of ihe equation—the difference between the left and right sides of an equation, or the value returned by an expressi

D Plot the expression or equation in the region of the answer. The PLOT application will show any local minimum, maximum, or discontinuity.□ Check the

Press SOLVE to restart from where it left off. a Enter a guess into the unknown variable’s field and press SO to restart the root-finder searching

To enter the equation to be solved:1. Put the equation (or properly-designed program) on stack level 1. You may type it in using the command line or

183. Press Q and then the unknown variable’s white menu key. The labeled result will be returned to stack level 1 and a message interpreting the resu

To create a customized SOLVR menu:ISequationkey-definitions1. Enter a solver-list in level 1 of the stack. The syntax of a solver-list equation C key

Finding All Roots of a PolynomialA symbolic polynomial, such as x.'^ + ix'^ — 7x + 9, can also be expressed as a vector of its coefficients:

To ewaluate a polynomial at a giwen walue:1. Enter the polynomial in coefficient form onto the stack.2. Enter the given value at which you want to e

183. Enter the array of constants in the Bs field.4. Move the highlight (if necessary) to the if“ field and press S The result array (with the same

See 14-17 for additional approaches to testing the accuracy of a computed array solution.Using the Finance SolverThe Finance Solver application provid

Whenever there is no cursor being displayed, pressing any of these six keys executes the operation indicated by the colored label above them:a (or (pi

The following cash flow diagram shows a loan from a borrower's pointof view.Present value (PV) (Loan)Money received is a positive numberEqual per

The following cash flow diagram shows lease payments at thebeginning of each period.PVACapitalized value of leasey 1 y 2 y 3 y 4 ^ iPMT PMT PMT

PVFV18interest rate per compounding period—which is the interest rate actually used in TVM calculations.The present value of the initial cash flow. To

Example: Otto Tailfin is financing the purchase of a car witha 3-year loan at 10.5% annual interest, compounded monthly. The purchase price of the ca

Step 3: Solve for the payment,g)® SOLVEMftLUE DF MDNEVgN: 36 I^VR:10.5PM: 8» 750. 80 PMT: B^'iEl'5— Pi'VR: 12 PM: 0.00 EndENTER PRY

Step 1: Open the Finance Solver (if necessary) and enter values forthe known T\'M variables.ii^fSOLATEim (ifnecessary) 3UU (ENTER)13.8 (ENTCR)

4. Store values for four TVM variables: I%YR, PV, PMT, and FV. These variables define the payment schedule. (You can calculate these using the TVM me

19Differential EquationsThe HP 48 can find a solution, to a differential equation expressed as y'(i) = where the initial value of the solution i

19FINALS Contains the independent variable’s final value, ¿final- You are trying to solve ?/(tFlNAL) = (some unknown).Specifies the solution variable.

6. Enter the initial value for the solution variable.7. Enter an acceptable error tolerance.8. (Optional:) Enter a step size. Normally, the solver

Лепи labelsMenu keys -ALGi HOME >3i£i1' fl+B'4'.'ECTF: MATR LI^T HVP REAL tA:?E/ -\-f % ^, Г. . . . . . . . . . j гV--------A

3. Highlightand pressSDLVE V'(TJ=Fa,VJi F: iF4V: iF*T:INDEP: X INIT: 0 FINAL:6.5SDLN: Y INIT: 0 FINAL:TDL:.0001 iTEP: Df It ISTIFFCALCULATE

i^fSÖLVE^fTlK ®1000 £3 Q SKSD © Y 0(In} (0 T ® (E) (T} (C^ 0 T (ENTER) 1000 (^ (ENTER) 1000 0 (c^ © T ® Q dD 0 T (ENTER) 0 T (ENTER) 0 (ENTER)1 (ENTER

y" = .5j/' + ,5y + M+1Step 1: Convert the equation into a first-order equation:Example: Solve this equation for tti(l) given that y{Q) = 0

Plotting Solutions to Differential EquationsYou can plot the solution to an initiahvalue by selecting the difFerential equation option of the PLOT dia

PLDT DPTIDNS?_______TDL: mil iTEP: Df It sifiXESH-VflR: 0 H-VIEW:-6.5 6.5V-VflR: 1 V-VIEW:-3.1 3.2H-TICK: 10 V-TICK: 10 ¿PIXELS ENTER flRSDLUTE

Step 1: Select PLOT Diff Eq mode, enter the equation, set theindependent variable to T, and set the initial and final values:Example: Graph y'

1. Press OEM)2. Select Diff Eq.3. Highlight ...STIFFand pressTVPE: Diff EqDegF: iFiV: AFiT:INDEP: K INIT: 0FINPUS. 5JDLN: Y INIT: 0gSTIFFUSE STIFF

: Plot the following equation given that y(0) = 1:y' = —1000 * {y — 8in(t)) + cos{t)Step 1: Select stiff, select radians, enter the function, t

Plotting a Phase Plane for a Vector-Valued SolutionThe HP 48 also lets you plot vector-valued equations and select which vector value is plotted on wh

Step 3: Enter the equation and initial values, set the solutionvariable toTYPE:F:INDER:SDLN:»PLOT V(T)=F(T.V)^^MDiff Eq Deg 'FW*W+C*<.5*T+n ’

To display the previous menu: Press (r^f MENU ).Occasionally you may be working primarily with a particular menu, but need to use commands in anothe

20Calculus and Symbolic ManipulationIntegrationYou can calculate symbolic integrals for expressions with known antiderivatives (indefinite integrals).

...INTEGRATE jEKPR:VAR: LQ:RESULT: Humeric NUMBER FURMAT: StdENTER EKPRESSI0NThe Numeric INTEGRATE Screen.20(5. Set the number

5. Enter the name of the original integration variable in the improper integral and press fSTO ).6. Enter the name of the new integration variable a

Step 2: Use CALC to access the stack, enter and du|3licate thetransformation expression.[NXT) CFiLC (©(TANICTY3: '1^(M*(K+1))' £: 'T

1. Press f^fEQUATIOiM 1, key in the multiple integral (include all integral signs), and press [ENTER). All limits must evaluate to a number.2. Set t

20The Accuracy Factor and the Uncertainty of Numerical IntegrationNumeric integration calculates the integral of a function f{x) by computing a weight

f(x)"'ä. ^xThe striped area is the value of the integral. The shaded area is the value of the uncert ainty of integration. You can see that

functions, labeled with “A” in appendix G. For example,Sums, differences, negations, and other selected patterns of such functions. For example, &apos

7. Press [EVAL) to simplify the closed-form result.To find the indefinite integral of a function:form.field (withoutbolic (press {*/-], if1 Press SYM

2EnteinO' and Edidng ObjectsThe basic items of information the HP 48 uses are called objects. For example, a real number, an equation, and a prog

EKPR:MftR:RESULT: Numeric VRLUE:ENTER EKPRESSIUN___________________...aiFFEBENTIOTEjThe Numeric DIFFERENTIATE Screen5. Enter the value at which you w

Creating User-Defined DerivativesIf you execute d for a function that has no built-in derivative, d returns a new function whose name is der followed

Implicit DifferentiationAn implicit function of, say, x and y is a function in which one of the variables (y ) is not directly expressed in terms of t

EXPR:VAR: ORDER:RESULT: NumericTAYLOR POLYNOMIAL IENTER EXPRESSIONThe TAYLOR POLYNOMIAL Screen2. Enter the function you wish to approximate into the

7. Press OK to derive the Taylor’s polynomial approximation for the translated point.8. Press fWl O S)(PUR^ to purge the K variable.9. Ent

Isolating a Single VariableTo solve for a variable that appears only once:1. Press ri^fSYMBOLICl ff1 ffl ffl OK to open the ISOLATE Hform.2. Enter t

solution as formal (symbolic) variables. If they exist in the current directory, they are evaluated when the quadratic is solved. (Purge a variable to

Sometimes you may want to solve for a variable that’s stored in another variable. To do this, you have to convert the algebraic so the hidden variable

A subexpression consists of a function and its arguments. The function that defines a subexpression is called the top-level function for that subexpre

subexpressions. This process continues until an expansion occurs at some level—no lower levels are checked.Manipulating SubexpressionsYou can rearrang

Example: Enter the number —123.4 in the command line.Step 1: Key in the digits.123 04123.4 iStep 2: Make the number negative.-123.44Press (cancel)

Operations in the Selection EnvironmentKeyDescriptionRULESSelects a menu of relevant rearrangement transformations for the specified subexpression.EDI

Note The following tables include examples ofI transformations in the formrbefore afterThe before and after algebraics are shown in their CO mm and-

The RULES Menu—Moving TermsKeyDescription eTMove-term-left. Moves right of the specified fu to the left of the functi H+B+ tC+iVi -+ H+C+c n+B-r

The RULES Menu—Building and Moving ParenthesesKey DescriptionParenthesize-neighbors. Parenthesizes the nearest neighbors of + or *. Has no effect if t

The RULES Menu—Commuting, Associating, and Distributing (continued)Key DescriptionDistribute-left. <H+B>*C ^ H*C+B*C< > ' c ^Distr

The RULES Menu—Rearranging ExponentialsKeyDescriptionL*Replace log-of-power with product-of-log.!... ( )Replace product-of-log with log-of-power.Repl

The RULES Menu—Automatic Multiple ExecutionKey DescriptionO L>-i-Multiple-distribute-right.(SMultiple-distribute-left.(Q f'iM ult ip le- asso

Step 2: Activate the Selection environment. Then move the selectioncursor to the = sign and get the RULES menu.® . .¡5) (5 times)RULESStep 3: Move t

You can also make conditional transformations- depends on a condition you specify.-whether they occur20To replace a sybexpression with a differen

Example: An extension of the half-angle formula for sine issin(2z) = 2 sin(2) cos(z)Create a transformation based on this formula and use it

InsertReplacemodeAlpha KeysaabpcAd 5 e£fefLAHBf1C D1ir E1f F)gyhni11kt1 XLG1Hi11i1J1i1 KJ Te1m'n0aPq1pLMiH)10p( QJ( Rk___JsatIu%V—w03XXSiiT1uJlVD

Symbolic Integration PatternsThis table lists the symbolic integration patterns used by the HP 48. These are the integrands that the HP 48 can integra

Symbolic Integration (continued)PatternAntiderivativel/(SINH(®)xCOSH(<i)) LN(TANH(0))l/{SINH(0)xTANH(</.))-INV(SINH(0))SQ(0) 0V-3TAN(0)2TAN(0)-0

21Statistic^ Dñcí DalaEntering Statistical DataData can be accumulated on the HP 48 in two different kinds of objects: arrays and lists. In general, l

4. Enter the data. Use a separate row for each individual record and a separate column for each variable within a record. For example, a data set con

4. Press OK to temporarily store the matrix in EDAT. To confirm this action, jiress OK ; to cancel the action, press C fl N C L. You may also use the

Step 2: Store the matrix as TEST and open the STAT application0 0 (hold) TEST (release)(HQ(F»1(stat1 okSIHGlE-VfiRlfISLE STATISTICSTYPE: Sample_MEflN

the current statistical1. Press (r^nfSTAT) iJi4 to open the Slr4L-LE--VHRiHBLt- г г j. fomi. (Aetualh . jou шал use anj of tlie SPAT application inpu

4. Move the highlight to the column to be deleted.5. Press (NXT1 --COL . The column is deleted.6. Press fENTER) to return the modified matrix to th

To compute a statistic for one variable:1. Press (r^fSTAT 1 OK to open the SINGLE-VARIABLESTFfr I ST ICS form.2. Enter or choose the data matrix con

Pressing Q once activates Alpha-entry mode for one character only. Pressing @ twice locks Alpha-entry mode. Alpha-entry mode then remains active until

Generating FrequenciesMany times, the most meaningful aspect of a data set is its distribution. Frequencies and frequency distributions are a common m

4. Hig0.6.Enter the column number where the data to be converted is located.it the field and enter the minimum value that adatum can be and still be

for that model. It also computes and returns the covariance (sample or population) and the correlation coefficient for the regression.To perform a reg

To plot a scatterplot of the data and the regression curve:1. Perform the regression as described above.2. Press fi^fSTAfl F’LUT SCflTFi to plot the

2. Enter or choose the data matrix containing the data with which you are computing.3. Enter the column numbers of the independent (M...

22PlottingUsing the PLOT ApplicationThe PLOT application lets you draw graphs of one or more functions in various formats, calculate roots and other p

TVPE: Function ¿-DegEO:INDEP: X H-VIEW:-6.5 6.5 _flUTDSCflLE V-VIEW;-3.1 3.2ENTER FUMCTIDNtS), TO PLDT__________The Default PLOT Screen222. If nec

1. Use the same general procedure as for plotting an expression, but make note of the following differences when the plot type is For equations whos

4. For Function, Polar, and Parametric plot types, put a check-mark in the SI MULT field (on the PLOT OPTIONS screen) if you want the plots of all ex

For F'urict i on, l-'olar. and F^aгanet r :i. c plot types, TRACE mode redefines the arrow keys. a and move the cursor

The Four CHARS ScreensCHBRflCTERi 0-63 ¡ a,,,0123456789: 5 <=>?KEV: CNDNEJ______NUM= 0H«iiaB8iiMBiiiagcBia!№iraniiCH

22KeyDescription(DEL)Erases the rectangular region defined by the cursor and the mark. It is a shortcut for EDIT (NXT)(STO)Places a copy of the curren

Setting Zoom DefaultsSeveral of the zoom operations make use of the current zoom factor and recenter option settings, which you can control.CtOrSa1.

22fiSTZoom-In. Decreases both horizontal and vertical scales by the current zoom factors.Zoom-Out. Increases both horizontal and vertical scales by th

Analyzing FunctionsThe PICTURT FCN menu lets you analyze the mathematical behavior of plotted functions. You use the graphics cursor to indicate the r

22The PICTURE FCN MenuKeyDescriptionin the PICTURE menu):R 0 0 TRoot. Moves the cursor to a root (intersection of the function and the r-axis) and dis

The PICTURE FCN Menu (continued)Key DescriptionExtremum. Moves the cursor to an extremum (local minimum or maximum) or other critical point and displa

Understanding the PLOT Reserved VariablesThe PLOT application makes it easy to declare the plot and display ranges, the scale and resolution of the pl

ZPAR stores zoom information: the horizontal and vertical scale factors, a recenter flag, and (sometimes) a copy of PPAR to be used by the Zoom-to-Las

Contents of the PPAR ListElementDescriptionDefault^min)A complex number representing the coordinates of the lower left corner of the display range.(-6

VPAR contains the current settings that determine the View Volume, eyepoint, and plotting density for the six plot types for functions of two variable

rfP Bfs,; B C'WKSl HEWLETT mL'KM PACKARDHP Part No. 00048-90126 Printed in Singapore

ObjectsDelimiters KeysExamplesReal numbernonej. 4» i"' 5Complex number< > (30K O B ¿i J |i 1 C a iString(3CZ)ArrayJ (SKIDC 4,8 -1.3 2,

Contents of the VPAR List (continued)ElementDescriptionDefaultleftThe smallest value for the horizontal axis of the input plane.-1rightThe largest val

23Plot TypesFunction PlotsThe Function plot type plots equations that return a unique f{x) for each value of x. It is the default j)lot type and the o

b. K H b‘ b.To enter computed endpoints, use fNXT) CFlL C (see page 24-6).When checked the vertical display range is automatically scaled based on sam

T T r':k'This determines the resolution of the plot. It is the horizontal distance (in units or pixels—see next field) between two plotted

Press (VAR) E; PLOTSwuirgiBasraiigffrM^After plotting, press (CANCEL) (r^(PLOT) to review the PLOT forms that generated the plot. Experiment changing

-VIEWi:FiUTOSCiiLEOPTSERASEDRAWEnter the vertical display range in the two fields, low endpoint in the left and high endpoint in the right. When check

TRACE Mode s and move the cursor along the plot of the current function, a moves the cursor to the next lower value of the independent variable and (

Parametric PlotsThe Default PARAMETRIC Plot ScreensTYPE: Parametric DegINDEP: K H-MIEH:-6.5 6.5 _ftUTOSCPLE V-VIEW:-3.1 3,2EHTEFi CnMPlEX-VftlUEP F

the plot accordingly, leaving you in the PICTURE environment when hnished.The Parametric PLOT OPTIONS FormINDEh:fM;fli-lESrni-lNFr23PI PELSTICl r iEnt

Special Notes Algebraic expressions should be entered in complex form, ' < F« G ) ' , where F and G are each expressions involving the i

4. Optional: Press OS (new line) to start a new row in the display.5. Key in the rest of the matrix. You don’t need to add C ] delimiters for subseq

Step 2: Set the independent variable, the display and plotting ranges,simultaneous plotting, and the tick-spacing as shown.L t W =-T T r:SI MLPLOT DP

Differential Equation PlotsDifferential equation plotting is covered in detail in chapter 19. For an additional example of a differential equation plo

The Default CONIC Plot ScreensPLOT ^^*PLDT OPTIDNS^^»TYPE: Conic De<5IHPEP: M LQ: Df 11 HI: Df ItEG: MiliiiaiM¿AXES ¿CONNECT DEPND: YINDEP: X H-VIE

between two plotted points. The default step-size for C is an interval equal to 1 pixel.When checked, the step-size is interpreted to represent pixel

Truth PlotsTruth plots evaluate expressions that return true (any nonzero real number) or false (0) results. At the coordinates for each pixel, the pi

plots are usually different than display range (see page24-3).HI: Enter the largest value of the independent variablethat you want plotted. Plotting

fVAR)After plotting, press (CANCEL) (r^fPLOT) to review the PLOT forms that generated the plot. Experiment by changing values or settings and redrawin

Return to the PLOT form, change the plot type to Truth, choose the truth expression INEQ into the EQ» field, and reduce the plotting range to the regi

Histogram PlotsA histogram divides the range of values of one variable into a number of bms and for each bin shows the number of data points for which

and draws the plot accordingly, leaving you in the PICTURE environment when finished.The Histogram PLOT OPTIONS FormEiS See the Function plot type.Se

right. In addition, you can use the following keys to edit data in the command line:Command Line OperationsKeyDescriptiona®Move the cursor left and ri

HUTuSChLEs When checked, the horizontal display range is setfrom 0 to n, where n is the number of data points in EDAT and the vertical display range i

The Scatter PLOT Formi:::. I"! i i b.Enter the data matrix or the name of the data matrix containing the data to be plotted.Enter the column nu

Plotting Functions of Two VariablesThere are six different plot types that can be used to help you visualize functions of two variables. Some of these

Output GridsSampling GridSlopefield/Ps-ContourTransforming Sampling Grid to Output GridA fourth plot type, YSlice, performs the same transformation as

23The YSLICE ViewThe final two, Wireframe and Pr-Surface, transform the 2-dimensional sample grid into a three-dimensional output surface. The plot th

Note that the three-dimensional coordinate system on the HP 48 is somewhat constrained compared to its abstract, mathematical counterpart. Specificall

The Slopefield PLOT Form23Shows the current angle mode. Change it by pressing one or more times or by using CHOOo.Enter the current expression, equati

Example 2: Plot the Slopefield of the differential equation,y'{x) = Then superimpose the solution of the equation with a particular initial cond

Step 8: Draw the plot without erasing first so as to superimpose theDiff Eq plot on the previous Slopefield plot.DR I23Wireframe PlotsThe Wireframe p

The Default WIREFRAME Plot ScreensPLDTiTVPE: Niref rameEO:INBEP: X STEPS: 10BEPNi: Y STEPS: 8ENTER FUHCTIDHtS)._TD PLDT__________^:)Я1яШ!Шта11ИМ||Г|

typing aids (for example, (SIN) types SIH< )). Other commands are executed immediately (for example, fSTol or fj^(PURGEl).Program-Entry M

i tiiExample:Enter the «/-coordinate of the eyepoint. It must be at least one unit smaller than the value for Y--NEflR» above. The greater the differe

The Default PS-CONTOUR Plot ScreensPLOTSINDEP:DEPNB: Y ÎTEPJ: 0ENTER FUNCTIDHtSJ_Tfl PLOT___________iJïïfcaiMiiiiiHaaBiïïiiiaijmMjraaïïBi,^^»Pl£T DPT

Press fVAR) EXflM f NXT1 P S C NAfter plotting, press (CANCEL) ft^fPLOT) to review the PLOT forms that generated the plot. Experiment by changing valu

STEPS: Enter the number of columns in the sampling grid.DEPND: Enter the name of the second independent variable.STEF'S: Enter the number of r

Gridmap PlotsThe GRIDMAP plot type transforms (maps) the specified rectilinear sampling grid via the current complex-valued function. The coordinates

The Gridmap PLOT OPTIONS FormX-LEFTiiK-RIGHT"Y-NEMRiiv-fhr;XX-LEFT s XX-RIGHTYY-HEnR: Y Y P H K "Example:Enter the horizontal display range

The Default PR-SURFACE Plot Screensplot!TYPE: Pr-Surface ¿:Deg EQ: MilililldiiiM^^INPEP: X STEPS: 10DEPNP: Y STEPS: 8ENTER FUNCTinNtSli^Tn PLOT____

Enter the x-axis range (“width’’The Pr-Surface PLOT OPTIONS FormX-“K i bh V N ELbHXEiiYES: 5 I Iof the View Volume.Enter the i/-axis range (“depth”

Press fVAR) EkFIM fNXTl PS URAfter plotting, press fCANCEL) (r^iPLOT) to review the PLOT forms that generated the plot. Experiment by changing values

24Pia? OptSc})?!!??Labeling and Locating the AxesTo label the coordinate axes with the variable names:After the plot is drawn, press EDIT (NXT) LHBEL.

Step 2: Process the command line to complete the calculation.(ENTER)R1: 10 wamiSmamBniiin3iff!>3TOia?H3iRecovering Previous Command LinesThe HP 48

3. Press (4^(PL0T) PPHR (NXT 1 flXES to store the intersection point.4. Press fr^fPLOT) E R R S E DRAW to redraw the plot using the new axes interse

Plotting Range vs. Display RangeThe plotting range is the range of the independent variable (or variables) over which the current equation is evaluate

Example: Assume PICT is its default size, shown in figure (a)below.To double the x range of PICT in the horizontal direction and keep the same scales

{#0#0}(10.2)(a){#0#0}24(20. 2)(c)Changing the Size of PICTTo extend the plotting range beyond the limits of the display:1. Change the the size of PIC

3. After all plot parameters are set, press ERASE DRfiW to draw the plot. You will only see a portion of the plot in the display.4. Press (4^(PICTUR

The following set of procedures illustrate how to accomplish theseapproaches to saving and restoring plots.To save the current plot picture in a varia

4. If the plot is a three-dimensional plot, press CD> type VPflK and press fSTO ) to restore VPAR.5. Press 0. type PPFiK and press (STO ) to rest

25i5li(? i&cgpali'iHii LibraryThe Equation Library is a collection of equations and commands that enable you to solve common science and engi

8. For each known variable, type its value and press the corresponding menu key. Press fNXT) if necessary to access additional variables.9. Optional

Because EQ and Mpar are variables, you can have a different EQ and Mpar for each directory in memory.Using the Menu KeysThe actions of the unshifted a

Viewing or Editing an ObjectLocation of ObjectViewing/EditingEnvironmentKeystrokes to View or EditLevel 1Command line RiKEDITlBest (see below)2)Level

Browsing in the Equation LibraryWhen you select a subject and title in the Equation Library, you specify a set of one or more equations. You can get t

Viewing Variables and Selecting UnitsAfter you select a subject and title, you can view the catalog of names, descriptions, and units for the variable

25Using the Multiple-Equation SolverThe Equation Library starts the Multiple-Equation Solver automatically if the equation set contains more than one

Solver Menu Keys (continued)OperationKey ActionSolve for allS) Pil-LCreates variables if necessary and solves for all variables not user-defined (or a

Meanings of Menu LabelslabelMeaning[IIBoIljValue xO not defined by you and not used in the last solution—it can change in the next solution.1...

Xi = Vo + a tiX2 = Vo + a to{X2 - xi) = a {to - h)To create more robust equations, you can include functions that ensure proper and faster ca

25Interpreting Results from the Multiple Equation SolverThe Multiple-Equation Solver solves for variables by repeatedly looking through the set of equ

Wrong units. A known or found variable may have units different from those you assumed. These are global variables. If the variable existed before thi

Using the Constants LibraryThe Constants Library contains a collection of common physical constants and quantities. You can use them in equations and

Constants Library (continued)NameDescription Value (SI)Roo Rydberg constant10973731.534 m“iaOBohr radius0.0529177249 nmBohr magneton9.2740154E-24 J/TN

2 Using the EDIT MenuWhenever the command line is present, you can press QdDiT) to get the EDIT menu. The EDIT menu is also displayed whenever you pe

25To put a constant from the library on the stack:1. Press pi^f EQ LIB ] COL IB CONLI to open up the Constants Library.2. Move the highlight to the

User-Defined UnitsThe Equation Library provides four user-defined units: “gmol” (gram-moles, mol), “Ibmol” (pound-moles, approximately 454 mol), ‘&quo

26Tiine Mariageiii'f^nlUsing the Clock (Date and Time)When you display the clock, it appears in the upper-right corner of the display. It shows t

To change the date or time;1. Press ©ItimD® UK to open the SE I Tint HMD Dfi I E dialog.TIME AND DflTE^^time: B:48:27 F)Mbate: 4 ^30 /93 M/D/YENTER

To set an appointment alarm:1. Press (acoMDffj OK to open the ShT HLflRrI dialog.MESSAGE:TIME: 9:31=00 AMDATE: 1 i' 3 -'94REPEAT: NoneENT

Responding to AlarmsWhen an appointment alarm comes due, the (<•)) annunciator turns on, the beeper sounds at short intervals for about 15 seconds,

case of a control alarm that executes a program to take measurementsat short intervals.To recover from a short-interval repeating alarm:B Press the fO

To automatically delete and reschedule them, press 43 Pj^fMODESl F'LFlG CF .To make them past-due and not reschedule them, press 43 m f^fMODESl F

27Tesng nn-d' Printing P?ds Transferring Data Between Two HP 48sTo transfer objects from one HP 48 to another:1. Line up the infrared ports by l

3Siadi_____________________________________________The stack is a series of storage locations for numbers and other objects. In general, you will use

PrintingWith certain exceptions, printing commands print objects according to these guidelines:m An object is printed with its delimiters. An objec

Setting Up the PrinterTo set up the HP 82240B infrared printer:1. Place the HP 48 and the printer on a flat surface. Aim the A (near the Hewlett-Pack

I PORT:I DEJECT;_DEL-SPflCE BELOV: 1.0 ¿LINEFI PRINT jCHPDSE PRINT PDRT—EglRi^— ! itaaiitaThe Infrared PRINT Screen4. Press CHOOS, move the highligh

PORT: Ñire□EJECT:_DEL-SPfiCE KLfiT: Newi ¿LINEFEftUp:9600 PARITY:None LEN:80 ENTER DEJECT(g) TO PRINTPRINT;The Wire PRINT Screen3. If necessary, p

27To print the object in level 1:1. Be sure that printer and HP 48 are properly set up for printing.2. If the port and print parameters are set prop

Transferring Data Between the HP 48 and a ComputerPreparing the Computer and the HP 48Use a Serial Interface Cable to connect the HP 48 and the comput

2. Keep the HP logo on the 4-pin connector facing up, then plug the cable into the HP 48. You should feel it lightly snap into place.,Not quite flush

xLflT»CHK s EiHUD i!IRITYOvRlSelect one of four character translation options (only available for Kermit). See page 27-15 for more details.Select one

Binary is much faster, but if you want to edit objects on the computer use ASCII.3. Computer. Execute the Kermit command to make it the server, such

1. Computer. Change to the directory where the files are to be stored.2. Computer. Run the program that has Kermit.3. HP 48. Press (r^iI/O 1 ffl OK

To use a one-argymenl command:1. Enter the argument into level 1 (or into the command line).2, Execute the command.Example: Use the one-argument co

Backing Up HP 48 MemoryYou can back up and restore the contents of the entire HOME directory in a fde on your computer. The HOME directory includes al

To restore HP 48 user memory from a computer file:1. Transfer the computer file to an HP 48 variable using one of the data transfer methods discussed

Using XMODEMThe XMODEM protocol built into the HP 48 doesn’t perform any CRC checking, but it will work with a computer-based XMODEM program that does

Using Other Serial ProtocolsYou can send and receive data and commands with serial devices that don’t use Kermit protocol, such as serial printers and

Summary of ASCII Data Translation OptionsOption 1 Option 2 Option 3Data Sent by HP 4810 ^ 10,13 10 10,1310 10,13128 ^ trans 128 ^ trans159 ^ trans 255

To transfer serial data %i'sih a non-Kermit serial dewice:1. Press S3QZ3 lopfi R and set up the I/O parameters to match the serial device. If ne

The I/O Menu—Serial I/O CommandsKeyProgrammableCommandDescriptionS)Q2o]SERIR:!Rfc.27b i 1 f 11XMITSRECVSTIMESBRKSends the string in level 1 without Ke

The I/O Menu—Serial I/O Commands (continued)KeyProgrammableCommandDescriptionfc: Li f- L tBUFLENReturns the number of characters in the input buffer t

28’anPorts and Piiyg-^n CardsPort Memory and Plug-In Card SlotsPort memory, also referred to as independent memory, is structureddifferently than user

2401 fsp^ 41= 7Since the HP 48’s stack retains previous results, it makes it especially easy to perform chain calculations.1. If necessar

Port 0Port 0 is the only port memory available on all HP 48s. The memory for port 0 is taken out of user memory—so objects stored in port 0 decrease t

Using Backup ObjectsThe HP 48 uses a special object type, the backup object, to store backup data. A backup object contains another object, its name,

28To ewaluate a tjackyp object:B Display the appropriate PORT menu, then press the menu key for the object, orB Enter the backup identifier for the ba

memory for another port). Level 2 contains a list of backup identifiers and library identifiers.To copy backup objects from a card into another HP 48:

CSUtiOn Executing RESTORE overwrites the entire contentsof user memory with the contents of the backup object. To save the stack, you can save it in

Libraries offer faster access to the variables used by applications. You can designate variables used in applications as “hidden” (unnamed) var

28you use, a port in one of the card slots, the appropriate slot must contain a RAM card set up as unmerged port memory.3. Press fSTO).4. Optional:

Installing and Removing Plug-In CardsThe two slots for installing plug-in cards are designated Card Slot 1 and Card Slot 2. Card Slot 1 is closest to

1. Do not use this procedure to replace the battery in a RAM card—it could cause loss of memory in the RAM card. To replace a battery, see “To change

4. Write the date of installation on the card using a fine-point,permanent marker. The date is important for determining when to replace the battery.

NoticeThis manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no wa

3 Manipulating the StackThe HP 48 enables you to reorder, duplicate, and delete specific objects on the stack.To swap the objects in levels 1 and 2:

1. Store any objects currently on the stack that you want to save. (Installing or removing any plug-in card erases the stack.)2. If the card you wish

6. Remove the port cover at the top of the calculator by pressing down against the grip area and then pushing in the direction shown. Removing the co

9. Slide the card firmly into the slot until it stops. When you first feel resistance, the card has about | inch to go to be fully seated.10. Replace

Expanding User Memory with Plug-In RAM CardsYou can extend built-in HP 48GX user memory by installing a RAM card into Card Slot 1 and merging its memo

28To merge memory on the RAM card in Card Slot 1 with yser memory:1. Turn off the calculator and make sure the card is not wnte-protected.2. Turn the

To free a merged RAM card and mo¥e backup objects there:1. Back up the desired objects into port 0—see “To back up an object” on page 28-3.2. Enter a

29ProgicaimiiitcRij the iiiPThis chapter is an introduction to some of the programming capabilites of the HP 48. For a comprehensive command listing a

The Contents of a ProgramAs mentioned above, a program contains a sequence of objects. As each object is processed in a program, the action that resul

Examples of Program ActionsProgramResults i: 1 2 :i-1 !!"Hello" i fl B2: "Hello" 1 « H P> s ’1+2’ :i-U 'l+2‘ s ’1+2’ +HUM

Step 2: Raise the value to the 4th power.4£: 2.10526315789E-Z1: 1.96438026103E-7Step S: Add the result to the original value.Q1: 2.10528280169E-2

So the following program takes two numbers from the stack and returns a numeric result:a b3-b:Calculations in a ProgramMany calculations in programs t

program you can use branching structures to control the execution flow.)You can take advantage of structured programming by creating “building-block”

In Program-entry mode (PRG annunciator on), command keys aren’t executed—they’re entered in the command line instead. Only nonprogrammable operations

Press fCANCEL).Enter a program that takes a radius value from the stack and calculates the volume of a sphere of radius r usingV = -7rr’’

Step 1: Enter the program.« + r ' 4^3*ir*r''3'^NUfl»•fli5gni8mafirH'aB)Hjiia4iiBifarHaIS)E3(3Q©S)R(ZDQ4 0 3 0S1I30 © Q R (F3

4. Take any action: To see the next program step displayed in the status area and then executed, press ;5:5T . To display but not execute the n

Using Programming StructuresA programming structure allows a program to make a decision about how it should execute depending on given

it’s automatically evaluated to a number—you don’t need EVAL.>NUM orIF begins the test-clause, which leaves a test result on the stack. THEN remove

Loop structures let a program execute a sequence of commands several times. To specify in advance horn' many times to repeat the loop, use a defi

the increment value is negative, the loop is executed if the counter is greater than or equal to finish. Otherwise, execution resumes following STEP.F

j Step 2: Add the two numbers.©1: 3.13?3560415Z|Restoring the Last Stack (UNDO)The UNDO command (r^f UNDO) restores the stack to the way it was befo

29The increment value can be positive or negative. If the increment is positive, the loop is executed again if counter is less than or equal to finish

Many conditions are automatically recognized by the HP 48 as error conditions—and they’re automatically treated as errors in programs.A command with a

29Using Local VariablesThere are disadvantages to using global variables in programs: After program execution, global variables that you no longer

l HOME }4:3!102:61 =£0thena creates local variable a = 20, a b creates local variables a = 6 and b = 20. + a b c creates local variables a = 10, 6 =

29want it evaluated—the program should execute EVAL after the object is put on the stack.Using Local Variables within SubroutinesBecause a program is

It takes an unlimited number of arguments (can use an unlimited number of local variables), but returns one result to the stack.If a program begins

programs contained in PLOTS each plot an example of a different plot type. The remaining objects are example programs that accomplish a variety of dif

There are no guarantees that such programs will run without errors on the HP 48G Series calculators. However, most older programs that use only User-R

30Customizing MenusA custom menu is a menu that you create. It can contain menu labels for operations, commands, and other objects

€ HOME i4-.1.23453: 2.3456Current£: 3.456?stack level ...—!► -{ fl 1.2345 }raiiiiRstack pointer1. Press (r»~|(STACKl (or t-s 1 !\

Commands. Almost all command names behave like normal command keys.You can include backup objects in the list defining a custom menu by tagging the

Step 5: Create a tagged object from the contents of levels 2 and 1.^THG l! MOLUME: .0010?5_r^3Step 6: Display the current contents of CST.CST£ yO

To specify functionality for shifted keys: Inside the CST list, replace the object by an embedded list of objects; [ object ^.nshifted objeciietts

User ModesTo actiwate User mode: If you want to execute only one operation (luSR), press (<^[USER~|. (It turns off after the operation.)B If you

1. Enter a list containing two parameters—the command to be assigned to the key followed by the three-digit key location number (see above).2. Press

Disabling User KeysYou can disable user keys that are unassigned—so they do nothing. This lets you control the user keys that are active, including as

To edit the user key assignments:1. Press f^(MODES) KEYS RCLK (the RCLKEYS command).2. Press QdH) and edit the key-assignment list.3. Press modes!

ASupport Batteries, and ServiceAnswers to Common QuestionsYou can obtain answers to questions about using your calculator from our Calculator Support

Q: What does an h m a number mean (for example,A: Exponent of 10 (for example, 2.51 x 10“^^), See “Keying In Numbers” on page 2-1 and “Setting the Dis

Q: What do three dots (,„) mean at either end of a display line?A: The three dots (called an ellipsis) indicate that the displayed object is too long

Interactive-Stack Operations (continued)Key DescriptionR 0 [... L..Moves the contents of the current level to level 1, and rolls upwards the portion o

Environmental LimitsTo maintain product reliability, avoid getting the calculator and plug-in cards wet, and observe the following temperature and hum

Under typical use, a RAM card’s battery should last between 1 and 3 years. Be sure to mark the card with the battery-installation date, and, in case t

Remove the calculator battery-compartment door by pressing down and sliding it off away from the calculator. Be careful not to press the calculator ’s

•5. Position the batteries according to the outlines in the bottom of the battery compartment. Avoid touching the battery terminals. Batteries are eas

CSUtion Make sure you turn on the calculator before youchange a RAM card battery. RAM cards run off the calculator batteries only while the calculato

5. Install a fresh, 3-volt 2016 coin cell in the plastic battery holder, and reinsert the holder (with battery) into the card. Be sure to install the

6. If the problem still exists, perform a memory reset. You may lose data during a memory reset, so do this only if you must:a. Press and hold IHD-b

1. Press and hold (ON ) 2. Press and release the “C” key (the key with C next to it).3. Release (M)- The empty stack display should appear.If the

To exit the keyboard test (system halt):1. Press and hold [ON).2. Press and release the “C” key (the key with C next to it),3. Release (ON). The em

5. Press and release the “D” key (the key with D next to it).6. Release (ON). A vertical line will appear at both sides and at the center of the dis

Most of the operations in the Interactive Stack menu have equivalent programmable commands (see “Stack Command Menu” on page 3-11).The redefined keybo

B will appear at the top left corner of the display. If OK appears to the right of IRLB, the calculator passes this test. If OK doesn’t appear, the ca

To return to normal calculator operation (system halt):1. Press and hold (ON).2. Press and release the “C” key (the key with C next to it).3. Relea

SHALL HEWLETT-PACKARD COMPANY BE LIABLE FOR CONSEQUENTIAL DAMAGES. Some states, provinces, or countries do not allow the exclusion or limitation of in

B In other countries: Contact your Hewlett-Packard sales office or dealer or write to the Corvallis Service Center (listed on the inside of the back c

B rrop MessagesThis appendix lists selected HP 48 messages, arranged alphabetically.Messages Listed AlphabeticallyMessageMeaning# (hex)H ]Alarm not ac

Messages Listed Alphabetically (continued)MessageMeaning# (hex)HP Solve application or ROOT returned same value at every sample point of current equat

Messages Listed Alphabetically (continued)Message Meaning# (hex)A Statistics command was executed when SDAT did not contain enough data points for cal

Messages Listed Alphabetically (continued)Message Meaning# (hex)Inualid NaPieReceived illegal filename, or server asked to send illegal filename.C17In

Messages Listed Alphabetically (continued)MessageMeaning# (hex)1 ri-B i G JiU D -B X- •“!L. i'-j N G ‘9Nonlinear curve fit attempted when SDAT ma

Example: Use the Interactive Stack to insert the number 1.2345 intothe command line, creating the list C Fi 1 = 2345 >.Step 1: Put these numbers

Messages Listed Alphabetically (continued)MessageMeaning# (hex)equat i onPlot or HP Solve application executed with nonexistent EQ.609Ho Room in PortI

Messages Listed Alphabetically (continued)Message Meaning# (hex)Object Hot in Port Attempted to access a nonexistent backup object or library.OOC\U|-r

Messages Listed Alphabetically (continued)MessageMeaning# (hex)Power LostCalculator turned on following a power loss. Memory may have been corrupted.0

Messages Listed Alphabetically (continued)MessageMeaning# (hex)T i P'!0OUt Printing to serial port: Received XOFF and timed out waiting for XON.C

Messages Listed Alphabetically (continued)MessageMeaning# (hex)Wrong firgunentUser-defined function128evaluated with an incorrect number of parentheti

ilenuiCNo.Name0Last Menu1 CST2 VAR3MTH4 MTH VECTR5MTH MATR6MTH MATR MAKE7MTH MATR NORM8MTH MATR FACTR9MTH MATR COL10MTH MATR ROW11 MTH LIST12 MTH HYP1

No. Name53 UNITS TEMP54UNITS ELEC55 UNITS ANGL56 UNITS LIGHT57 UNITS RAD58 UNITS Vise59UNITS Commands60 PRG ERROR IFERR61PRG ERROR62 CHAR63 MODES64 MO

DSystem FlagsThis appendix lists the HP 48 system flags in functional groups. You can set, clear, and test all flags. The default state of the flags i

System Flags (continued)FlagDescription-11and-12Binary Integer Base.HEX: -11 set, -12 set. DEC: -11 clear, -12 clear. OCT: -11 set, -12 clear. BIN: -1

System Flags (continued)flagDescription-27Display of symbolic complex numbers.Clear: Displays symbolic complex numbers in coordinate form (i.e.Set: Di

stack Command MenuThe following table describes the programmable commands that manipulate the stack. These commands are available from the f#^(STACK)

System Flags (continued)Flag Description-36I/O Receive Overwrite.Clear: If file name received by HP 48 matches existing HP 48 variable name, new varia

System Flags (continued)FlagDescription-45thru-48Number of Decimal Digits.Combined states of flags —45 through —48 sets number of decimal digits in Fi

System Flags (continued)Flag Description-57 Alarm Beep.Clear: Alarm beep enabled. Sei: Alarm beep suppressed.-58Verbose Messages.Clear: Parameter vari

fable of UnitsEHP 48 UnitsUnit (Full Name) Value in SI Unitsa (Are)100A (Ampere)1 Aacre (Acre)4046.87260987arcmin (Minute of arc)2.90888208666 X 10&ap

HP 48 Units (continued)Unit (Full Name)Value in SI Unitsdyn (Dyne).00001 kg-m/s2erg (Erg).0000001 kg-m^/s^eV (Electron volt) 1.60217733 X 10-1® kg-m®/

HP 48 Units (continued)Unit (Full Name)Value in SI Unitskip (Kilopouiid-force)4448.22161526 kg-m/s^knot (Nautical miles per hour).514444444444 m/skph

HP 48 Units (continued)Unit (Full Name)Value in SI Unitspk (Peck).0088097675psi (Poxmds per square inch)6894.75729317 kg/m-s^pt (Pint).000473176473 m®

FTable of Byilt-ln EquationsThe Equation Library consists of 15 subjects (corresponding to the sections in the table below) and more than 100 titles.

Subjects and Titles (continued)3: Fluids (29,29)1: Pressure at Depth (1,4)2: Bernoulli Equation (10,15)3: Flow with Losses (10,17) 4: Flow in Full Pip

Subjects and Titles (continued)9: Optics (11,14)1: Law of Refraction (1,4)4:Spherical Reflection (3,5)2: Critical Angle (1,3)5; Spherical Refraction (

Command/DescriptionExampleInput OutputOVER Returns a copy of the object in level 2.1 it 11: ' flB 'PICK Returns a copy of the object in leve

Operatic"r hThis index contains reference information for all operations in theHP 48. For each operation, this index shows: Name. The name asso

Name, Key, or LabelDescription, Type, and Keys PageAssociate left.O (4^ Í EQUATION) K U L t b H20-23Executes M until no change.O fi^l f EQUATION) (◄ )

Name, Key, or LabelDescription, Type, and KeysPageAMORTCalculates the amount of principal, interest, and balance for a nmnber [x) of payments for the

Name, Key, or LabelDescription, Type, and KeysPage^ARRYCombines numbers into array.C fPRG) TVPE -iflRR14-4ASINArc sine of a number (a;). A f^fASIN)12-

Name, Key, or LabelDescription, Type, and KeysPageBEEPSornids beep at a frequency {y Hz) for x seconds.C fPRGlfNXTl OUT iNXTl BEEP4-10BEGToggles payme

Name, Key, or LabelDescription, Type, and KeysPageB^R Converts a binary integer (¿,’) to a real nmnber.C fMfiTl BfiSE BAR15-3CALCCopies the contents o

Name, Key, or labelDescription, Type, and KeysPageCHOOSECreates a user-defined choose box from a title string (c), a list of objects (>/), and the

Name, Key, or LabelDescription, Type, and KeysPageCNTRRedraws graph with center at current cursor position.O (PICTURE 1 2:0 CiM (nxtI cm r22-8-»COLTra

Name, Key, or LabelDescription, Type, and KeysPageCONCreates a constant array from a list of dimensions (y) and the constant number {x).C iMTH) MFiTR

4ModesThe HP 48 operates using many different modus, depending on the nature of the operation it's performing. Many of these modes are controlled

Name, Key, or LabelDescription, Type, and KeysPageGRDIRCreates a directory named x.C fiilf MEMORY) DIR CRDIRH-4CROSS Cross product of two vectors (y X

Name, Key, or LabelDescription, Type, and KeysPageDATERetuiras system date.C fi-DiTIMEl DFlTE16-2DATE+Adds or subtracts a number of days (r) from a da

Name, Key, or LabelDescription, Type, and KeysPageDEL^ Deletes all characters from cursor to start of next word.i^ilf EDIT 1 DEL -J- О ... ED I T ; D

Name, Key, or LabelDescription, Type, and KeysPageDNEG Double negate.0 RiliEQUATION 1 RUL.ES DMEG20-21DOBegins indefinite loop.C fPRG) BRCH DCi DO29-1

Name, Key, or LabelDescription, Type, and Keys PageDRPN Drops all objects from stack at and below the current stack pointer.O ii¥liSTACK)(NXlH DRPH3-8

Name, Key, or LabelDescription, Type, and KeysPageEEXTypes E or moves cursor to existing exponent in command line.O fEEX)2-2EGV Computes the right eig

Name, Key, or LabelDescription, Type, and KeysPageERASE Erases PICT.O (T^fPLOTl tNlHot22-1ERRM Returns last error message.C fPRG ) ÍNXT1E R R 0 R ERR

Name, Key, or LabelDescription, Type, and KeysPageE" Replace power-product with power-of-power. O |#t1íEQUATION )(2) RLiL ty h""20-25E(

Name, Key, oi’ LabelDescription, Type, and KeysPageFORBegins a definite loop with beginning (y) and ending (x) loop-counter values.C fPRG) EiKUH I-UF

Name, Key, or LabelDescription, Type, and KeysPageGETIGets element in specified position (r) from array or list (2/) and increments index.C fPRGl LIST

Contents1. Tlie Keyboard and BisplayOrganization of the Display ... 1-1The Status Area, Ann

B Beep modeB Clock display modeB Fraction mark modeSetting the Display ModeThe display mode controls how the HP 48 displays numbers. (Notethat numbers

Name, Key, or LabelDescription, Type, and KeysPageHEXSets hexadecimal base.C iMTH) BASE НЕл15-1HISTOGRAMSelects HISTOGRAM plot type.C r^iliPLOTUNXTl S

Name, Key, or LabelDescription, Type, and KeysPageIFERRBegins test danse.C (PRGl (NXT) E R R 0 R IFERR I h E R R29-15QiferrTypes IFERR THEN END.O iPRG

Name, Key, or LabelDescription, Type, and KeysPageINFODisplays information about the most recent computation by the root-finder.O (1^(solve! S0LVE INF

Name, Key, or LabelDescription, Type, and KeysPageKERRM Returns text of most recently-received KERMIT error packet.c raflT^iNXfl KERRH-10KEYReturns nu

Name, Key, or LabelDescription, Type, and Keys PageLINEDraws line from mark to cursor,O r^TlfPICTURE 1 EDIT LINE9-3SEINEReturns best-lit line for data

Name, Key, or LabelDescription, Type, and KeysPageLOGFITSet curve-fitting model to logarithmic.C r^fSTAT) 2PflR riODL LUGFILQReturns the LQ factorizat

Name, Key, or LabelDescription, Type, and KeysPageMARKSets mark at cursor position. fiiliPICTURElixl0 (^(PICTURE) EinriNrri MfiRK9-3MATCHAccesses the

Name, Key, or LabelDescription, Type, and KeysPageMENUToggles the softkey menu on and off,PICTURE inO f^TKPICTURE) EDIT fNXTl riENU22-6MERGElMerges pl

Name, Key, or LabelDescription, Type, and KeysPageMROOTSolves a set of equations for the specified variable (r) starting with only user-defined values

Name, Key, or LabelDescription, Type, and KeysPageNOTRetiims the binary or logical NOT of x.iPRGl ST (NXT) ROT H-15F fMTHl BFISE fNXT] LOGIC NOT15-4NO

^^«CftLCULftTDRNUMANSIFixedCDDRScientificar¿EEEngineeringCHDDSE NUMEER DISPLAY FORMATThe Number Format Choose BoxSelect a number format and press OKIf

Name, Key, or LabelDescription, Type, and KeysPageOKAccepts the values of aU the fields as they are currently displayed or performs the main action of

Name, Key, or LabelDescription, Type, and Keys PagePCOEF Finds the coefficients of the polynomial with the specified axray of roots (r).C i+ili SOLVE

Name, Key, or LabelDescription, Type, and Keys PagePINITInitializes all ports containing RAM without erasing data.C fiiliLIBRARYl fNXT) P I H I T28-14

Name, Key, or LabelDescription, Type, and Keys PagePREDY Returns predicted value for dependent variable, given value of independent variable (r).C fi^

Name, Key, or LabelDescription, Type, and Keys PagePURGPurges selected objects or alanns.fFRiMEMORY 1 fNXT ) PURG.5-10O ((-► )[TTME J BroHse Harms...

Name, Key, or LabelDescription, Type, and KeysPageQUADSolves a fii'st or second order equation (y) for a given variable (r).C fiilÍSYMBOLIC] QLIH

Name, Key, or LabelDescription, Type, and KeysPageRGL Recalls the selected object to the stack. O MEMORY 1Í NXT 1 RCL5-9RCLALARM Recalls specified ala

Name, Key, or LabelDescription, Type, and KeysPageRECV Prepares the HP 48 to receive data.O Trcuisfer. . Kb.L' V27-11REPEATBegins loop clause

Name, Key, or LabelDescription, Type, and KeysPageRKFUses a list [z)—containing the name of the time variable, the name of the solution variable, and

Name, Key, or LabelDescription, Type, and KeysPageROLLD“Rolls down” X levels of the stack so that level 2 (y) moves to level x.C r^lSTACK) ROLLD3-12RO

To set the angle mode directly from the keyboard: Press QIraQ to switch between Radians mode and Degrees mode. (If Grads mode had been previously se

Name, Key, or LabelDescription, Type, and KeysPageRRBRotates binary integer (a:) right by one byte.C (MTHl BñSE ÍÑxD BYTE RRB15-5RREFComputes the redu

Name, Key, or LabelDescription, Type, and KeysPageR-^CCombines separate real (y) and imaginary (.r) components into one complex number (or array).fPRG

Name, Key, or LabelDescription, Type, and KeysPageSENDSends the specified object(s) in the manner designated in the input form.27-10SEQGenerates a seq

Name, Key, or LabelDescription, Type, and KeysPageSIZE Finds dimensions of list, array, string, algebraic object, or graphics object (a:).fPRGl LIST E

Name, Key, or LabelDescription, Type, and KeysPageSORTSorts the elements in a list (r) in ascending order. C iMTHl L ibl HiJKi17-6SPHERE Sets spherica

Name, Key, or LabelDescription, Type, and Keys PageSTEPExecutes the next step in a step-wise differentiation.Q ff^lfSYMBOLIC 1 Differentiate . . . ii:

Name, Key, or LabelDescription, Type, and KeysPageSTO=(. Miiltiplies contents of specified variable by specified number or other object.C fiilfMEMORY)

Name, Key, or LabelDescription, Type, and Keys PageSVDCompute the singular value decomposition of a rectangular matrix (x).c Í MTH1 M ñ 1 K i- ñ u 1 h

Name, Key, or LabelDescription, Type, and KeysPageTANK Hyperbolic tangent of x.A fMTHl H't'F-' iHNH12-3TANLDraws the line tangent to th

Name, Key, or LabelDescription, Type, and KeysPageTLINEIn PICT, toggles pixels on the line defined by two coordinates {y and x).C fPRG 1 H i U 1 ! L.

x'" b' xyThree-Dimensional Display ModesRectangular Cylindrical Spherical[a b c][rxy c][rzGzct)]Coordinate Systems for 3D VectorsTo set

Name, Key, or LabelDescription, Type, and KeysPageTVARSReturns variables containing specified object type (r).G fi^KMEMORY) DiK 1 VFiF;SH-30TVMDisplay

Name, Key, or LabelDescription, Type, and KeysPageUTPFReturns probability that Snedecor’s F random variable is greater than r, given the nmnerator (z)

Name, Key, or LabelDescription, Type, and KeysPageVTYPERetioriis type number of object stored in local or global name (r).C fPRGl TYPE fNMHVTYPEH-31VZ

Name, Key, or LabelDescription, Type, and KeysPageWSLOGReturns a series of strings recording the date, time, and cause of each Warmstart event.C Must

Name, Key, or LabelDescription, Type, and KeysPageXXRNGSets the coordinates XXjeft (y) and XX^gj^j (r) establishing the width of the 3D target mapping

Name, Key, or LabelDescription, Type, and KeysPageYYRNGSets the coordinates YYfar (2/) XXnear establishing the width of the 3D target mapping range (f

Name, Key, or LabelDescription, Type, and KeysPageZTRIGSets the horizoBtal scale so that every ten pixels represent 7t/2 and sets the ver

Name, Key, or LabelDescription, Type, and KeysPage<Tests whether y < x.F fpezn TEST <H-36< Tests whether y x.F fpRG) TESTH-36>Tests whe

Name, Key, or LabelDescription, Type, and KeysPages+ Adds data point (a/) to matrix in UDAT.c («tKstatI Dm ! H ¿+H-39s-Subtracts data point (x) from m

HCommandsAMORT Command: Amortizes a loan or investment based upon the current amortization settings.Level 1-Level 3Level 2Level 1n-principal

4 Setting the BeepBy default, the HP 48 sounds a “beep” whenever an error occurs. You can turn this beeper on and off.1. Press |T»lfMODE

ARRY—> Command: Takes an array and returns its elements as separate real or complex numbers. Also returns a list of the dimensio

CENTR Command: Adjusts the first two parameters in the reserved variable -P-PA-K, ’ ^rriin 5 ?/min '* and |/max j so that the pointrepresented

COLZ Command: Specifies the independent-variable and dependent-variable columns of the current statistics matrix (the reserved variable SDAT).Level 2L

+DATE Command: Sets the system date to date.Level 1Level 1dateDECR Command: Takes a variable on level 1, subtracts 1, stores thenew value back into th

DOERR Command: Executes a “user-specified” error, causing a program to behave exactly as if a normal error had occurred during program execution.Level

ERRN Command: Returns the error calculator error.number of the most recentLevel 1 —Level 1T^^errorEYEPT Command: Specifies the coordinates of the ey

FANNING Function: Calculates the Fanning friction factor of certain fluid flows.Level 2 Level 1 Level 1^x/D•^fanning^ X1D'symb'-' FA NN

HEAD Command: Returns the first element of a list or string.Level 1Level 1{ odji ... objn } "String"^ obJi -+ "element^"IFT Comman

INDEP Command: Specifies the independent variable and its plotting range.Level 2 Level 1 + Level 1•’^start'global'{ global }{ global }{ rt -

LIBE VAL Command: Evaluates unnamed library functions.Level 1-Level 1^^function-LIBS Command: Lists the title, number, and port of each library attach

To set the fraction mark:1. Press iTRfMODES).2. Highlight the FM|: field, and press v'CHK (or [+/-)) until the desired setting is shown (checke

LR Command: Uses the currently selected statistical model to calculate the linear regression coefficients (intercept and slope) for the selected depen

MCALC Command: Designates a variable as a calculated value (not user-defined) for the Multiple-Equation Solver.Level 1Level 1‘name’{ list }"ALL&q

MROOT Command: Uses the Multiple-Equation Solver to solve for one or more variables using the equation set in Mpar.Level 1 Level 1‘name‘ ^ X"ALL&

NOT Command: Returns the one’s complement or logical inverse of the argument.Level 1-Level 1#«1#ri2T/F-0/1" string.^"” string2"'sy

OBJ^ Command: Separates an object into its components onto the stack. For some object types, the number of components is returned to level 1.Level 1 ^

PARITY Command: Sets the parity value in the reserved variable 10 PAR.Level 1 ^ Level 1^parityPATH Command:directory.Returns a list specifying the pat

PMIN Command: Specifies <.x, y'> as the coordinates at the lower left corner of the display.Level 1Level 1(x,y)PREDV Command: Returns the p

PROMPT Command: Displays the contents of "prompt" in the status area, and halts program execution.Level 1 Level 1"prompt"PSDEV Com

QUOTE Function: Returns its argument unevaluated.Level 1 ^Level 1'symb' —^'symb'obj objRATIO Function: Prefix form of / (divide) g

RCLALARM Command: Recalls a specified alarm.Level 1-Level 1n d e X-{ date time \epeat >RCLMENU Command: Returns the menu number of the currently di

3. Use the arrow keys to scroll through the flags. A check-mark to the left of the flag number indicates that the flag is set. The text describes how

REPL Command: Replaces a portion of the level 3 target object with the level 1 object, beginning at a position specified in level 2.Level 3Level 2 Lev

RKFERR Command: Returns the absolute error estimate for a given step h when solving an initial value problem for a differential equation using the Run

RRKSTEP Command: Computes the next solution step {hnext) to an iiitial value problem for a differential equation, and displays the method used to arri

SDEV Command: Calculates the sample standard deviation of each of the m columns of coordinate values in the current statistics matrix (reserved variab

SNEG Cominand: Replaces the contents of a variable with its negative.Level 1Level 1'name' —>SOLVEQN Command; Starts the multiple equation

STO+ Command: Adds a number or other object to the contents ofa specified variable.Level 2Level 1 Level 1obj'name''name' objSTO- C

STOX Cotnitiand; Stores obj in the reserved variable EDAT.Level 1 Level 1obj —>^STR Command: Converts any object to string form.Level 1 ^ Level 1ob

TIME Command: Returns the system time in the form HH.MMSSs.Level 1-Level 1^ timeTINC Command: Calculatesa temperature increment.Level 2 Level 1-Level

TVARS Command: Lists all global variables in the current directory that contain objects of the specified types.Level 1-Level 1^type--{ global ...}{ ^t

VAR Command: Calculates the sample variance of the coordinate values in each of the m columns in the current statistics matrix (SDAT).Level 1 ^Level 1

To set or clear seweral flags at once:1. From the stack, enter onto level 1 a list of the flag numbers you wish to set or clear.2. Do one of the fol

WAIT Command: Suspends program execution for specified time, or until a key is pressed.Level 1 ^Level 10^key-1 -+^keyWHILE Command: Starts the WHILE .

ZX”'2 Command: Sums the squares of the values in the independent-variable column of the current statistical matrix (reserved variable EDAT).Level

XVOL Command: Sets the width of the view volume in the reserved variable VPAR.Level 2Level 1 ^Level 1•’‘’left •’‘rightXXRNG CommandSpecifies the x ran

YCOL Command: Specifies the dependent variable column of the current statistics matrix (reserved variable S;DAT).Level 1Level 1YRNG Command: Specifies

ZVOL Command:variable VPAR.Sets the height of theview volume in the reservedLevel 2Level 1-Level 1•’‘'low ’‘’high-< Function: Tests whether o

> Function: Tests whether oneobjectis greater than another object.Level 2 Level 1-Level 1Xy-0/1#rii#«20/1" string-^"” string2 ”0/1X &apos

== Function: Tests if two objects are equal.Level 2 Level 1Level 1ob/'iObj20/1(x,0)X0/1X (x,0)0/1z'symb''z==symb''symb&a

Z Function: Calculates the value of a finite series.Level 4 Level 3 Level 2 Level 1Level 1'indx'^tinalsmnd ^su mindx' 'init'

Inde]IndexSpecial characters5 annunciator. 1-20 Hi annunciators, 1-2, 1-6 tX annunciator, 1-2, 2-2(oi) annunciator, 1-2, 26-4, A-1, A-4^ annunciator

MODES OperationsKeyDescriptionNumber Format. Modes (Í4^ I [MODES) ! • ГiT )STDSets the display mode to Standard.F I X Sets the display mode to Fix usi

Indexalgebraicsaction in programs, 29-2 array elements in, 14-12 as graphics objects, 7-13 as strings, 7-14 collecting terms, 20-18 converting to grap

Indexdimensionless units, 10-7,10-8HMS format, 12-7 angular units converting, 10-7 animationgraphics objects, 9-10 YSLICE plots, 23-23, 23-33 annuncia

Indexextracting columns, 14-6 extracting elements, 8-8, 14-7 extracting real part, 14-14 extracting rows, 14-6 Frobenius norm, 14-8 in algebraics, 14-

Indexrotating, 15-5 shifting, 15-5 boxesdrawing, 9-8 branching structuresconditional structures, 29-10 loop structures, 29-12 program element, 29-3 br

Indexinsert and replace modes, 2-12inserting stack object, 3-9 keying in special characters,2-4multiple arguments, 3-2 multiple objects, 2-7 operation

Indexangular units, 10-7binary integers to real integers,15- 3complex arrays to real arrays, 14-13complex numbers to real numbers, 12-13, 12-14 dates

Indexuser-defined units, 10-14,25-15Cylindrical coordinate mode,4-5, 12-11, 13-1 Cylindrical mode, 4-10d (decimal base marker), 15-1 dateconverting to

Indexdirectories, 5-3 backing up, 28-3 changing current, 5-8 creating, 5-7 current directory, 5-3 custom menu in, 30-3 Ecjuation Library, 25-3 evaluat

Indexenvironments best, 2-11, 3-7 editing, 2-10 EquationWriter, 7-2 exiting, 1-8 Interactive Stack, 3-6 MatrixWriter, 8-2 Selection, 7-10, 20-19 EQcre

Indexsolving quadratic, 20-15 solving symbolically, 20-14, 20-15equations (Equation Library) calculation form, 25-4 designing, 25-8 display form, 25-4

5HemonThe HP 48 has two types of memory:m Read-only memory (ROM). ROM is memory that’s dedicated to specific operations and cannot be altered. The HP

Indexdifferentiating, 20-9 integrating numerically, 20-1 integrating symbolically, 20-7 plotting, 22-1 rearranging, 20-17, 20-27 solving, 18-2solving

Indexfractionsconverting real numbers to, 16-5in Equation Writer, 7-4 freeing merged memory, 28-16,28-17function analysis, 22-9 FUNCTION plots, 23-1 d

Indexguessed solutionshelp find solution, 25-10, 25-11SOLVE application, 18-1, 18-3, 18-5 guesses solutionshelp find solution, 25-11h (hex base marker

Indexinsert cursor, 2-12 integer part of real number, 12-9 integralsaccuracy, 20-6and Taylor polynomials, 20-9 definite, 20-1, 20-7 lERR contains unce

Indexdisabling user keys, 30-7 entering delimiters, 2-5 entering objects, 2-5 entering special characters, 2-4Equation Writer, 7-2 in PICTURE environm

Indexconcatenating, 17-3, 17-6 counting elements in, 17-7 creating from keyboard, 17-1 creating from stack, 17-1 dividing two, 17-4 entering, 2-5 find

Indexdisassembling into vectors, 14-4, 14-5 eigenvalues, 14-20 eigenvectors, 14-21 entering, 2-6entering with Matrix Writer,8-2, 14-1extracting diagon

IndexMTH VECTR, 13-2, 13-4 PICTURE FCN, 22-10 PRG STK, 3-11 RULES, 20-21 UNITS Catalog, 10-1, 10-2, 10-6UNITS Command, 10-1 VAR, 5-11 menu keys labels

IndexMparcreated by Equation Library, 25-2, 25-6MTH BASE menu, 15-1, 15-4 MTH HYP menu, 12-3 MTH PARTS menu, 12-9 MTH PROB menu, 12-4, 12-5 MTH REAL m

Indexentering, 2-5entering in programs, 29-5,29-6HP 48-HP 48 I/O, 27-1 HP 48-PC I/O, 27-9 in custom menus, 30-1 printing, 27-2storing in variables, 5-

4. ModesUsing the MODES Application... 4-1Setting the Display Mode...

SystemAvailable MemoryUser Memory; Home ; Port 01 1 1 1 1 1A B CD1 1 1 ! 1 1E ; F G ; HPartitions move depending on current allocation of memory Schem

IndexplotsEDAT and, 22-1, 22-12 EPAR and, 22-16 adding graphical elements,9-3analyzing, 22-9 converting coordinates, 9-9 coordinate types, 9-7 equatio

Indexremoving, 28-14 piug-in portsinstalling cards, 28-9 list of backup objects, 28-4 removing cards, 28-14 searching, 28-4 testing, A-12 type of memo

Indexare sequences of objects, 29-1, 29-2“building-block”, 29-5 calculation styles, 29-4 compared to libraries, 28-6 conditional structures, 29-10, 29

Indexbattery preserves memory, 28-15battery type, A-5 expanding user memory, 5-1, 28-16for backup objects, 28-3 free before removing, 28-14 freeing, 2

IndexSCATTER plots, 23-17 comparing to regression, 23-21from Statistics, 23-20 Scientific display mode, 4-2 scrolling in EquationWriter, 7-2, 7-10, 7-

Indexusing units with, 18-6 SOLVE differential equation solveraccuracy of results, 19-5 STIFF solver, 19-4 SOLVE input forms, 6-7 SOLVEQN command, E-1

Indexupper-tail probabilities, 12-5 StatisticsEDAT data, 21-1 EPAR parameters, 21-12 BAR plots, 23-19 current matrix, 21-1, 21-2 data structure, 21-1

Indexunder-determined, 14-14, 14-15, 14-17Taylor’s polynomials and derivatives, 20-13 calculating, 20-12 t distribution, 12-5 temperaturescalculations

Indexcalculations withtemperatures, 10-11 consistent units, 10-8 converting angular units,10-7converting units, 10-6 converting units of temperature,

Indexinternal structure, 29-18, 29-19nesting, 11-8 plotting, 24-2user-defined transformations, 20-27user-defined units, 10-14, 25-15 user flags, 1-3,

LAST Variable Storage (E): Contains the three temporary variables~TAST CMD, LAST STACK, and LAST ARCC-that save copies of the previous commands, stack

Indexstates, 25-8too many known, 25-11 too many unknown, 25-10 unexpected solutions, 25-10 wrong states, 25-11 variables (Solver)global, 25-2, 25-5, A

Contacting Hewlett-PackardFor Information about Using the Calculator. If you have questions about how to use the calculator, first check the table of

Part 1; FundamentalsThe Keyboard and Display 4: ModesEntering and Editing Objects 5: MemoryStackPart 2: Special Entry EnvironmentsInput Forms and Ch

Current pathYou always have immediate keyboard access to the variables stored in the current directory. Pressing the fVAl^ key brings up a menu (the V

Using The Variable Browser ApplicationThe Variable Browser is an application designed to facilitate the way you view and organize the HOME memory sect

You can’t use the name PICT, which is used by the HP 48 to contain the current graphics object.Certain names are legal variable names, but are used by

3. Enter the new object in the OBJECT'S field. ’Vou can do this severalways: Key tlie object into the command line and press fENTER). Use

directory that starts with that letter and repeat until the desired variable is highlighted.3. Press v'CHK (or press to include the variable in

To recall a variable to the stack:1. Press |7R(MEMORY).2. Select the variable you want to recall.3. Press (NXT1 RCL .4. Exit the Browser when done

To move a variable:1. Press iTRfMEMORY).2. Select the variable(s) you want to move.3. Press MOVE .NHME: MOVE TD:MOVE VflRIftELEtSJPPnRENTER Vm NftM

To determine the size of wariables:1. Press fr^lMEMORSH-2. Select the variable or variables that you want to “measure.”3. Press S I ZEi from the se

8.7. The Equation WriterHow the Equation Writer Application Is OrganizedConstructing Equations...Enterin

Update the contents of a variable. Put the newly edited contents of the variable on stack level 1 and press Q followed by the variable’s menu key.

Step 5: Clear the stack and purge OPTION from memory.(CLEAR)1:n OPT 10 (♦ iHPURG)Defining VariablesThe HP 48’s DEFINE command can create variables fr

the short programEvaluate them from the VARSte-p 1: From the stack, display the VAR menu.fVARl'1:Step 2: Evaluate ALG, B, and A. Because none o

Although they appear identical on the stack, there are two important differences between formal variable names (that have no associated objects) and q

5 Special Memory OperationsOccasionally the HP 48 may seem to freeze while executing something, and won’t respond to the (CANCEL) key. This can happen

Sometimes the HP 48 may freeze up and won’t respond to (0N}-Q because it isn’t accepting input from the keyboard. At these times, you need to execute

Once you’ve initiated the memory reset, the calculator beeps and displays the following screen:Memory Reset Prompt3. Press YES if you want to try and

No Room To Show Stack—This message appears when the HP 48 completes all pending operations but doesn’t have enough free memory to display the stack. W

To respond to the “Oyt Of Memory” prompts: To delete the indicated object, press YES . To keep the indicated object, press HO To stop the pro

6InpRiit Foniìs and ListsAlthough the HP 48 screen is small compared to a standard computer screen, it is approximately the size of the avera

Calculating with Temperature Units... 10-11Creating User-Defined Units...

Input forms use four basic kinds of fields: Data fields. These accept data of a particular kind directly from the keyboard. The fields labeled INDEP

When you press fENTER) oi to enter data that has beentyped into the command hue the next field is automatically selected. Otherwise, you must move th

Selecting Options in Input FormsTo select an option from a list field:1. Select the list field.2. Select an option for that field using one of the f

3. Edit the object using the standard command line editing procedures,4. Press (ENTER) or UK .meihile in thearm:1. Select the data (or extended dat

To reset the value of a field to its default:Select the field.Do one of the followinii; Press (IMXTI KbSE m Press CMD- Select.le (or Keset V-alue) f

When You Finish Entering Data into an Input FormInput forms are designed to help you enter data and prepare to execute a larger task. The data you ent

1. Enter a title string for the input form (use |2. Enter a list of field specifications. If more than one field is specified, enclose each field sp

7ionWriterThe HP 48 features the Equation Writer application, which makes it easy to enter and review algebraic expressions and equations in the form

How the EquationWriter Application Is OrganizedIn the EquationWriter application, keys corresponding to algebraic functions enter the function name or

Constructing EquationsTo start the EquationWriter application: Press («^(equation ). The EquationWriter is accessible from the stack or from any fie

13. Vectors and Ti’aiisibriiisDisplaying 2D and 3D Vectors... 13-1Entering 2D and 3D Vectors...

A number or alpha character and the divide bar, square-root symbol, or Kth root term—for example, BNoteAll multiplication (even implied multiplication

2, Press 0 to end the argument and display the right parenthesis.To include parenthesized terms:1. Press S30 to display the left parenthesis.2. Pre

To include units:1. Key ill the number part.2. Press fr^fT) to start the unit expression.3. Key in the unit expression.4. Press © to end the expre

Leaving and then restarting the Equation Writer application turns implicit parentheses on. If you turn off implicit parentheses after keying in Q, or

EquationWriter ExamplesAt the end of each of the following examples, you can either press fENTERl to put the equation on the stack, or press fi^fCLEAR

fi^( EQUATION 1(S(H) 3 ® ©Y ®@@ ©X ©2 fCOSl S)© © ©X ©(ZD 2 ©®Sxaiiiple: Key in this expression:"1 \'T-1X'iM + l. _ ^2M + dxPi^fEQUA

To edit by backspacing:1. Press Q until you delete the error.2. Complete the expression correctly.To edit the full equation:1. If the equation ends

4. Optional: Press EX PR at any time to highlight the current subexpression. (Press it again to turn off the highlight.)5. Press EDIT to put the curre

Step 3: Insert the integrand into the expression.(3(EcDStep i: Complete the subexpression. Then key in the remainder ofthe expression, inserting the

Summary of EquationWriter OperationsOperations in the EquationWriter ApplicationKeyDescription®Starts a numerator.Ends a subexpression. C®(Q or f^fT)