Hp 48G Instrukcja Użytkownika

48G eQuick ~jriesStart GuideHEWLETT PACKAHO 40Ua

About the Quick Start GuideThe HP ^8G Senes Quick Start Guide is designed to help you learn how to use the HP 48. It is organized into lessons, each o

Lesson 35: Transferring Objects Via InfraredThe HP 48 has bot.h wired and infrared serial input/oiitput ports to allow yon to transfer objects to and

Lesson 36: Using an Equation Set from the Equation LibraryThe Equation Library is a collection of equations and commands that enable you to solve simp

Step Jf.- View the five equations in the F'roject i le Mot ion set.All five are used interchangeably in order to solve for missing vari

Step 2: Enter the known values. Define xO and yO as 0. Notice thatthe iiienn labels turn black as you store values.0050(nxt)65R: 65_m4:3:O-£- 1:l3ril

Step 6: Enter the new value for the elevation angle (30 degrees),store the previously computed initial velocity { vq ) , and then solve for P

To attach a library to user memory manually:1. Change to the director}' to which you want to attach the library. To access the library from all

Lesson 37: Adding and Using LibrariesA library is a collection of pre-programmed commands that act as extensions to the built-in command set. The HP 4

9If Things Go WrongWhenever you run into problems—either following examples in this manual or solving your own problems--you can use these hints to ge

Lesson 39: TroubleshootingIf the HP 48 is stuck in an unfamiliar state:B Press [cancel) several times, until you see the normal stack display.To undo

3. At the same time, press the left and right menu keys (A and F), then release them.4. Release th(' fON 1 key.5. PressThe above steps also er

Lesson 1: Getting ReadyHere are a few filings to do to prepare the HP 48 before you begin.Turning the HP 48 On and Off► Press fON ) to turn the machin

If you suspect that your calculator is malfunctioning:1. Run the self-test;a. Turn on the calculator.b. Press and hold fON ).c. Press and release

Contacting Hewlett-PackardFor Information about Using the Calculator. If you have questions about how to use the calculator that are not covered in th

ContentsStart HereIntroducing the HP 48 ArithmeticUnderstanding and Using Memory Solving EquationsPlotting Equations and Analyzing Graphs Calculus, St

Setting the Time and Date1. Open llie TIME application,chooseime and date:ISET TIME AND OATE^^^^TIME:WÍ-45-57 ñMDATE:1 3 /94 M.-'D/YENTER HOURmiP

2This chapter provides a brief introduction to the HP 48 --an overview of its design, operating fundamentals, and far-ranging mathematical power. Spec

Lesson 2: Mathematical Objects and the HP 48The mathematical and scientific disciplines use a wide variety of objects ill the process of describing an

By design, the HP 48 makes it easy to move between one type of object and another as one solves a problem, explores data, or communicates results. It

Example: Enter some objects onto the stack: 39.3, { 1 2 4 8 }, (4,.5)7, .99479.Step 1: Enter the first number.39.3 (ENTER)Step 2: Type the delimite

Editing an Object in the Command LineYou probably noticed that as soon as you begin typing in an object, it appears “below” the stack on a line of its

Removing Objects from the StackExample: Now remove (“drop”) objects from the stack.Step 1: Drop just the object in level 1. Notice that all other obj

Lesson 3: Entering CharactersThere are over 200 characters available on the HP 48. They can be used in text strings and, with a few restrictions, in v

Regulatory InformationU.S.A.The HP 48 generates and uses radio frequency energy and may interfere with radio and television reception. The HP 48 compl

Special CharactersThe CHARS feature allows you to find any character and ]5ut it into the cornmand line as if you had typed it fr

Lesson 4: Using MenusThe HP 48 employs 49 keys to access over a thousand operations. This greatly extended keyboard is due primarily to the use of men

Lesson 5: A Brief Tour of the HP 48As compact and powerful as the stack is for manipulating objects, there are many kinds of problem-solving situation

Creating Matrices: QYou can also enter a. mat rix in a, form similar t.o its depiction in books—using the special MalrirWrHer entry feature. It can cr

Creating Pictures: QPICTURE provides access to the HP 48 graphics“blackboard” (called PICT). Graphs are plotted and freehand drawings are created and

Plotting Functions: |QPLOT allows \'oii to select any one of 15 plot types. The input, form you see adjiist.s to sliow tlie options available for

Printing and Data Transfer: (QThe 1/0 application allows you to print objects or to transfer data between two HP 48s or between the HP 48 and a comput

Setting Calculator Modes: QYou visited MODES in lesson 1, It is used to set the various calculator modes and to change flag settings.CftLCULftTDFi MOD

3ArithmeticThis chapter shows you how to;► Calculate using real numbers. k Calculate using fractions.► Calculate using symbolic variables.► Calculate

mHEWLETTPACKARDHP Part No. 00048-90126 Printed in Singapore Edition 5

Lesson 6: Doing ArithmeticThere are actually two different ways that you can “do" arithmetic on the HP 48. The stack method is

This process of entering numbers onto the stack and using numbers fronr tlie stack during calculations underlies everything the HP 48 does. This apirr

Example: Calculate15(ENTER).06 (ENTER) 14.5 ¡3 ©1: 17.2413793103CTjitiiaiSmBfftHaBiKnBfanBiaaaaAlgebraic methodThe HP 48 i.s as proficient with alge

Exaiupl«?: C'alculateIcEearICD 15 0LijJtll) -06 @ 14.5 (EVAL11: 1?.Z413?93103crainaiSi?niifiiHiiiiiwjiil-i4nwi^^HiUsing the EquationWriterWhen

a i c±j©20iC±)® 3 0 1 [+) ^ 5 0 3 (01-1¿11+31+cr.01+Step 2: Advance the cursor until it is outside of the closingparenthesis. C'urreiitly,

Lesson 7: Finding and Using More Math FunctionsThe HP 48 has many more matli functions than can be fit onto the keyboard—even using the two shift-keys

Lesson 8: Arithmetic with FractionsFractions—whether they are proper, improper, or mixed—can be represented on the HP 48 as algebraic ex

Lesson 9: Arithmetic with SymbolsArithmetic using syml:)olic variables is very nnich like arithmetic using numbers. You can make symbolic cal

Lesson 10: Arithmetic with Complex NumbersThe complex-number capabilities of the 111’ 48 can affect the results of real-number operations. Certain cal

Step 2: Enter the polar number on the stack. It’s converted to matchthe current coordinate mode (in this case. Rectangular mode).(enter)£: ..l! (-5.0

NoticeTills niamial and any examples contiiined herein are provided “as is” and are suiDject to change without notice. Hewlett-Packard Company makes n

Example: Find the square roots of 8 — 6i.Step 1: Type the complex number.l-hn...jl8f^l6fVT|(8 -6)EaisMiBgaT?nK»iBB3toiStep 2: Find the principal s

Lesson 11: Arithmetic including UnitsYou needn’t calculate with numbers separated from their natural measurement units if you use the HP 48. A unit ob

Converting UnitsExample: Convert iimercury).p'l (atmospheres) to pnMHg (millimeters ofStep 1: Create the unit object 10...atci(3NXT 10

One final example illustrates the ability of the HP 48 to factor the unit expression.Example: Factor H (Newtons) out of 3=:Step 1: Enter the unit ob

4V>^mg Pterin-aryAlthough the Stack can contain manj’ objects, they can all be deleted with one press of the key. A better place to sto

Lesson 12: Understanding MemoryThus far it. has been convenient to think of the HP 48 as a calculator—albeit an advanced calculator. However, when con

Notice that there are several kinds of variables indicated in the diagram: System variables. These variables are hidden from you, but are

Lesson 13: Creating (Naming) VariablesTo name an ol)ject is to create a global variable. You store an object in user-memory by giving it a name. You c

Example: Find tiie square root of 3 and store the value in a variablenamed tS (using the Variable Browser).Step 1: Find the square root, of 3.3®1:

About the Quick Start Guide... 1-2Lesson 1: Getting Ready...

Lesson 14: Organizing VariablesWhenever a variable is created, it is put into the current directory. Directories let you organize variables into meani

Step 2: Select the Ei-lflMPLES directory and switch to it. Notice thatthe directory line says i HOME EXAMPLES > This illustrates that EX

You will often want to modify a variable sometime after you’ve created it. This, too can be easily accomplished using the Variable Browser.

The Variable Browser also allows you to purge variables—several at a time, if you wish—so that unneeded variables don't occupy valuable

The variables in the current directory are conveniently available to be used in calculations and expressions. Pressing the fVAR) key brings up a menu

5lionsThis chapter provides a brief introduction to the SOLVE application. The lessons take you through examples of the primary kinds of equation-solv

Lesson 17: Solving for a Variable—NumericallyIf you want a mimeric solution for an unknown in an equation, you can use the root-finding application (H

Step S: Since RATFUNC only has one variable, it must be theunknown variable. Solve for x by highlighting its field and pressing S 0 L V E.(T) SOLVEEQ

Step 1: You’re already working with RATFUNC, and the x variablefield is highlighted, so you are ready to enter the guess.2 f^fenter!^^»SDLVE ECiUflTI

To decide which case it is, you should find the value of the expression at the Sign Reversal point,Exaiiiphn Find the value of the expression at the c

4.5.6.Lesson 11Arithmetic including Units...3-13Converting Units...

Step 1: Move the highlight to the EQ: field (if necessary) and enterthe equation. (6 can be typed using falfr^F or selecting it from CHARS.

Lesson 18: Solving for a Variable— SymbolicallyThe HP 48 also allows you to isolate a varialhe syiiibolically—that is, rearrange an expression so tlia

Step 4- Define a new variable, TH, from this equation. &) stores the expression to the right of the equal sign (' Q.--''U.---'

Lesson 19: Finding all Roots of a PolynomialA polynomial has tiie same number of roots as its degree—although not all of these roots will be

Step Jf.- Exit the SOLVE application and view the results on the Stack.or (CANCElTlI'- Roots'-C (0.H,1.00) (0.1.5-10 Solving Equations

Lesson 20: Solving a System of Linear EquationsThe HP 48 can solve a system of linear equations. To create your system of equations, you can either ch

Step 3: Enter the vector of constants (B) and solve the system13 fspD 113 (ENTER)fim vFSOLVE SVSTEM[[ 3 1 2 ] C 1 1 E: [ 13 -1 13 ][251]ENTER SOLUTIO

6Plotting Egyatioii-s and GraphsThis chapter provides a brief introduction to the PLOT application. The lessons take you through examples of:

Lesson 21: Plotting a FunctionA function takes one or more arguments as inputs and transformsthem inathematically into exactly one output. A function

Step 3: The independent variable, x, and its default rangev'lEW) need no changing. To let the calculator automatically scale the vertical axis f

8. S|)ticial featiii'esLesson 35: Transferring Objects Via Infrared . . . .Lesson 36: Using an Equation Set from the EquationLibrary ...

Lesson 22: Modifying the Display of a PlotThere are several display options that are set on the PLOT OPTIONS screen. The default settino;s

Lesson 23: Plotting Several FunctionsTo plot several functions on the same display, you must enter a list of functions in the EQ field of the Plot scr

Step 3: Enter the list of checked fiinctions into the EQs field and seta vertical display range of -4 to 4 (large enough to display the “largest’’ fu

Lesson 24: Plotting Functions in Three DimensionsThere are six different plot types that can be used to help you visualize functions of two variables.

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

Step 3: Set the size of the View Volume and location of the eyepoint.OPTS 1 fENTER) 1(ENTER) 1 (ENTER) 1(ENTER) .4 (^ (ENTER) .4 (ENTER) 0 (ENTER)

Lesson 25: Introducing the Plot TypesThere are fifteen different kinds of plots that the HP 48 can draw. Each of them is discussed in detail in the HP

Plot Type and Description ExampleTruthPlots trutli-valiied functions, such as inequalities, by testing each point in the range to determine if the fu

Plot Type and Description ExampleWii'eframePlots a perspective, wireframe view of tlie surface determined by a function of two variables.(Shown:

Lesson 26: Finding Roots GraphicallyIn Lesson 17, yon found all of the roots of a polynomial using the SOLVE application. This lesson shows you how to

Step You can see that there are three real roots (where the plot crosses the r-axis, but you cannot see the whole function very well. Zoom the vertica

Lesson 27: Finding Slope, Tangents, and Critical PointsThe following examples show you other kinds of analysis you can|)erform on the currently plotte

Step 4'- Move the cursor to x = 0.3, and draw the line tangent to thefunction at that point.IQ (i time.s)(l\]XT) (to redisplay the menu) (MXT

Lesson 28: Areas Under CurvesThe FiN:EFi command in the PICTURE FCN menu hnds a definite integral based on the current function. That is, it calculate

Step Optional. Shade t,he area between tlie current function and the ,7'-axis, and between the r-values represented by the mark and the cursor. N

7-CiiCjnceH-'This chapter shows you a few examples of the high-powered mathematics of which the HP 48 is capable. The examples you’ll explore are

Lesson 29: Finding DerivativesExample: Find the slope of f(x) = 5.c- - - at x = i.Step 1: Select Difrom the SYMBOLIC' menu.(S ®0 KDiFFERENimTEE

Step Enter the value at which you are evaluating the derivative, and calculate.(¥) -5 (ENTER)1: 29Example: Find the symbolic derivative of f{x) = o.

Lesson 30: Finding IntegralsThe examples in this lesson illustrate how to find numerical and symbolic integrals.Example: Evaluate:»1(2.Y + 5)fLYStep

Step Change the KtSULT's field to Humeric, if necessary. (3D (if necessary)...j^^^^KlNTEQRflTEiEKPR: ‘ 2*X-6*K^4+5' Vflfi: K 1-n

1i'USElWelcome to the community of problem-solvers.As easy-to-use as a calculator. The HP 48(1 Series calculators use a special graphical interfa

Step 2: Enter the variable and limits of integration.(B©x (ENTER) 0 (ENTER) ©S)A (ENTER)i INTEGRftTE EXPfi: ' a''-2*X-X''-3&

Lesson 31: Data and StatisticsStatistical data, for the HP 48 are represented by matrices. Sucli a matrix contains a row for each data point and a col

Step 2: If you had already entered this data set (as a matrix) andUS would allow you tostored it with a name, pressing select it now for statistical

Lesson 32: Regression Analysis of Paired DataThe HP 48 can fit any one of four statistical models to a set of datapairs. Once again the data must be i

Step S: Enter the target value for CPI (,r-variable) and predict thePPI value (.^-variable) using the best-fitting model. Note that the IIP 48 determ

Lesson 33: Differential EquationsThe examples in this lesson show you how to solve an initial-value prolilem for a first-order differential equation a

Step Jf-. Highlight thesolution field and solve the problem.® © £SOLVE riTJ:F(T..Y>^^^®F- ' l.--a+T'''2>-2*Y'^2'I

Step 3: Cliange to the Plot Options form to set the tolerance (10^'), the horizontal plotting range (-1 to 8), and the vertical plotting range (-

Lesson 34: Linear AlgebraThe HP 48 includes a number of useful linear algebra commands in (die MTH MATRIX command menu. You will find commands for fin

8SpecThis chapter shows you how to:► Transfer objects between two HP 48s using the infrared port.► Find and use an equation set from the built-in Equa