13-26 | HP 39gs Graphing specs

Example

Suppose you want to know the potential energy of a mass of 5 units according to the equation E = mc2 .

1.Enter 5

2.Press and then press .

3.Select light s...from the Physics menu.

4.Press . The menu closes and the value of the selected constant is copied to the edit line.

5.Complete the equation as you would normally and

press to get the result.

13-26

Using mathematical functions

Image 178

HP 39gs Graphing manual 13-26

Contents

Users guide Edition3 Part Number F2223AA-90001 USA Printing HistoryEdition December June Contents 10-1 Using variables in equations10-6 11-8 11-111-4 11-9 Introduction 14-1 Storing and recalling variables 14-2 13-24Program constants 13-24 Physical constants 13-25 14-4 18-30 18-718-9 19-1 Service Regulatory information Hewlett Packard’s Calculators web site can be found at PrefaceManual conventions Function, Polar, ParametricPage Getting started On/off, cancel operationsHome Parts of the display To adjustDisplay Contrast Menu keys KeyboardInfrared or cable Displays the Views menu. See Aplet control keysAplet library on Aplet views on Entry/Edit keys Button performs Shifted keystrokes Helpwith Math keys Program CommandsMenus Inactive keys Reset input form values Input forms Mode settings You use the Modes input form to set the modes for Home Setting a mode Aplets E-lessons Press to return to Home Sequence Sequence functions U in terms of n, or Example x = cost and y = sintPolar Another sequence, such as Un 1 Quad Explorer aplet Transformations reflected in the equation Aplet library Symbolic view Plot viewPress to display the aplet’s Symbolic view Aplet views Select Plot-Detail Select Plot-TableSelect Overlay Plot Plot Setup Numeric Setup Symbolic Setup Aplet view configurationSketch view Mathematical calculations Where to startTo save aplet configuration Entering expressions Explicit and implicit multiplication Long results Negative numbers Scientific notation powersUsing 23 3 EEX Parentheses Entering Calculates Sin 45 + π Input Output Last input Edit line Last output Getting started Storing a value in a variable Accessing the display history Clearing the display history Using fractionsSetting Fraction mode Setting fraction precision Select Fraction calculationsFraction Enter the calculation Evaluate the calculation Converting decimals to fractionsFraction as Complex numbers This example, the fraction precision is set to Catalogs and editors Aplets and their views About the Symbolic viewDefining an expression Symbolic view Aplet views Independent variable in the expressions is T Aplets Evaluating expressionsSelect Function Home Setting up the plot Plot view setup About the Plot view ΘRNG Plot view settingsΘSTEP Reset plot settings Exploring the graph Trace a graph To move between relations To jump directly to a value To turn trace on/off Zoom within a graphZoom options Factors SquareSet Auto Scale Un-zoom Now un-zoom To box zoom Other views for scaling and splitting the graph Views menu options Making each pixel=1 unit. Not Unit. Resets default values forSplit the screen Pixel=π/24 radian, 7.58, or Integer scaling Overlay plotsDecimal scaling Trigonometric Setting up the table Numeric view setup About the numeric view Exploring the table of numbers Numeric view settingsNUM view menu keys Zoom within a table Integer Numstart and Numstep Clear data Building your own table of numbersBuild a table Numtype Build Your Own Build Your Own menu keys Example plotting a circle Function Reset the graph setup to the default settingsFunction aplet, specify the functions Display the functions in numeric formPage Getting started with the Function aplet Function apletAbout the Function aplet Open the Function aplet Specify a grid for the graph Define the expressions Set up the plotPlot the functions Plot the functions Scale Change the scale Trace a graphSelect Auto Times Analyse graph with FCN functions Select Root Select Slope Select Signed area To find the extremum of the quadratic Select Extremum Explore the table Display the numeric viewDisplay the table of values Symbolic definition F1 is displayed at Bottom of the screen Symbolic definition A columnDisplay the symbolic definition for the F1 column To display Select Plot FCN Function aplet interactive analysisOr to choose a variable Extremum FCN functionsRoot Slope Intersection Symbolic view. DisplaysShading area Cursor. You need to have at Plotting a piecewise-defined function Getting started with the Parametric aplet Parametric apletAbout the Parametric aplet Define the expressions Set the angle measure to degrees Set up the plot Plot the expressionSet angle measure Select Degrees Plot a triangle graph over the existing circle graph Overlay plot Display the numbers120 Page Open the Polar aplet Polar apletGetting started with the Polar aplet Select Polar Explore the graph Display the numbers Display the Plot view menu key labels About the Sequence aplet Sequence apletGetting started with the Sequence aplet Sequence Define the expression Specify plot settingsOpen the Sequence aplet Menu keys to assist in the entry of equations Select Cobweb Plot Setup, set the Seqplot option to CobwebPlot the sequence Display the . Display the table of values for this examplePage Solve aplet About the Solve aplet Define the equation Enter known variables Getting started with the Solve apletOpen the Solve aplet Select Solve Solve the unknown variable Plot the equation Modes is set to Comma, use instead Copies the highlighted value to Plot the equation for variable aSolve aplet’s NUM view keys are Displays other pages of variables, if Use an initial guess Interpreting results Plotting to find guesses Consider the equation of motion for an accelerating body To highlight T Plot the graph Press until the cursor is at the intersection Using variables in equations Select Linear Linear Solver apletOpen the Linear Sequence aplet Solver Solver was able to find solutions for x, y, and z as Hence we need the three-equation input form Linear Solver aplet Page Triangle Solve aplet About the Triangle Solver aplet Open the Triangle Solver aplet Triangle Solver Errors Not enough data Addition, you cannot specify only angles and no lengths About the Statistics aplet Statistics apletGetting started with the Statistics aplet Enter the data into the columns Enter dataSelect Statistics To move to the next column Choose fit and data columns Explore statistics Select a fit in the Symbolic setup viewValue is To move to the FIT1 field Setup plot Plot the graph Draw the regression curveDisplay the equation for best linear fit Slope m is 425.875. The y-intercept b is To highlight Predict valuesStat-Two Entering and editing statistical data Statistics aplet’s Numeric view keys are Statistics Variable expression to the edit line Expression in standard Mathematical form. Press When DoneCopies the column variable or Expression Data sets will need to be selected Clear is usedAgain before re-use Save data Edit a data set Plot a histogram of the data Delete data Insert data Sort data values To choose the fit Angle SettingDefining a regression model Fit models To define your own fit Computed statistics 7,8,15,16,17 Two-variable PlottingColumns for a linear fit only Histogram Box and Whisker Plot Plot typesTo plot statistical data Scatter Plot Fitting a curve to 2VAR dataCorrelation coefficient Relative Error Setting up the plot Plot setup viewPlotting mark 2VAR Connected points 2VAR Statistics aplet’s Plot view keys Trouble-shooting a plotErases the plot According to the current regression Calculating predicted valuesFind predicted values Model Statistics aplet 10-21 Page Getting started with the Inference aplet Inference apletAbout the Inference aplet Open the Inference aplet Table below summarizes the options available Symbolic view Inference aplet’s Symb view keys Select Hypoth Test Setup-NUMSelect the inferential method Enter data Test 1 μ Are explained in the feature of this aplet Importing sample statistics from the Statistics aplet C1 column, enter the random numbers If the Decimal Mark setting in the Modes input formStatistics aplet opens in the Numeric view Produced by the calculator 529 295 952 259 925 592 Inference Set up the interval calculationOpen Inference aplet Select Conf Interval Specify a 90% Confidence interval in the C field Display Numeric view Display Plot viewTo move to the C field Menu name Hypothesis testsOne-Sample Z-Test Inputs Two-Sample Z-Test Results Test 1π One-Proportion Z-TestPopulation 2 standard Measures the strength of the evidence for a selected Two-Proportion Z-Test One-Sample T-Test Sample standard deviation With the α level that you Two-Sample T-Test Pooled? Confidence intervals One-Sample Z-Interval Two-Sample Z-Interval One-Proportion Z-Interval Two-Proportion Z-Interval One-Sample T-Interval Two-Sample T-Interval Pooled Critical T Critical value for T Using the Finance Solver Background 3 4 Compounding period -- which is Performing TVM calculations PMT Example 1 Loan calculations Example 2 Mortgage with balloon payment Example 3 Amortization for home mortgage Calculating AmortizationsTo calculate amortizations To continue amortizing the loan Example 4 Amortization for home mortgage Math menu Using mathematical functionsMath functions Name. Note You do not need to press first Syntax Math functions by categoryFunction categories Functions common to keyboard and menus Evalue Keyboard functionsValue1+ value2 , etc E5 returns Returns LOG100 returns ABS1,2 returns ∂ s1s1 2+3*s1 returns 2*s1+3 Calculus functionsNthroot 8 returns S1,2*X+3,X ARG Complex number functionsTaylor Conj Maxreal ConstantsConversions Minreal Hyperbolic trigonometry List functions Loop functions Polycoef Matrix functionsPolynomial functions Polyeval Comb Probability functionsPolyroot Perm Real-number functions Fnroot DEG→RADFloor Frac MAX INTMant MIN Round TotalRAD→DEG Sign Xpon Symbolic functionsTwo-variable statistics Isolate Quote Test functionsQuad QUADX-12-7,X returns Not Trigonometry functionsIfte XOR Symbolic calculations Finding derivatives To find derivatives in Home Evaluate the function Show the result To find derivatives in the Function aplet’s Symbolic viewSelect F2X and evaluate it You could also just define To find the indefinite integral using formal variablesFor example, to find the indefinite integral Program constants and physical constants Program constants Physical constants 13-26 Variables and memory management Introduction Storing and recalling variables Calculations To use variablesTo clear a variable Open the Vars menu Vars menuPress Example Add the contents of two list variables, and to storeNames or values of variables into programs Result in another list variable 14-6 To store into a graphics variable on That you can configure using17-5 for more information on Variable To access an apletX0, Y0 to X9, Y9 Symbolic view. See Aplet variables on page R-7 Details of variables within the category Memory ManagerLine, press and press To delete variables in a categoryPage Matrices MatricesVectors Matrix Variables Matrix Catalog keys Creating and storing matricesPOLYROOT1,0,-1,0 M1 To create a matrix in the Matrix Catalog Working with matrices To transmit a matrix Make a choice Deletes the highlighted cells, rowOr column you are prompted to Moves to the first row, last row, first To store one element Matrix arithmeticCreate the second matrix Matrices 15-7 Solving systems of linear equations Open the Matrix catalog and create a vector Select Real matrix Argument conventions Matrix functions and commandsAbout commands About functions DET CondCross DOT Rownorm MakematRank Rref Examples Transposing a Matrix Reduced-Row Echelon Form Matrices 15-15 Page Lists You can create, edit, delete, send, and receive named List catalog keys Create a list List edit keys To display one Displaying and editing listsTo display a list Element Press , and press A listTo insert an element 1. Open the List catalog 148 L12 Transmitting lists List functionsDeleting lists To delete a list CONCAT1,2,3,4 returns 1,2,3,4 2,3 returns 5,10,15CONCATlist1,list2 ΔLISTlist1 ΠLISTlist 23 27 Calculates the product of all elements in listΠLIST2,3,4 returns Finding statistical values for list elements 16-10 Your work is automatically saved. Press any view key Aplet note viewTo write a note in Note view Or to exit the Notes view Space key for text entry Contents of variablesCommands Alpha-lock for letter entry Sketch keys Aplet sketch viewTo draw a line To draw a box Draw keys Press to continue drawing, or press Mynote For a name Opens the selected note forBegins a new note, and asks Another HP 39gs or PC Press instead Contents of a Program Structured Programming Programming Be simple-or it can be divided further into other Program catalogOpen Program Catalog Programs that perform smaller tasks Program catalog keys Create a new program Creating and editing programsPress Progrm to open the Program catalog Press to paste the command into the program editor On the left, use or to highlight a commandEdit a program 1. Press Progrm to Editing keys Using programs Run a program Debug a program Stop a program Transmit a program Customizing an aplet Aplet naming convention Example Configuring the Setviews menu option programs Save the aplet ’’My Entry2’’’’EXP.ME2’’3 Setviews ’’’’ ’’’’18’’My Entry1’’’’EXP.ME1’’1 ’’ ’’’’EXP.SV’’0 ’’’’’’EXP.ANG’’0 Programming commands’’Start’’’’EXP.S’’7 Select Aplet commandsCheck Setviews Associating programs with your aplet Auto-run programs ViewNumber ProgramNameIncluding standard menu options IF...THEN...END Branch commandsUncheck Uncheck n END IF... THEN... ElseEND CASE...END Iferr Then ELSE… If A==1 RUN Drawing commandsStop Freeze BOXErase Line Graphic commands PLOT→ GrobxorMakegrob →PLOT Loop commands Matrix commands Scale RandmatRedim Scaleadd Print commands Prompt commands Dispxy ClrvarDisp Disp 3A is 2+2 51.52HELLO DisptimeEditmat matrixname Input GetkeyMsgbox Stat-One commands Stat-One and Stat-Two commandsStat-Two commands Storing and retrieving variables in programs Plot-view variables Indep GridHmin/Hmax InvCross Recenter IsectLabels Root Simult S1mark-S5markSeqPlot Slope Tmin / Tmax Umin/UmaxUstep Tracing Ycross TstepXcross Ytick Ymin / Ymax Yzoom Symbolic-view variables S1fit...S5fit Cubic S2fit Digits Numeric-view variablesC1...C9, C0 Format NumIndep NumColNumFont NumRow NumZoom NumStepNumType StatMode Following aplet variable is available in Note view Sketch variablesPageNum Graphicname Extending aplets Creating new aplets based on existing aplets Solve Open the Solve aplet and save it under the new nameDegrees Using a customized aplet Resetting an apletChoose the sine formula in E1 Sending and receiving aplets Downloading e-lessons from the webHewlett-Packard’s Calculators web site can be found at To transmit an aplet Sorting items in the aplet library menu list To sort the aplet list To delete an aplet Expression line# Reference informationGlossary Cross matrix1,matrix2 Vector One-dimensional array of values Editor and catalog Matrix Two-dimensional array of valuesRecord using the Program editor Set to Comma and enclosed To erase all memory and reset defaults Resetting the HP 39gsTo reset using the keyboard If the calculator does not turn on Operating detailsBatteries To install the main batteries To install the backup battery Variables Home variables Area Root Extremum Slope Isect Function aplet variablesAngle Parametric aplet variables Parametric aplet variables are Category Available name Plot Polar aplet variables Polar aplet variables are Category Available names Plot Sequence aplet variables Sequence aplet variables are Category Available name Plot Solve aplet variables are Category Available name Plot Solve aplet variablesDigits NumCol Format NumRow Statistics aplet variables Math functions are Category Available name Calculus Math menu categoriesMath functions Hyperb Category Available name Matrix Polynom Cobweb Stairstep Degrees Grads RadiansStandard Sci Fixed Eng Fraction Stat1Var Stat2Var Compt w... Compton Wavelength, λc Branch Program commandsProgram commands are Category Command Aplet Print Category Command Stat-Two Status messages Find its proper syntax Also be correct. Look upFunction name in the index to Function value, root, extremumPage Limited Warranty HP 39gs Graphing Calculator Warranty period 12 monthsPage Service Canada 905 206-4663 or Rotc = Rest of the country Regulatory information Xxxx This marking is valid for EUPage Page Index Branch structures 18-17 build your own table Contrast Freeze 18-20 Line 18-20 Pixoff 18-20 Pixon 18-20 Tline Grobor Acosh Alog Asinh Atanh Cosh EXPPage Page Angle measure 1-10 decimal mark 1-11 number format Trigonometric scaling 2-14 two-variablestatistics Sending and receiving 18-8 structured Menu lists 1-8 speed searches Navigate around 3-8 numeric values 3-7 numeric view setup Page