Using mathematical functions, Math functions, Math menu

Using mathematical functions

Math functions

The HP 39G/40G contains many math functions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob. on the MATH menu) contains functions for working with probability.

To use a math function, you enter the function onto the command line, and include the arguments in parentheses after the function. You can also select a math function from the MATH menu.

The MATH menu

The MATH menu provides access to math functions and programming constants.

The MATH menu is organized by category. For each category of functions on the left, there is a list of function names on the right. The highlighted category is the current category.

•When you press >0$7+@, you see the menu list of Math functions. The menu key 07+_indicates that the MATH FUNCTIONS menu list is active.

Using mathematical functions

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$HP 40G manual Using mathematical functions, Math functions, Math menu$

Contents

USER’S Guide Page Contents Parametric aplet Importing Sample Statistics from the Statistics aplet Inference aplet Variables and memory management Programming Index Manual conventions Preface@, &26@, +20@, etc +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etc Preface Home On/off, cancel operationsGetting started Parts of the display To adjust the contrast To clear the displayDisplay Annunciator Description KeyboardMenu keys Key Meaning Aplet control keys $/3+$@ +,7@175@ 75@ Helpwith Shifted keystrokesKey Description +,7@$/3+$@ Math keys Program commands Inactive keys To search a menu To cancel a menuMenus Reset input form values Mode settingsSetting Options Input forms Setting Options Press+20@ to return to Home Setting a modeAplets E-lessons Aplet Use this aplet to explore Name N T Quad Explorer aplet *,*A, keys Trig Explorer aplet Aplet library Symbolic view Plot view Numeric viewAplet views Aplets are stored in the Aplet library Views menu contains the Plot-Table view Plot Setup Numeric Setup Symbolic Aplet view configurationConfiguration To change views Entering expressions Mathematical calculationsLong results Negative numbers Example @4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ Scientific notation powersExplicit and implicit multiplication @ 45 @6+,7@π Entering Calculates+,7@√ 85@9 +,7@√ @85 @9 @ Clearing numbers Using previous results 50175@ @25 175@175@ 175@ updates ANS from 50 to 75 to Key Function Accessing the display history$/3+$@ a 175@ Setting Fraction mode Using fractionsSee Setting fraction precision below for more information Clearing the display history Setting fraction precision Return to Home and enter the calculation Fraction calculations Converting decimals to fractions@@@2@3 Evaluate the calculation Converting a number to a fraction Complex numbersComplex results To enter complex numbers + iy Storing complex numbers Catalog/Editor ContentsCatalogs and editors Memory manager Plot Goto function Differences between the HP 38G and the HP 39G/40GStatistics Pred function Trig Explorer and Quadratic Explorer apletsPage Defining an expression Symbolic view About the Symbolic viewAplets and their views Aplet views Aplets and their views Home Evaluating expressionsAplets $56@ Symb view keys$7+@ +,7@CLEAR Plot view settings Setting up the plot Plot view setupAbout the Plot view 175@ or Reset plot settings +,7@*A Exploring the graphPlot view keys Zoom within a graph Trace a graphTo jump directly to a value To turn trace on/ off Zoom options Multiplies horizontal scale, using Divides horizontal scale only, usingDivides vertical scale only, using Multiplies vertical scale only, using =220Un-zoom 018ZoomPress *k, to move to the bottom of the Zoom list =220Zoom Out =220X-Zoom Out =220X-Zoom=220Y-Zoom =220Y-Zoom Out To box zoom To set zoom factors Options Other views for scaling and splitting the graph Menu key copies the right plot to the left Overlay plots About the numeric viewDecimal scaling Integer scaling Trigonometric scaling Reset numeric settings Setting up the table numeric view setupNumeric view settings Zoom within a table Exploring the table of numbersNUM view menu keys Arrow keys to place the cursor in the independent variable Building your own table of numbersColumn, then enter the value to jump to 175@, the values for the dependent variables are Clear data Build Your Own menu keys +,7@√@9 Example plotting a circle$3/7@ Select About the Function aplet Function apletGetting started with the Function aplet Open the Function aplet Plot the functions Define the expressions@75@175@ Plot the functions With FCN functions Change the scale Trace a graphTrace the linear function Times Root value is displayed at the bottom of the screen Find the greater of the two roots of the quadratic functionSelectRoot Move the cursor to x = 1 by pressing the *A,or 2Select.SlopeChoose the end value for @.2 Display the numeric setup Display the numeric view Set up the tableTo find the extremum of the quadratic Display the numeric view Explore the table Match the table settings to the pixel columns in the graphDisplay a table of numeric values Move to X = Area Extremum Isect Root Slope Function aplet interactive analysis Function Description Access FCN variables FCN functions Two selected expressions Symbolic view. DisplaysCursor. You need to have at least $3/ @ Select Plotting a piecewise defined function example=  Page About the Parametric aplet Parametric apletGetting started with the Parametric aplet Open the Parametric aplet Define the expressions 360 Set angle measure Set up the plot Plot the expression+,7@PLOT Plot a triangle graph over the existing circle graph Overlay plot Display the numbers+,7@ Plot 120Page Getting started with the polar aplet Polar apletOpen the Polar aplet +,7@CLEAR 46+,7@π 2.a Explore the graph Display the numbers Sequence aplet Sequence aplet starts in the Symbolic viewAbout the Sequence aplet Getting started with the Sequence aplet Keys to assist in the entry of equations Define the expression Plot the sequence Display the table Plot Setup, set the Seqplot option to CobwebPlot the Fibonacci sequence Select CobwebPage About the Solve aplet Solve aplet Define the equation Define known variables Getting started with the Solve apletOpen the Solve aplet @ Select Auto Solve the unknown variable Plot the equationSolve for the unknown variable a ≈20 times Solve aplet’s NUM view keys Number format Use an initial guess Message Condition Interpreting results Root- Finder at work At2 x = v0t + Plotting to find guesses$/3+$@X 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight T To move cursor to the intersection Plot the graph Home variables Using variables in equationsInitial guess 3175@*k,*k,*k About the Statistics aplet Statistics apletGetting started with the Statistics aplet 1400 920 1100 2265 2890 2200 175@1 175@ 175@5 175@ 175@4 175@ Open the Statistics aplet Enter dataTo move to the next column 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@ Select2. Linear Choose fit and data columns Explore statistics Setup plotSelect a fit in the Symbolic setup view To move to the FIT1 +2field Display the equation for the best linear fit $7+@ S to highlight Entering and editing statistical dataTo highlight 6175@ +,7@ FXUVRU Statistics aplet’s NUM view keys 160 175@ 165 175@ 170 175@ 175 175@ 180 175@ $56@ Height cm Frequency Sets will need to be selected againBefore re-use Delete data Angle SettingSave data Insert data Sort data values Defining a regression model 2VARTo choose the fit Select the Sort Order option. You can choose either Fit model Meaning Fit models To define your own fit= m lnx + b = ax3+bx2+cx+d. Needs at least Statistic Definition Computed statisticsOne-variable Columns for a linear fit only Two-variable You can plot PlottingTo plot statistical data Histogram Box and Whisker Plot Scatter Plot Plot types Fitting a curve to0182VAR data Relative ErrorCorrelation Coefficient Plotting mark 2VAR Connected points 2VAR Setting up the plot Plot setup view Trouble-shooting a plot Statistics aplet’s Plot view keys Find predicted values Calculating predicted valuesPage Inference aplet Default the input form contains example data. This exampleAbout the Inference aplet Example data Open the Inference aplet Getting started with the Inference apletInference aplet’s Symb view keys Hypothesis Tests Confidence Intervals ∝.a∝ Define the inferential method Field name Definition Importing Sample Statistics from the Statistics aplet Open Statistics aplet. Note Reset current settingsPlot test results Open the Statistics aplet @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@ Calculate statistics Open Inference aplet 2one.a Choose inference method and typeImport the data Specify a 90% confidence interval in the C field Display Numeric view Display Plot viewE, to move to Field Display the confidence interval in the Plot view One-Sample Z-Test Hypothesis testsMenu name Inputs Result Description Two-Sample Z-TestResults One-Proportion Z-Test H0 π1 = π2 Two-Proportion Z-TestSuccesses in the two populations is equal Test 1 ∝ One-Sample T-TestSelected hypothesis against the null hypothesis. The null Hypothesis is that the sample mean has some assumed value Two-Sample T-Test Sample 2 standard deviation Sample 1 standard deviation Confidence interval calculations that the HP 39G/40G can Confidence intervalsPerform are based on the Normal Z-distribution or Student’s Confidence level Two-Sample Z-Interval Two populations, ∝1 ∝2, when the population standardConfidence interval for the difference between the means Deviations, σ1 and σ2, are known Sample success count One-Proportion Z-Interval Successes in two populations Two-Proportion Z-IntervalSample 1 success count Sample 2 success count One-Sample T-Interval Two-Sample T-Interval Page Math menu Using mathematical functionsMath functions Calculus Loop Stat-Two Complex Matrices To select a functionFunction categories Functions common to keyboard and menus Math functions by categorySyntax Keyboard functions +,7@ACOS +,7@ASIN+,7@ATAN +,7@√ +,7@ABS ValuepowerABSvalue +,7@ n Taylor Calculus functionsVariableexpression Lower,upper,expression,variable Conj Complex number functionsARG Hyperbolic trigonometry Constants Alog List functionsEXP EXPM1 Matrix functions Loop functionsIterate Recurse Polycoef Polynomial functionsPolyeval Polyform Comb Probability functionsPerm Random Utpf UtpcUtpn Utpt Real-number functions →HMS HMS→INT Mant Change MODTotal RAD→DEG Sign Statistics-TwoTruncate Xpon Isolate Symbolic functionsLINEAR? Quad Quote Trigonometry functions Symbolic calculations in the Function aplet Symbolic calculationsUsing formal variables Home To find derivatives Finding derivativesGG@$/3+$@S1 Evaluate the function GG@@$/3+$@ To find derivatives in the Function aplet’s Symbolic view +,7@GG@0 @ $/3+$@ S1 @ 3 @ To find the indefinite integral using formal variablesShow the result format Thus, substituting X for S1, it can be seen that 10-26 Introduction Variables and memory management To store a value Storing and recalling variablesNumeric Precision To store the results of a calculation To use variables Vars menuCalculations 65 @$/3+$@A 175@ +,7@LIST Names or values of variables into programs $56@ *e,*e,*e,*A 2contents,.a is copied to the command line$/3+$@L3175@ List names directly from the keyboard Category Available names To copy the value of the variable into the edit line To access an aplet variableAplet variables Start the Memory Manager. a list of variable categories Memory ManagerIs displayed +,7@MEMORYPage Vectors MatricesMatrices Matrix Variables Matrix Catalog keys Creating and storing matrices+ 7@CLEAR +,7@*e, or Select the type of matrix to create To create a matrix in the matrix catalog To transmit a matrix Working with matricesClears all elements from the matrix +,7@*k, *e 728 672? To multiply and divide by a scalar Matrix arithmetic175@ 2175@*e 175@ 4175@ 175@ 8 175@ $/3+$@M1 j@$/3+$@M2 175@ $/3+$@M1@ $/3+$@M2 175@ +,7@MATRIX1 175@ Solving systems of linear equations175@7 175@ +,7@MATRIX About functions Matrix functions and commands Argument conventions Eigenvv EigenvalIdenmat Inverse Rownorm RankRref Schur Trace ExamplesTRN Identity Matrix Transposing a Matrix Reduced-Row Echelon Form Creating lists ListsCreate a list in the List Catalog Open the List catalog List catalog keys List edit keys Create a list To display a list Displaying and editing listsTo display one element To edit a list @ /@ To insert an element in a list To store one element 16a*e Transmitting lists Deleting listsTo delete a list To delete all lists List functions $/3+$@L5175@ $/3+$@L 5175@ $7+@L *A$7+@L *A,Select $/3+$@A @ POSlist, element Calculates the product of all elements in listCalculates the number of elements in a list Sorts elements in ascending order $/3+$@ L1 175@ Finding statistical values for list elements89@65@ 0@89 Go to the Numeric view To display calculated statistics 180@67$76aPage To write a note in Note view Aplet note view+,7@letter Your work is automatically saved. Press any view key +,7@ Cmds +,7@%.63$= To draw a line Aplet sketch viewSketch keys You can adjust the size of the box by moving the cursor Where you want any corner of the box to beTo draw a box Draw keys Highlight2. the variable name you want to use and press KeysPress 2.again to affix the label To create a note To import a graphics variable+,7@NOTEPAD Name of the note is ‘MYNOTE’ Begins a new note, and asks for Opens the selected note forTransmits the selected note to Another HP 39G/40G or PC 14-8 Programming Contents of a Program Structured Programming Open Program catalog Program catalog +,7@*k, or *e Program catalog keys Create a new program Creating and editing programs +,7@CMDS Enter commands Edit a programA,*e To enter functions more to come Editing keys Run a program From HOME, type RUN programname. or Using programsDebug a program Stop a program Copy a Working with programsProgram Transmit a program Delete a program About customizing an aplet Delete the contents of a programDelete all Programs $3/7@Select Aplet naming conventionCustomizing an aplet example Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Aplet commands Programming commandsCheck Select Syntax for the command is as follows Command syntax Auto-run programs Uncheck Branch commandsIF...THEN...END If test-clause IF... then Iferr trap-clause Then error-clause ENDELSE... END CASE...END Iferr Then END Drawing commands Graphic commands Grobnot →GROBGrobor Grobxor Loop commands Matrix commands Redim RandmatScale Scaleadd Prompt commands Print commands Disptime DispDisp linenumbertextitem Editmat matrixname Input Input nametitle,labelhelpdefaultGetkey Prompt MsgboxWait Wait seconds Stat-Two commands Stat-One and Stat-Two commandsStat-One commands Plot-view variables Storing and retrieving variables in programsArea Axes Extremum CoordFastRes Grid Indep HwidthInvCross Isect Recenter Nmin / NmaxRoot S1mark-S5mark Slope SimultStatPlot Umin/Umax Tracing Tmin / TmaxTstep Xcross Ytick XtickXmin / Xmax Ymin / Ymax Xzoom Symbolic-view variablesYzoom Angle R1...R9, R0 X1, Y1...X9,Y9 X0,Y0U1...U9, U0 E1...E9, E0 Digits Numeric-view variablesC1...C9, C0 NumCol FormatNumFont NumIndep NumStart NumRowNumStep NumType PageNum Creating new aplets based on existing aplets Extending aplets $/3+$@ C @ 175@ Aplet Keys$/3+$@ H 175@ $1@ $/3+$@ θ @ 180@ 35 175@ $3/ @Select Downloading e-lessons from the web Resetting an apletSolve for the missing Length of the ladder is approximately 8.72 metres To transmit an aplet Sending and receiving aplets To delete an aplet Sorting items in the aplet library menu listTo sort the aplet list Canada Reference informationRegulatory information Warranty LED safety Reference information To reset using the keyboard Resetting the HP 39G/40G 21@ key To erase all memory and reset defaultsIf the calculator does not turn on Cross matrix1,matrix2 Glossary Batteries Operating temperature 0 to 45C 32 to 113FOperating details Category Available name Menu maps of the Vars menuHome variables are User-named Function aplet variablesModes Function aplet variables are Parametric aplet variables are Parametric aplet variablesPlot-FCN Polar aplet variables are Polar aplet variables Sequence aplet variables are Sequence aplet variables Solve aplet variables are Solve aplet variables Stat-One Statistics aplet variablesStatistics aplet variables are Math functions Menu maps of the Math menuMath functions are Calculus = = Polynom Program constants Category Command Program commands +,7@ Memory Selected status messagesMessage Meaning Current screen Function value, root, extremumOr intersection is not visible Index Index Index Index Index Index Index Index Index Index Index Index Index