Chapter Algebraic and arithmetic operations | HP 49g guide

Chapter 5

Algebraic and arithmetic operations

An algebraic object, or simply, algebraic, is any number, variable name or algebraic expression that can be operated upon, manipulated, and combined according to the rules of algebra. Examples of algebraic objects are the following:

•	A number:	12.3, 15.2_m, ‘π ’, ‘e’, ‘i’
•	A variable name:	‘a’, ‘ux’, ‘width’, etc.
•	An expression:	‘pD^2/4’,’f(L/D)(V^2/(2g))’,

•An equation: ‘p*V = n*R*T’, ‘Q=(Cu/n)*A(y)*R(y)^(2/3)*√ So’

Entering algebraic objects

Algebraic objects can be created by typing the object between single quotes directly into stack level 1 or by using the equation writer [EQW]. For example, to enter the algebraic object ‘π *D^2/4’ directly into stack level 1 use:

An algebraic object³„ì*~dQ2/4`can also be built in the Equation Writer and then sent to the stack, or operated upon in the Equation Writer itself. The operation of the Equation Writer was described in Chapter . As an exercise, build the following algebraic object in the Equation Writer:

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HP 49g manual Chapter Algebraic and arithmetic operations, Entering algebraic objects

Contents

Graphing calculator User’s manualPage Preface Page Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbers Operations with lists Solution to equations Matrices and linear algebra Vectors Vector Analysis Applications GraphicsCalculus Applications Multi-variate Calculus Applications Probability Distributions Differential EquationsStatistical Applications Service, W-2 Regulatory information, W-4 Limited Warranty W-1Numbers in Different Bases Basic Operations Chapter Getting startedBatteries Contents of the calculator’s display Tool menu MenusAssociated with the six soft menu keys, F1 through F6 Introducing the calculator’s keyboard Setting time and datePage Alpha function, to enter the upper-case letter P Selecting calculator modes~„p 23.0 Operating Mode √ 3.*5.-1/3.*3./23.3+EXP2.5 Lets try now the expression proposed earlier Number Format and decimal dot or comma Page Page Page Angle Measure Coordinate System Selecting CAS settings Selecting Display modes Explanation of CAS settings Selecting the display font Selecting properties of the line editor Selecting properties of the Stack Selecting properties of the equation writer EQW References Creating arithmetic expressions Chapter Introducing the calculatorCalculator objects Editing expressions in the stack Result³5*„Ü1+1/7will be shown„ÜR3as follows -2Q3`.5 Resulting…in³5*„Ü1+1/7the output„ÜR3-2Q3`.5 + y Creating algebraic expressions Using the Equation Writer EQW to create expressions Edited expression*„Ü5+1/3looks as follows + 2 ⋅ 5 + ~‚n For this example, the Home Organizing data in the calculatorHome directory Subdirectories Variables Locks the alphabetic keyboard in lower case. When lockedTyping variable names Creating variables Name Contents Type 3V5K~a12` ³~„r/„Ü ‚å‚é~„r³„ì Checking variables contents Using the right-shift key followed by soft menu key labels @PURGE@J@@p1@@` Using function Purge in the stack in Algebraic modeUsing function Purge in the stack in RPN mode Deleting variables Choose boxes vs. Soft Menu Undo and CMD functionsWe use Show Prog menu list and select Memory ‚¯ Page Not shown in this screen. To Find it we use Display now shows To activate the Order command we press the soft menu key Chapter Calculations with real numbers Operation key, namely Examples in ALG modeExamples of real number calculations Directly on the stack For both, ALG and RPN modes, using the Equation Writer Key. When Combination When calculating in the stack in ALG modeRPN mode, enter the number first, then the function, e.g „¸Page \„¸45`‚¹ RPN mode Hyperbolic functions and their inverses Real number functions in the MTH menu Pressing shows the remaining options Units menu With unitsKey or Page Key or Keystroke sequence to navigate Through the menus Available unitsFor Set of units Labels will be listed With the keyboard, e.g.,will produce the entry Attaching units to numbers Operations with units Using Ubase to convert to the default unit 1 m results 12m 3250mi Different terms in parentheses, e.g These operations produce the following output @@OK@@-˜Physical constants in the calculator Unit conversions Exit constants library When selected, constants are shown with units attachedWhen selected, constants are shown without units Copies value with or without units to the stack Like this Display shows what is called a tagged value Here Defining and using functionsWhich produces ‘LNx+1 + EXPx’ ‚@@@H@@ You could try Entered by using Definitions Setting the calculator to Complex modeTo work with complex numbers select the CAS complex mode Chapter Calculations with complex numbers Polar representation of a complex number Entering complex numbersTo enter the unit imaginary number type the I key Simple operations with complex numbers Cmplx menu through the MTH menu Cmplx menus Cmplx menu in the keyboard Function Droite equation of a straight line Functions applied to complex numbers Reference Function Droite is found in the command catalog Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects Variable menu Press To recover Functions in the ALG menu @HELP@` Catalog To complete the operation To execute the command Operations with transcendental functions Expansion and factoring using log-exp functionsExpansion and factoring using trigonometric functions Trig menu, triggered by using Shows the following menu Functions in the Arithmetic menuNumbers or to polynomials. The remaining options 1. Integer Horner function PolynomialsX6-1 = X5-5*X4+25X3-125X2+625X-3125X+5+15624 Quotient and Remainder functions VariablePcoef function Proot function Peval function FractionsSIMP2 function Partfrac function Propfrac functionFcoef function Froots function Step-by-step operations with polynomials and fractions Reference Symbolic solution of algebraic equations Chapter Solution to equationsFunction Isol Function Solve Page Function Zeros Function Solvevx Numerical solver menu Enter vector of coefficients Polynomial EquationsSolve equation Page Page Solving equations with one unknown through NUM.SLV Financial calculations Solution shown is X 4.5006E-2 Solution to simultaneous equations with MslvPage Reference Creating and storing lists Chapter Operations with listsChanging sign Addition, subtraction, multiplication, division Functions‚Napplied to lists When applied to lists, acts a concatenation operatorExample Inverse 1/x Lists of complex numbersLists of algebraic objects MTH/LIST menu Sorts elements in increasing order Calculate increment among consecutive elements in listCalculate summation of elements in the list Calculate product of elements in the list SEQ function SEQ function, available through the command catalog , takesMAP function Reference General row vector Vector Vector of algebraics Chapter VectorsEntering vectors Typing vectors in the stack Stored into variables Mode Then, ‚íinVectors can also be entered by using the matrix writer Storing vectors into variables in the stack WID Key is used to edit the contents of a selected cell Selected Key will add a column full of zeros at the locationCell of the spreadsheet Function Delete Will delete Addition, subtraction Simple operations with vectorsUsed in the following exercises Absolute value function Multiplication by a scalar, and division by a scalar Examples MTH/VECTOR menuMagnitude Dot product Cross product Entering matrices in the stack Chapter Matrices and linear algebra Typing in the matrix directly into the stack Display in RPN mode will look very similar to these Addition and subtraction Operations with matrices RPN mode, try the following eight examples Multiplication Cij = aik ⋅ bkj , for i = 1,2, , m j = 1,2, , n Page Function Trace Solution of linear systemsCharacterizing a matrix The matrix Norm menu Function DET Can be written as the matrix equation A⋅x = b, if Using the numerical solver for linear systemsPress Following input form will be provide right 2x1 + 3x2 -5x3= @SOLVE Solution by division of matrices Solution with the inverse matrix Graphs options in the calculator Chapter Graphics Plotting an expression of the form y = fx Them simultaneously if in RPN mode Use a range of -4 toAs an example, lets plot the function Press Then To recover the menu, and return to the PlotAlso, check that for x = -1.48 , y = Here is picture Suggested early, namely x = You will be returned to normal calculator displayZoom factor = 0.5. Toggle To see the table, press Soft menu key To return to normal calculator display press Fast 3D plotsKey simply changes the font in the table from small to big, Option Decimal Produces x-increments Option Integer Values of 10 and 8 for the Step data Find Fast3DYou can change Orientation @EDITL Press To leave the Edit environment Reference$ Function lim Chapter Calculus ApplicationsCalc Calculus menu Limits and derivatives Including some limits Infinity symbol is associated with Key, .eMenu within the Calcl menu Functions INT, INTVX, RISCH, Sigma and Sigmavx Anti-derivatives and integralsIf and only if, fx = dF/dx, and C = constant Xdx = F b − F a ⋅ x − x o n Functions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus Applications Y dA = b Φ x , y dydx = Multiple integrals Del operator Chapter Vector Analysis ApplicationsGradient Curl DivergenceAlternatively, use function Deriv as follows Chapter Differential Equations Solution to linear and non-linear equationsCALC/DIFF menu Function Ldec Ldec Which can be simplified to Function Desolve= K1⋅e-3x+ K2⋅e5x + K3⋅e2x + 450⋅x2+330⋅x+241/13500 DESOLVE` Variable Odetype Laplace transform and inverses in the calculator Laplace Transforms Fourier series for a quadratic function Function FOURIER`Where Exercises. Function Collect is available in the ALG menu Thus = 1/3, c MTH/PROBABILITY.. sub-menu part Chapter Probability DistributionsFactorials, combinations, and permutations Random numbers „´The Normal distribution MTH/PROB menu partStudent-t distribution F distribution Chi-square distribution Entering data‚Ù5 Chapter Statistical Applications Now Sample vs. population Obtaining frequency distributions Ƒ3.Fitdata Fitting data to a function y = fxCan be used Lines in RPN mode Obtaining additional summary statistics When that field is selected StatisticsTo access the summary stats… option, use Using Key select all the options for outputs, i.e Press to obtain the following results Confidence intervalsOffers the following options Interpreted as follows Interval information @GRAPH Return to the previous results screen, and/or press Corresponding interval limits 21.88424 and 24.51576. Press @@@OK@@@ Select ∝ ≠ 150. Then, press Result is With system flag 117 set to Soft menus, the Base menu shows Chapter Numbers in Different BasesBase menu Writing non-decimal numbers @HEX Chapter Using SD cardsStoring objects in the SD card Purging an object from the SD card Recalling an object from the SD card Limited Warranty Service Rotc = Rest of the country Canada 905 206-4663 or 800- HP USA Regulatory information