Chapter Calculations with real numbers | HP 49g guide

Chapter 3

Calculations with real numbers

This chapter demonstrates the use of the calculator for operations and functions related to real numbers. The user should be acquainted with the keyboard to identify certain functions available in the keyboard (e.g., SIN, COS, TAN, etc.). Also, it is assumed that the reader knows how to change the calculator’s operating system (Chapter 1), use menus and choose boxes (Chapter 1), and operate with variables (Chapter 2).

Examples of real number calculations

To perform real number calculations it is preferred to have the CAS set to Real (as opposed to Complex) mode. Exact mode is the default mode for most operations. Therefore, you may want to start your calculations in this mode. Some operations with real numbers are illustrated next:

• Use the	key for changing sign of a number.
For example, in ALG mode,					.
Y\	3.2.5\75\2Y`..25`
In RPN mode, e.g.,
• Use the	key to calculate the inverse of a number.
For example, in ALG mode,					.
In RPN mode use				.
		4`Y+-*/
• For addition, subtraction, multiplication, division, use the proper
operation key, namely,
Examples in ALG mode:
	6			+
			3		5`
Examples in RPN242*2mode: `/4					+Page 3-1

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HP 49g manual Chapter Calculations with real numbers, Examples of real number calculations

Contents

User’s manual Graphing calculatorPage Preface Page Table of Contents Calculations with real numbers Calculations with complex numbers Algebraic and arithmetic operations Solution to equations Operations with lists Vectors Matrices and linear algebra Multi-variate Calculus Applications GraphicsCalculus Applications Vector Analysis Applications Differential Equations Probability DistributionsStatistical Applications Limited Warranty W-1 Service, W-2 Regulatory information, W-4Numbers in Different Bases Chapter Getting started Basic OperationsBatteries Contents of the calculator’s display Menus Tool menuAssociated with the six soft menu keys, F1 through F6 Setting time and date Introducing the calculator’s keyboardPage Selecting calculator modes Alpha function, to enter the upper-case letter P~„p Operating Mode 23.0 √ 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 Explanation of CAS settings Selecting Display modes Selecting the display font Selecting properties of the line editor Selecting properties of the Stack References Selecting properties of the equation writer EQW Editing expressions in the stack Chapter Introducing the calculatorCalculator objects Creating arithmetic expressions Result³5*„Ü1+1/7will be shown„ÜR3as follows -2Q3`.5 Resulting…in³5*„Ü1+1/7the output„ÜR3-2Q3`.5 Creating algebraic expressions + y Using the Equation Writer EQW to create expressions Edited expression*„Ü5+1/3looks as follows + 2 ⋅ 5 + ~‚n Subdirectories Organizing data in the calculatorHome directory For this example, the Home Locks the alphabetic keyboard in lower case. When locked VariablesTyping variable names Name Contents Type Creating variables 3V5K~a12` ³~„r/„Ü Checking variables contents ‚å‚é~„r³„ì Using the right-shift key followed by soft menu key labels Deleting variables Using function Purge in the stack in Algebraic modeUsing function Purge in the stack in RPN mode @PURGE@J@@p1@@` Undo and CMD functions Choose boxes vs. Soft MenuWe use Show Prog menu list and select Memory ‚¯ Page Display now shows Not shown in this screen. To Find it we use To activate the Order command we press the soft menu key Operation key, namely Examples in ALG mode Chapter Calculations with real numbersExamples of real number calculations For both, ALG and RPN modes, using the Equation Writer Directly on the stack Combination When calculating in the stack in ALG mode Key. WhenRPN mode, enter the number first, then the function, e.g „¸Page RPN mode \„¸45`‚¹ Real number functions in the MTH menu Hyperbolic functions and their inverses Pressing shows the remaining options With units Units menuKey or Page Labels will be listed Available unitsFor Set of units Key or Keystroke sequence to navigate Through the menus Attaching units to numbers With the keyboard, e.g.,will produce the entry Using Ubase to convert to the default unit 1 m results Operations with units Different terms in parentheses, e.g 12m 3250mi Unit conversions @@OK@@-˜Physical constants in the calculator These operations produce the following output Copies value with or without units to the stack When selected, constants are shown with units attachedWhen selected, constants are shown without units Exit constants library Defining and using functions Like this Display shows what is called a tagged value HereWhich produces ‚@@@H@@ ‘LNx+1 + EXPx’ Entered by using You could try Chapter Calculations with complex numbers Setting the calculator to Complex modeTo work with complex numbers select the CAS complex mode Definitions Entering complex numbers Polar representation of a complex numberTo enter the unit imaginary number type the I key Simple operations with complex numbers Cmplx menus Cmplx menu through the MTH menu Cmplx menu in the keyboard Functions applied to complex numbers Function Droite equation of a straight line Function Droite is found in the command catalog Reference Chapter Algebraic and arithmetic operations Entering algebraic objects Simple operations with algebraic objects Press To recover Variable menu @HELP@` Functions in the ALG menu To execute the command Catalog To complete the operation Trig menu, triggered by using Expansion and factoring using log-exp functionsExpansion and factoring using trigonometric functions Operations with transcendental functions Functions in the Arithmetic menu Shows the following menuNumbers or to polynomials. The remaining options 1. Integer Polynomials Horner functionX6-1 = X5-5*X4+25X3-125X2+625X-3125X+5+15624 Proot function VariablePcoef function Quotient and Remainder functions Fractions Peval functionSIMP2 function Propfrac function Partfrac functionFcoef function Step-by-step operations with polynomials and fractions Froots function Reference Chapter Solution to equations Symbolic solution of algebraic equationsFunction Isol Function Solve Page Function Solvevx Function Zeros Numerical solver menu Polynomial Equations Enter vector of coefficientsSolve equation Page Page Financial calculations Solving equations with one unknown through NUM.SLV Solution to simultaneous equations with Mslv Solution shown is X 4.5006E-2Page Reference Chapter Operations with lists Creating and storing listsChanging sign Addition, subtraction, multiplication, division When applied to lists, acts a concatenation operator Functions‚Napplied to listsExample MTH/LIST menu Lists of complex numbersLists of algebraic objects Inverse 1/x Calculate product of elements in the list Calculate increment among consecutive elements in listCalculate summation of elements in the list Sorts elements in increasing order SEQ function, available through the command catalog , takes SEQ functionMAP function Reference Typing vectors in the stack Chapter VectorsEntering vectors General row vector Vector Vector of algebraics Storing vectors into variables in the stack Mode Then, ‚íinVectors can also be entered by using the matrix writer Stored into variables Key is used to edit the contents of a selected cell WID Function Delete Will delete Key will add a column full of zeros at the locationCell of the spreadsheet Selected Simple operations with vectors Addition, subtractionUsed in the following exercises Multiplication by a scalar, and division by a scalar Absolute value function Dot product MTH/VECTOR menuMagnitude Examples Cross product Chapter Matrices and linear algebra Entering matrices in the stack Display in RPN mode will look very similar to these Typing in the matrix directly into the stack Operations with matrices Addition and subtraction Multiplication RPN mode, try the following eight examples Cij = aik ⋅ bkj , for i = 1,2, , m j = 1,2, , n Page Function DET Solution of linear systemsCharacterizing a matrix The matrix Norm menu Function Trace 2x1 + 3x2 -5x3= Using the numerical solver for linear systemsPress Following input form will be provide right Can be written as the matrix equation A⋅x = b, if @SOLVE Solution with the inverse matrix Solution by division of matrices Chapter Graphics Graphs options in the calculator Them simultaneously if in RPN mode Use a range of -4 to Plotting an expression of the form y = fxAs an example, lets plot the function Here is picture To recover the menu, and return to the PlotAlso, check that for x = -1.48 , y = Press Then To see the table, press Soft menu key You will be returned to normal calculator displayZoom factor = 0.5. Toggle Suggested early, namely x = Option Decimal Produces x-increments Option Integer Fast 3D plotsKey simply changes the font in the table from small to big, To return to normal calculator display press Find Fast3D Values of 10 and 8 for the Step dataYou can change Orientation @EDITL Reference$ Press To leave the Edit environment Limits and derivatives Chapter Calculus ApplicationsCalc Calculus menu Function lim Infinity symbol is associated with Key, .e Including some limitsMenu within the Calcl menu Anti-derivatives and integrals Functions INT, INTVX, RISCH, Sigma and SigmavxIf and only if, fx = dF/dx, and C = constant Xdx = F b − F a Functions TAYLR, TAYLR0, and Series ⋅ x − x o n Reference Chapter Multi-variate Calculus Applications Partial derivatives Multiple integrals Y dA = b Φ x , y dydx = Chapter Vector Analysis Applications Del operatorGradient Divergence CurlAlternatively, use function Deriv as follows Solution to linear and non-linear equations Chapter Differential EquationsCALC/DIFF menu Ldec Function Ldec Function Desolve Which can be simplified to= K1⋅e-3x+ K2⋅e5x + K3⋅e2x + 450⋅x2+330⋅x+241/13500 Variable Odetype DESOLVE` Laplace Transforms Laplace transform and inverses in the calculator Function FOURIER` Fourier series for a quadratic functionWhere Exercises. Function Collect is available in the ALG menu Thus = 1/3, c Chapter Probability Distributions MTH/PROBABILITY.. sub-menu partFactorials, combinations, and permutations Random numbers MTH/PROB menu part „´The Normal distributionStudent-t distribution Chi-square distribution F distribution Chapter Statistical Applications Entering data‚Ù5 Sample vs. population Now Obtaining frequency distributions Fitting data to a function y = fx Ƒ3.FitdataCan be used Lines in RPN mode Using Key select all the options for outputs, i.e When that field is selected StatisticsTo access the summary stats… option, use Obtaining additional summary statistics Confidence intervals Press to obtain the following resultsOffers the following options Interpreted as follows @GRAPH Interval information Corresponding interval limits 21.88424 and 24.51576. Press Return to the previous results screen, and/or press @@@OK@@@ Select ∝ ≠ 150. Then, press Result is Writing non-decimal numbers Chapter Numbers in Different BasesBase menu With system flag 117 set to Soft menus, the Base menu shows @HEX Using SD cards ChapterStoring objects in the SD card Recalling an object from the SD card Purging an object from the SD card Limited Warranty Service Canada 905 206-4663 or 800- HP Rotc = Rest of the country Regulatory information USA