HP 49g Examples of real number calculations

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, \2.5`.

In RPN mode, e.g., 2.5\.

•Use the Ykey to calculate the inverse of a number. For example, in ALG mode, Y2`.

In RPN mode use 4`Y.

•For addition, subtraction, multiplication, division, use the proper operation key, namely, +-*/.

Examples in ALG mode:

3.7+5.2`

6.3-8.5`

4.2*2.5`

2.3/4.5`

Examples in RPN mode:

3.7` 5.2+

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Contents

Page Page Page Page Chapter 1 – Getting Started Chapter 2 – Introducing the calculator Chapter 3 – Calculations with real numbers Chapter 4 – Calculations with complex numbers Chapter 5 – Algebraic and arithmetic operations Chapter 6 – Solution to equations Chapter 7 – Operations with lists Chapter 8 – Vectors Chapter 9 – Matrices and linear algebra Chapter 10 – Graphics Chapter 11 – Calculus Applications Chapter 12 – Multi-variateCalculus Applications Chapter 13 – Vector Analysis Applications Chapter 14 – Differential Equations Chapter 15 – Probability Distributions Chapter 16 – Statistical Applications Chapter 17 – Numbers in Different Bases Chapter 18 – Using SD cards Limited Warranty – W-1 Basic Operations Batteries Turning the calculator on and off Adjusting the display contrast Contents of the calculator’s display Menus The TOOL menu Setting time and date Introducing the calculator’s keyboard Page Selecting calculator modes Operating Mode Page Page Number Format and decimal dot or comma •Standard format: •Fixed format with decimals: Page Page Angle Measure Coordinate System Selecting CAS settings •Press the Hbutton to activate the CALCULATOR MODES input form Explanation of CAS settings •Indep var: The independent variable for CAS applications. Typically, VX = ‘X’ Modulo Numeric Approx Selecting the display font Selecting properties of the line editor _Small Changes font size to small _Full page Allows to place the cursor after the end of the line Selecting properties of the Stack Selecting properties of the equation writer (EQW) References Calculator objects Editing expressions in the stack Creating arithmetic expressions 1.0 + Page Page Creating algebraic expressions 2L 1 + Using the Equation Writer (EQW) to create expressions Page NOTE  x + 2∝⋅ ∆ y  + e Organizing data in the calculator The HOME directory Subdirectories Variables Typing variable names Creating variables Name Contents Type Page Page Checking variables contents Page Deleting variables Using function PURGE in the stack in Algebraic mode Using function PURGE in the stack in RPN mode UNDO and CMD functions CHOOSE boxes vs. Soft MENU Page Page Page Examples of real number calculations Page Page Using powers of 10 in entering data Page Real number functions in the MTH menu Using calculator menus: Hyperbolic functions and their inverses Page Note: Operations with units The UNITS menu Page Available units Attaching units to numbers Note Operations with units Page Unit conversions Physical constants in the calculator Page Defining and using functions Page Reference Definitions Setting the calculator to COMPLEX mode Entering complex numbers Polar representation of a complex number Simple operations with complex numbers The CMPLX menus CMPLX menu through the MTH menu CHOOSE boxes CMPLX menu in the keyboard Functions applied to complex numbers Function DROITE: equation of a straight line Page Entering algebraic objects Simple operations with algebraic objects The same results are obtained in RPN mode if using the following keystrokes: Functions in the ALG menu To complete the operation press @@OK@@. Here is the help screen for function COLLECT: For example, for function SUBST, we find the following CAS help facility entry: Operations with transcendental functions Expansion and factoring using log-expfunctions Expansion and factoring using trigonometric functions Functions in the ARITHMETIC menu FACTORS:SIMP2: Polynomials The HORNER function HORNER(‘X^3+2*X^2-3*X+1’,2)= {‘X^2+4*X+5, 2, 11} i.e., X3+2X2-3X+1= (X2+4X+5)(X-2)+11.Also The variable The PCOEF function The PROOT function The QUOTIENT and REMAINDER functions The PEVAL function Fractions The SIMP2 function The PROPFRAC function The PARTFRAC function The FCOEF function The FROOTS function Step-by-stepoperations with polynomials and fractions Page Symbolic solution of algebraic equations Function ISOL Function SOLVE Page Function SOLVEVX Function ZEROS Numerical solver menu Notes: Polynomial Equations Page Page Financial calculations Solving equations with one unknown through NUM.SLV Solution to simultaneous equations with MSLV Page Page Creating and storing lists Operations with lists of numbers Changing sign Addition, subtraction, multiplication, division Functions applied to lists Lists of complex numbers Lists of algebraic objects The MTH/LIST menu Page The SEQ function The MAP function Entering vectors Typing vectors in the stack Storing vectors into variables in the stack Using the matrix writer (MTRW) to enter vectors Page Page Simple operations with vectors Changing sign Addition, subtraction Multiplication by a scalar, and division by a scalar Absolute value function The MTH/VECTOR menu Magnitude Dot product Cross product Entering matrices in the stack Typing in the matrix directly into the stack Operations with matrices Addition and subtraction Multiplication for Page tr(A) = ∑n aii  an1 Using the numerical solver for linear systems , and Solution with the inverse matrix Solution by “division” of matrices Graphs options in the calculator Plotting an expression of the form y = f(x) f (x) = 1 exp(− x 2 ) Generating a table of values for a function Page Fast 3D plots Page Page Page The CALC (Calculus) menu Limits and derivatives Function lim Functions DERIV and DERVX ∫f (x)dx = F (x) + C f (x)dx = F (b) − F (a) ⋅ (x − xo )n Functions TAYLR, TAYLR0, and SERIES Page Partial derivatives ∂∂x (x cos( y)) = cos( y), ∂∂y (x cos( y)) = −x sin( y) φ (x, y)dA = b g ( x )φ (x, y)dydx grad divF curl The CALC/DIFF menu Solution to linear and non-linearequations Function LDEC Function DESOLVE y(x) = 5 ⋅ exp(− x3 / 3) ⋅ (∫ exp(x3 / 3) ⋅ dx + C0 ) The variable ODETYPE Laplace Transforms Laplace transform and inverses in the calculator L{ f (t)} F (s) = ∫0 f (t) = ∑ cn Page Page The MTH/PROBABILITY.. sub-menu- part Factorials, combinations, and permutations 1)(n 2)...(n Random numbers The MTH/PROB menu - part The Normal distribution The Student-tdistribution The Chi-squaredistribution The F distribution Entering data Calculating single-variablestatistics Page Obtaining frequency distributions Fitting data to a function y = f(x) Page Obtaining additional summary statistics summary stats… Confidence intervals 6. Conf Interval Page Hypothesis testing Page Page The BASE menu Writing non-decimalnumbers Page Using SD cards Storing objects in the SD card Recalling an object from the SD card Purging an object from the SD card Page Service Europe Country : Telephone numbers Austria Page Regulatory information USA „Reorient or relocate the receiving antenna „Relocate the calculator, with respect to the receiver Connections to Peripheral Devices