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HP 49g Chapter Solution to equations, Symbolic solution of algebraic equations, Function Isol

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Chapter 6

Solution to equations

Associated with the 7key there are two menus of equation-solving functions, the Symbolic SOLVer („Î), and the NUMerical SoLVer (‚Ï). Following, we present some of the functions contained in these menus.

Symbolic solution of algebraic equations

Here we describe some of the functions from the Symbolic Solver menu. Activate the menu by using the keystroke combination „Î. With system flag 117 set to CHOOSE boxes, the following menu lists will be available:

Functions ISOL and SOLVE can be used to solve for any unknown in a polynomial equation. Function SOLVEVX solves a polynomial equation where the unknown is the default CAS variable VX (typically set to ‘X’). Finally, function ZEROS provides the zeros, or roots, of a polynomial.

Function ISOL

Function ISOL(Equation, variable) will produce the solution(s) to Equation by isolating variable. For example, with the calculator set to ALG mode, to solve for t in the equation at3-bt = 0 we can use the following:

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HP 49g manual Chapter Solution to equations, Symbolic solution of algebraic equations, Function Isol

Contents

User’s manual Hp 49g+ graphing calculatorPrinting History Preface Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbersOperations with lists Solution to equationsMatrices and linear algebra VectorsVector Analysis Applications GraphicsCalculus Applications Multi-variate Calculus ApplicationsProbability Distributions Differential EquationsStatistical Applications Limited Warranty W-1 Using SD cardsNumbers in Different Bases Basic Operations Chapter Getting startedBatteries Contents of the calculator’s display Tool menu MenusIntroducing the calculator’s keyboard Setting time and datePage Selecting calculator modes 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 settingsSelecting the display font Selecting properties of the line editor Selecting properties of the Stack Selecting properties of the equation writer EQW ReferencesCreating arithmetic expressions Chapter Introducing the calculatorCalculator objects Editing expressions in the stackPage Page 2L 1 + + 2 L + y Creating algebraic expressionsUsing the Equation Writer EQW to create expressions Page + 2 ⋅ 5 + + e  x + 2µ ⋅ ∆y Home directory Organizing data in the calculatorSubdirectories Typing variable names VariablesCreating variables Page Page Checking variables contents Page Deleting variables Using function Purge in the stack in Algebraic modeUndo and CMD functions Using function Purge in the stack in RPN modeChoose boxes vs. Soft Menu Show Prog menu list and select Memory Page References Examples of real number calculations Chapter Calculations with real numbersPage Page Using powers of 10 in entering data Page Hyperbolic functions and their inverses Real number functions in the MTH menuPage Units menu Operations with unitsPage Available units Attaching units to numbers Operations with units Page Unit conversions Physical constants in the calculatorEngl Defining and using functions ‘LNx+1 + EXPx ‘ Reference Chapter Calculations with complex numbers Setting the calculator to Complex modeDefinitions Polar representation of a complex number Entering complex numbersSimple operations with complex numbers Cmplx menu through the MTH menu Cmplx menusCmplx menu in keyboard Function Droite equation of a straight line Functions applied to complex numbersReference Entering algebraic objects Chapter Algebraic and arithmetic operationsSimple operations with algebraic objects `‚¹ Collect Functions in the ALG menuPage Expansion and factoring using trigonometric functions Expansion and factoring using log-exp functionsOperations with transcendental functions Functions in the Arithmetic menu Horner function PolynomialsQuot and Remainder functions VariablePcoef function Proot functionPeval function FractionsSIMP2 function Partfrac function Propfrac functionFcoef function Froots function Step-by-step operations with polynomials and fractions− 5X 2 + 3X − Reference Symbolic solution of algebraic equations Chapter Solution to equationsFunction Isol Function Solve Page Function Zeros Function SolvevxNumerical solver menu @SOLVE@ Polynomial EquationsSolve for coefficients ˜@SYMB@ Solving equations with one unknown through NUM.SLV Financial calculationsSolution to simultaneous equations with Mslv Page Reference Changing sign Chapter Operations with listsCreating and storing lists Operations with lists of numbersAddition, subtraction, multiplication, division Functions applied to lists Lists of algebraic objects Lists of complex numbersMTH/LIST menu ∆LIST MAP function SEQ functionEntering vectors Chapter VectorsTyping vectors in the stack Storing vectors into variables in the stack Using the Matrix Writer Mtrw to enter vectorsPage Page Addition, subtraction Simple operations with vectorsAbsolute value function Multiplication by a scalar, and division by a scalarMagnitude MTH/VECTOR menuDot product Cross product Chapter Matrices and linear algebra Using the Matrix WriterEntering matrices in the stack Typing in the matrix directly into the stack Addition and subtraction Operations with matricesMultiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Page Function Trace Solution of linear systemsCharacterizing a matrix The matrix Norm menu Function DET=  a Using the numerical solver for linear systems M x2 Solution by division of matrices Solution with the inverse matrixGraphs options in the calculator Chapter Graphics= 1 exp− x Plotting an expression of the form y = fxGenerating a table of values for a function Page Fast 3D plots Left-1 Right1 Near-1 Far Low High Step Indep Depnd Page Reference Function lim Chapter Calculus ApplicationsCalc Calculus menu Limits and derivativesFunctions Deriv and Dervx Xdx = F x + C Anti-derivatives and integralsFunctions INT, INTVX, RISCH, Sigma and Sigmavx Definite integrals Infinite seriesFunctions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus ApplicationsΦ x, ydydx Multiple integrals∇ = i ⋅ ∂ + j ⋅ ∂ + k ⋅ ∂ ∂x ∂y ∂z Chapter Vector Analysis ApplicationsDel operator GradientCurl DivergenceChapter Differential Equations Solution to linear and non-linear equationsCALC/DIFF menu Function Ldec Yx = 5 ⋅ exp−x3 / 3 ⋅ expx3 / 3 ⋅ dx + C0 Function DesolveDesolve Variable OdetypeLaplace transform and inverses in the calculator Laplace TransformsFourier series for a quadratic function Fourier series= ∑ c n Function FourierPage Reference − 2... − + 1 = − r Chapter Probability DistributionsMTH/PROBABILITY.. sub-menu part Factorials, combinations, and permutationsRandom numbers Normal distribution MTH/PROB menu partStudent-t distribution F distribution Chi-square distributionEntering data Chapter Statistical ApplicationsCalculating single-variable statistics Page Obtaining frequency distributions Fitting data to a function y = fx 195238095238 + 2.00857242857*X Correlation Covariance Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Base menu Chapter Numbers in Different BasesWriting non-decimal numbers HEX DEC OCT BIN Chapter Using SD cardsStoring objects in the SD card Purging an object from the SD card Recalling an object from the SD cardLimited Warranty Service HP Invent USA Regulatory information