Differential Equations, Probability Distributions | HP 49g manual

Chapter 14 – Differential Equations, 14-1

The CALC/DIFF menu, 14-1

Solution to linear and non-linear equations, 14-1

Function LDEC, 14-2

Function DESOLVE, 14-3

The variable ODETYPE, 14-4

Laplace Transforms, 14-5

Laplace transform and inverses in the calculator, 14-5

Fourier series, 14-6

Function FOURIER, 14-6

Fourier series for a quadratic function, 14-6

Reference, 14-8

Chapter 15 – Probability Distributions, 15-1

The MTH/PROBABILITY.. sub-menu – part 1, 15-1

Factorials, combinations, and permutations, 15-1

Random numbers, 15-2

The MTH/PROB menu – part 2, 15-3

The Normal distribution, 15-3

The Student-t distribution, 15-3

The Chi-square distribution, 15-4

The F distribution, 15-4

Reference, 15-4

Chapter 16 – Statistical Applications, 16-1

Entering data, 16-1

Calculating single-variable statistics, 16-1

Obtaining frequency distributions, 16-3

Fitting data to a function y = f(x), 16-4

Obtaining additional summary statistics, 16-6

Confidence intervals, 16-7

Hypothesis testing, 16-9

Reference, 16-11

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HP 49g manual Differential Equations, Probability Distributions, Statistical Applications

Contents

Hp 49g+ graphing calculator User’s manual Printing History Preface 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 Probability 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 Menus Tool menu Setting time and date Introducing the calculator’s keyboardPage 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 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 expressionsPage Page Creating algebraic expressions 2L 1 + + 2 L + y Using the Equation Writer EQW to create expressions Page + 2 ⋅ 5 +  x + 2µ ⋅ ∆y  + e Home directory Organizing data in the calculatorSubdirectories Variables Typing variable names Creating variables Page Page Checking variables contents Page Using function Purge in the stack in Algebraic mode Deleting variables Undo 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 Chapter Calculations with real numbers Examples of real number calculationsPage Page Using powers of 10 in entering data Page Real number functions in the MTH menu Hyperbolic functions and their inversesPage Operations with units Units menuPage Available units Attaching units to numbers Operations with units Page Physical constants in the calculator Unit conversions Engl Defining and using functions ‘LNx+1 + EXPx ‘ Reference Chapter Calculations with complex numbers Setting the calculator to Complex modeDefinitions Entering complex numbers Polar representation of a complex number Simple operations with complex numbers Cmplx menus Cmplx menu through the MTH menu Cmplx menu in keyboard Functions applied to complex numbers Function Droite equation of a straight line Reference Chapter Algebraic and arithmetic operations Entering algebraic objects Simple operations with algebraic objects `‚¹ Functions in the ALG menu CollectPage Expansion and factoring using trigonometric functions Expansion and factoring using log-exp functionsOperations with transcendental functions Functions in the Arithmetic menu Polynomials Horner function Proot function VariablePcoef function Quot and Remainder functions Peval 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 Solvevx Function Zeros Numerical solver menu Polynomial Equations @SOLVE@ Solve for coefficients ˜@SYMB@ Financial calculations Solving equations with one unknown through NUM.SLV Solution to simultaneous equations with Mslv Page Reference Operations with lists of numbers Chapter Operations with listsCreating and storing lists Changing sign Addition, subtraction, multiplication, division Functions applied to lists Lists of algebraic objects Lists of complex numbersMTH/LIST menu ∆LIST SEQ function MAP function Entering vectors Chapter VectorsTyping vectors in the stack Using the Matrix Writer Mtrw to enter vectors Storing vectors into variables in the stackPage Page Simple operations with vectors Addition, subtraction Multiplication by a scalar, and division by a scalar Absolute value function Magnitude 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 Operations with matrices Addition and subtraction Multiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Page Function DET Solution of linear systemsCharacterizing a matrix The matrix Norm menu Function Trace =  a Using the numerical solver for linear systems M x2 Solution with the inverse matrix Solution by division of matrices Chapter Graphics Graphs options in the calculator Plotting an expression of the form y = fx = 1 exp− x Generating a table of values for a function Page Fast 3D plots Left-1 Right1 Near-1 Far Low High Step Indep Depnd Page Reference Limits and derivatives Chapter Calculus ApplicationsCalc Calculus menu Function lim Functions Deriv and Dervx Xdx = F x + C Anti-derivatives and integralsFunctions INT, INTVX, RISCH, Sigma and Sigmavx Infinite series Definite integrals Functions TAYLR, TAYLR0, and Series Reference Chapter Multi-variate Calculus Applications Partial derivatives Multiple integrals Φ x, ydydx Gradient Chapter Vector Analysis ApplicationsDel operator ∇ = i ⋅ ∂ + j ⋅ ∂ + k ⋅ ∂ ∂x ∂y ∂z Divergence Curl Chapter Differential Equations Solution to linear and non-linear equationsCALC/DIFF menu Function Ldec Function Desolve Yx = 5 ⋅ exp−x3 / 3 ⋅ expx3 / 3 ⋅ dx + C0 Variable Odetype Desolve Laplace Transforms Laplace transform and inverses in the calculator Function Fourier Fourier series= ∑ c n Fourier series for a quadratic functionPage Reference Factorials, combinations, and permutations Chapter Probability DistributionsMTH/PROBABILITY.. sub-menu part − 2... − + 1 = − r Random numbers Normal distribution MTH/PROB menu partStudent-t distribution Chi-square distribution F distribution Entering 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 Recalling an object from the SD card Purging an object from the SD card Limited Warranty Service HP Invent Regulatory information USA