Fourier series for a quadratic function | HP 50g guide

Fourier series for a quadratic function

Determine the coefficients c0, c1, and c2 for the function g(t) = (t-1)2+(t-1), with period T = 2.

Using the calculator in ALG mode, first we define functions f(t) and g(t):

Next, we move to the CASDIR sub-directory under HOME to change the value of variable PERIOD, e.g.,

„(hold) §`J@)CASDI`2K@PERIOD `

Return to the sub-directory where you defined functions f and g, and calculate the coefficients. Set CAS to Complex mode (see chapter 2) before trying the exercises. Function COLLECT is available in the ALG menu (‚×).

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HP 50g manual Fourier series for a quadratic function

Contents

User’s manual HP 50g graphing calculator Printing History Preface 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 Calculus Applications Graphics Vector Analysis Applications Multi-variateCalculus ApplicationsDifferential Equations Probability Distributions Statistical Applications Using SD cardsNumbers in Different Bases Equation Library Batteries Chapter Getting startedBasic Operations Page Tool menu Contents of the calculator’s displayMenus Introducing the calculator’s keyboard Setting time and date ALPHA-Left-Shift function, to enter the lower-case letter p Selecting calculator modes √ 3.*5.-1/3.*3./23.3+EXP2.5 Operating ModePage Lets try now the expression proposed earlier Fixed format with decimals Number Format and decimal dot or commaStandard format Scientific format Engineering format Decimal comma vs. decimal point Coordinate System Angle Measure Selecting CAS settings Explanation of CAS settings Selecting Display modes Selecting properties of the line editor Selecting the display font Selecting properties of the Stack Selecting properties of the equation writer EQW References Calculator objects Chapter Introducing the calculatorEditing expressions in the stack Creating arithmetic expressionsPage Page 2L 1 + + 2 L + y Creating algebraic expressions Using the Equation Writer EQW to create expressions + 2 ⋅ 5 + ⎛ x + 2 ∝ ⋅ ∆y ⎞ Home directory Organizing data in the calculator Typing variable names VariablesSubdirectories Creating variables Algebraic mode RPN mode Page Checking variables contents Deleting variables Listing the contents of all variables in the screenUsing function Purge in the stack in Algebraic mode Using function Purge in the stack in RPN mode Choose boxes vs. Soft Menu Undo and CMD functions @@OK@@ References Examples of real number calculations Chapter Calculations with real numbersPage Using powers of 10 in entering data Page Hyperbolic functions and their inverses Using calculator menusReal number functions in the MTH menu Page Units menu Operations with unitsPage Attaching units to numbers Available units Unit prefixes Operations with units Unit conversions Quit Physical constants in the calculatorPage Defining and using functions Reference Definitions Setting the calculator to Complex modeChapter Calculations with complex numbers Entering complex numbers Polar representation of a complex number Cmplx menu through the MTH menu Simple operations with complex numbersCmplx menus Forms the complex number x,y out of real numbers x Cmplx menu in keyboard Functions applied to complex numbers Function Droite equation of a straight line Page Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects Functions in the ALG menu Collect Operations with transcendental functions Expansion and factoring using log-exp functions Expansion and factoring using trigonometric functions FACTORSSIMP2 Functions in the Arithmetic menu Horner function PolynomialsVariable Pcoef function Proot function FractionsQuot and Remainder functions Peval function Propfrac function SIMP2 functionPartfrac function Fcoef function − 5X 2 + 3X − Step-by-step operations with polynomials and fractionsFroots function Reference Function Isol Chapter Solution to equationsSymbolic solution of algebraic equations Function Solve Page Function Zeros Function Solvevx Numerical solver menu Polynomial Equations Finding the solutions to a polynomial equation Enter vector of roots Generating an algebraic expression for the polynomial Financial calculations Function Steq Solving equations with one unknown through Solution to simultaneous equations with Mslv Reference Page Creating and storing lists Chapter Operations with listsOperations with lists of numbers Changing sign Addition, subtraction, multiplication, division Page Functions applied to lists Lists of complex numbers MTH/LIST menu Lists of algebraic objectsPage MAP function SEQ functionPage Typing vectors in the stack Chapter VectorsEntering vectors Storing vectors into variables in the stack Moving to the right vs. moving down in the Matrix Writer Using the Matrix Writer Mtrw to enter vectors Press @GOTO@ 3@@OK@@ 3@@OK@@ @@OK@@ to move to position 3,3 Addition, subtraction Simple operations with vectors Absolute value function MTH/VECTOR menuMultiplication by a scalar, and division by a scalar Cross product MagnitudeDot product Reference Entering matrices in the stack Using the Matrix WriterChapter Matrices and linear algebra Typing in the matrix directly into the stack Operations with matrices Multiplication by a scalar Addition and subtractionMultiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Matrix-vector multiplicationMatrix multiplication Term-by-term multiplication Raising a matrix to a real power Inverse matrix Identity matrix Function DET Characterizing a matrix The matrix Norm menuFunction Trace TrA = ∑aii Using the numerical solver for linear systems Solution of linear systems ⎢x2 = ⎢1 Solution by division of matrices Solution with the inverse matrix References Graphs options in the calculator Chapter Graphics = 1 exp− x Plotting an expression of the form y = fxPage Generating a table of values for a function Fast 3D plots Keep the default plot window ranges to read Reference Page Calc Calculus menu Chapter Calculus ApplicationsLimits and derivatives Function lim Lim f Functions Deriv and Dervx Anti-derivatives and integralsFunctions INT, INTVX, RISCH, Sigma and Sigmavx Xdx = F x + C Definite integrals = ∑ Infinite seriesFunctions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus Applications Multiple integrals Gradient Chapter Vector Analysis ApplicationsDel operator Curl Divergence Chapter Differential Equations Solution to linear and non-linear equationsCALC/DIFF menu Function LdecPage Variable Odetype Function Desolve Laplace transform and inverses in the calculator Laplace Transforms Function Fourier Fourier seriesLf t= F s = 0∞ f t ⋅ e− st dt 2inπt Fourier series for a quadratic function Reference Page MTH/PROBABILITY.. sub-menu part Chapter Probability DistributionsFactorials, combinations, and permutations − r + Random numbers Student-t distribution MTH/PROB menu partNormal distribution F distribution Chi-square distribution Entering data Chapter Statistical Applications Sample vs. population Calculating single-variable statistics Obtaining frequency distributions Page 195238095238 + 2.00857242857*X Correlation Covariance Fitting data to a function y = fx Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Page Base menu Chapter Numbers in Different Bases Writing non-decimal numbers Formatting an SD card Chapter Using SD cardsInserting and removing an SD card Storing objects on the SD card Accessing objects on an SD card Purging an object from the SD card Recalling an object from the SD card Specifying a directory on an SD card Purging all objects on the SD card by reformatting `#EQLIB #EQNLI Chapter Equation Library Step 30 ##¢0#- L *!!!!!!V0!!!!!+ Reference Limited Warranty W-2 Europe Asia Pacific Country Telephone numbers Service America Country Telephone numbers Federal Communications Commission Notice Regulatory information Canadian Notice Korean Notice