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HPg graphing calculator
user’s guide
H
Edition 1
HP part number F2229AA-90006
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Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNIS
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Preface You have in your hands a compact symbolic and numerical computer that will facilitate calculation and mathematical analysis of problems in a variety of disciplines, from elementary mathematics to advanced engineering and science subjects. Although referred to as a calculator, because of its compact format resembling typical hand-held calculating devices, the HP 50g should be thought of as a graphics/programmable hand-held computer. The HP 50g can be operated in two different cal
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For symbolic operations the calculator includes a powerful Computer Algebraic System (CAS) that lets you select different modes of operation, e.g., complex numbers vs. real numbers, or exact (symbolic) vs. approximate (numerical) mode. The display can be adjusted to provide textbook-type expressions, which can be useful when working with matrices, vectors, fractions, summations, derivatives, and integrals. The high-speed graphics of the calculator produce complex figures in very little time.
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Table of contents Chapter 1 - Getting started ,1-1 Basic Operations ,1-1 Batteries ,1-1 Turning the calculator on and off ,1-2 Adjusting the display contrast ,1-2 Contents of the calculator’s display ,1-2 Menus ,1-3 SOFT menus vs. CHOOSE boxes ,1-4 Selecting SOFT menus or CHOOSE boxes ,1-5 The TOOL menu ,1-7 Setting time and date ,1-7 Introducing the calculator’s keyboard ,1-11 Selecting calculator modes ,1-12 Operating Mode ,1-13 Number Format and decimal dot or comma ,1-17 Angle Measure ,1-2
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Chapter 2 - Introducing the calculator ,2-1 Calculator objects ,2-1 Editing expressions on the screen ,2-3 Creating arithmetic expressions ,2-3 Editing arithmetic expressions ,2-6 Creating algebraic expressions ,2-7 Editing algebraic expressions ,2-8 Using the Equation Writer (EQW) to create expressions ,2-10 Creating arithmetic expressions ,2-11 Editing arithmetic expressions ,2-17 Creating algebraic expressions ,2-19 Editing algebraic expressions ,2-21 Creating and editing summations, derivat
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Other flags of interest ,2-66 CHOOSE boxes vs. Soft MENU ,2-67 Selected CHOOSE boxes ,2-69 Chapter 3 - Calculation with real numbers ,3-1 Checking calculators settings ,3-1 Checking calculator mode ,3-2 Real number calculations ,3-2 Changing sign of a number, variable, or expression ,3-3 The inverse function ,3-3 Addition, subtraction, multiplication, division ,3-3 Using parentheses ,3-4 Absolute value function ,3-4 Squares and square roots ,3-5 Powers and roots ,3-5 Base-10 logarithms and powe
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Physical constants in the calculator ,3-29 Special physical functions ,3-32 Function ZFACTOR ,3-32 Function F0λ ,3-33 Function SIDENS ,3-33 Function TDELTA ,3-33 Function TINC ,3-34 Defining and using functions ,3-34 Functions defined by more than one expression ,3-36 The IFTE function ,3-36 Combined IFTE functions ,3-37 Chapter 4 - Calculations with complex numbers ,4-1 Definitions ,4-1 Setting the calculator to COMPLEX mode ,4-1 Entering complex numbers ,4-2 Polar representation of a complex
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FACTOR ,5-5 LNCOLLECT ,5-5 LIN ,5-5 PARTFRAC ,5-5 SOLVE ,5-5 SUBST ,5-5 TEXPAND ,5-5 Other forms of substitution in algebraic expressions ,5-6 Operations with transcendental functions ,5-7 Expansion and factoring using log-exp functions ,5-7 Expansion and factoring using trigonometric functions ,5-8 Functions in the ARITHMETIC menu ,5-9 DIVIS,5-9 FACTORS ,5-9 LGCD,5-10 PROPFRAC ,5-10 SIMP2 ,5-10 INTEGER menu ,5-10 POLYNOMIAL menu ,5-10 MODULO menu ,5-11 Applications of the ARITHMETIC menu ,5-
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The PROOT function ,5-21 The PTAYL function ,5-21 The QUOT and REMAINDER functions ,5-21 The EPSX0 function and the CAS variable EPS ,5-22 The PEVAL function ,5-22 The TCHEBYCHEFF function ,5-22 Fractions ,5-23 The SIMP2 function ,5-23 The PROPFRAC function ,5-23 The PARTFRAC function ,5-23 The FCOEF function ,5-24 The FROOTS function ,5-24 Step-by-step operations with polynomials and fractions ,5-25 The CONVERT Menu and algebraic operations ,5-26 UNITS convert menu (Option 1) ,5-26 BASE conve
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Variable EQ ,6-26 The SOLVR sub-menu ,6-26 The DIFFE sub-menu ,6-29 The POLY sub-menu ,6-29 The SYS sub-menu ,6-30 The TVM sub-menu ,6-30 Chapter 7 - Solving multiple equations ,7-1 Rational equation systems ,7-1 Example 1 – Projectile motion ,7-1 Example 2 – Stresses in a thick wall cylinder ,7-2 Example 3 - System of polynomial equations ,7-4 Solution to simultaneous equations with MSLV ,7-4 Example 1 - Example from the help facility ,7-5 Example 2 - Entrance from a lake into an open channel
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List size ,8-10 Extracting and inserting elements in a list ,8-10 Element position in the list ,8-11 HEAD and TAIL functions ,8-11 The SEQ function ,8-11 The MAP function ,8-12 Defining functions that use lists ,8-13 Applications of lists ,8-15 Harmonic mean of a list ,8-15 Geometric mean of a list ,8-16 Weighted average ,8-17 Statistics of grouped data ,8-18 Chapter 9 - Vectors ,9-1 Definitions ,9-1 Entering vectors ,9-2 Typing vectors in the stack ,9-2 Storing vectors into variables ,9-3 Usi
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Changing coordinate system ,9-12 Application of vector operations ,9-15 Resultant of forces ,9-15 Angle between vectors ,9-15 Moment of a force ,9-16 Equation of a plane in space ,9-17 Row vectors, column vectors, and lists ,9-18 Function OBJ ,9-19 Function LIST ,9-20 Function DROP ,9-20 Transforming a row vector into a column vector ,9-20 Transforming a column vector into a row vector ,9-21 Transforming a list into a vector ,9-23 Transforming a vector (or matrix) into a list ,9-24 Chapter 10
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Function VANDERMONDE ,10-13 Function HILBERT ,10-14 A program to build a matrix out of a number of lists ,10-14 Lists represent columns of the matrix ,10-15 Lists represent rows of the matrix ,10-17 Manipulating matrices by columns ,10-17 Function COL ,10-18 Function COL ,10-19 Function COL+ ,10-19 Function COL- ,10-20 Function CSWP ,10-20 Manipulating matrices by rows ,10-21 Function ROW ,10-22 Function ROW ,10-23 Function ROW+ ,10-23 Function ROW- ,10-24 Function RSWP ,10-24 Function R
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Function TRAN ,11-15 Additional matrix operations (The matrix OPER menu) ,11-15 Function AXL ,11-16 Function AXM ,11-16 Function LCXM ,11-16 Solution of linear systems ,11-17 Using the numerical solver for linear systems ,11-18 Least-square solution (function LSQ) ,11-24 Solution with the inverse matrix ,11-27 Solution by “division” of matrices ,11-27 Solving multiple set of equations with the same coefficient matrix ,11-28 Gaussian and Gauss-Jordan elimination ,11-29 Step-by-step calculator pr
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Function QXA ,11-53 Function SYLVESTER ,11-54 Function GAUSS ,11-54 Linear Applications ,11-54 Function IMAGE ,11-55 Function ISOM ,11-55 Function KER ,11-56 Function MKISOM ,11-56 Chapter 12 - Graphics ,12-1 Graphs options in the calculator ,12-1 Plotting an expression of the form y = f(x) ,12-2 Some useful PLOT operations for FUNCTION plots ,12-5 Saving a graph for future use ,12-7 Graphics of transcendental functions ,12-8 Graph of ln(X) ,12-8 Graph of the exponential function ,12-10 The PP
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Fast 3D plots ,12-34 Wireframe plots ,12-36 Ps-Contour plots ,12-38 Y-Slice plots ,12-39 Gridmap plots ,12-40 Pr-Surface plots ,12-41 The VPAR variable ,12-42 Interactive drawing ,12-43 DOT+ and DOT- ,12-44 MARK ,12-44 LINE ,12-44 TLINE ,12-45 BOX ,12-45 CIRCL ,12-45 LABEL ,12-45 DEL ,12-46 ERASE ,12-46 MENU ,12-46 SUB ,12-46 REPL ,12-46 PICT ,12-46 X,Y ,12-47 Zooming in and out in the graphics display ,12-47 ZFACT, ZIN, ZOUT, and ZLAST ,12-47 BOXZ ,12-48 ZDFLT, ZAUTO ,12-48 HZIN, HZOUT, VZIN
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The SYMBOLIC menu and graphs ,12-49 The SYMB/GRAPH menu ,12-50 Function DRAW3DMATRIX ,12-52 Chapter 13 - Calculus Applications ,13-1 The CALC (Calculus) menu ,13-1 Limits and derivatives ,13-1 Function lim ,13-2 Derivatives ,13-3 Functions DERIV and DERVX ,13-3 The DERIV&INTEG menu ,13-4 Calculating derivatives with ∂ ,13-4 The chain rule ,13-6 Derivatives of equations ,13-7 Implicit derivatives ,13-7 Application of derivatives ,13-7 Analyzing graphics of functions ,13-8 Function DOMAIN ,13-9 F
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Integration with units ,13-21 Infinite series ,13-22 Taylor and Maclaurin’s series ,13-23 Taylor polynomial and reminder ,13-23 Functions TAYLR, TAYLR0, and SERIES ,13-24 Chapter 14 - Multi-variate Calculus Applications ,14-1 Multi-variate functions ,14-1 Partial derivatives ,14-1 Higher-order derivatives ,14-3 The chain rule for partial derivatives ,14-4 Total differential of a function z = z(x,y) ,14-5 Determining extrema in functions of two variables ,14-5 Using function HESS to analyze extr
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Checking solutions in the calculator ,16-2 Slope field visualization of solutions ,16-3 The CALC/DIFF menu ,16-3 Solution to linear and non-linear equations ,16-4 Function LDEC ,16-4 Function DESOLVE ,16-7 The variable ODETYPE ,16-8 Laplace Transforms ,16-10 Definitions ,16-10 Laplace transform and inverses in the calculator ,16-11 Laplace transform theorems ,16-12 Dirac’s delta function and Heaviside’s step function ,16-15 Applications of Laplace transform in the solution of linear ODEs ,16-17
