User manual HP 49G+ GRAPHING CALCULATOR

[. . . ] hp 49g+ graphing calculator user's manual H Edition 2 HP part number F2228-90001 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. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN. Copyright 2003 Hewlett-Packard Development Company, L. P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego, CA 92123 Printing History Edition 2 December 2003 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. [. . . ] If the equation to be solved for has all numerical coefficients, a numerical solution is possible through the use of the Numerical Solver features of the calculator. Numerical solver menu The calculator provides a very powerful environment for the solution of single algebraic or transcendental equations. To access this environment we start the numerical solver (NUM. SLV) by using , . This produces a dropdown menu that includes the following options: Page 6-5 Following, we present applications of items 3. Appendix 1-A, in the calculator's user's guide, contains instructions on how to use input forms with examples for the numerical solver applications. Whenever you solve for a value in the NUM. SLV applications, the value solved for will be placed in the stack. This is useful if you need to keep that value available for other operations. There will be one or more variables created whenever you activate some of the applications in the NUM. SLV menu. Polynomial Equations Using the Solve poly. . . option in the calculator's SOLVE environment you can: (1) find the solutions to a polynomial equation; (2) obtain the coefficients of the polynomial having a number of given roots; and, (3) obtain an algebraic expression for the polynomial as a function of X. Finding the solutions to a polynomial equation A polynomial equation is an equation of the form: anxn + an-1xn-1 + . . . + a1x + a0 = 0. We want to place the coefficients of the equation in a vector: [3, 2, 0, -1, 1]. To solve for this polynomial equation using the calculator, try the following: , ~~ @SOLVE@ The screen will show the solution as follows: Select Solve poly. . . Enter vector of coefficients Solve equation Page 6-6 Press ` to return to stack. The stack will show the following results in ALG mode (the same result would be shown in RPN mode): All the solutions are complex numbers: (0. 432, -0. 389), (0. 432, 0. 389), (0. 766, 0. 632), (-0. 766, -0. 632). Generating polynomial coefficients given the polynomial's roots Suppose you want to generate the polynomial whose roots are the numbers [1, 5, -2, 4]. Enter vector of roots Solve for coefficients Press ` to return to stack, the coefficients will be shown in the stack. Press ~ to trigger the line editor to see all the coefficients. Page 6-7 Generating an algebraic expression for the polynomial You can use the calculator to generate an algebraic expression for a polynomial given the coefficients or the roots of the polynomial. The resulting expression will be given in terms of the default CAS variable X. To generate the algebraic expression using the coefficients, try the following example. Enter vector of coefficients Generate symbolic expression Return to stack. The expression thus generated is shown in the stack as:'X^3+5*X^2+-2*X+4' To generate the algebraic expression using the roots, try the following example. Enter vector of roots Generate symbolic expression Return to stack. The expression thus generated is shown in the stack as: '(X-1)*(X-3)*(X+2)*(X-1)'. The resulting expression is: 'X^4+-3*X^3+ -3*X^2+11*X-6'. Page 6-8 Financial calculations The calculations in item 5. in the Numerical Solver (NUM. SLV) are used for calculations of time value of money of interest in the discipline of engineering economics and other financial applications. [. . . ] If HP is unable, within a reasonable time, to repair or replace any product to a condition as warranted, you will be entitled to a refund of the purchase price upon prompt return of the product with proof of purchase. HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use. 2. 3. 4. 5. Warranty does not apply to defects resulting from (a) improper or inadequate maintenance or calibration, (b) software, interfacing, parts or supplies not supplied by HP, (c) unauthorized modification or misuse, (d) operation outside of the published environmental specifications for the product, or (e) improper site preparation or maintenance. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL. [. . . ]