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Anleitung Zusammenfassung
The function requires having as input the expression for the equation and the name of the variable to solve for. Examples in ALG mode are shown next: To use function ZEROS in RPN mode, enter first the polynomial expression, then the variable to solve for, and then function ZEROS. The following screen shots show the RPN stack before and after the application of ZEROS to the two examples above (Use Complex mode in the CAS): The Symbolic Solver functions presented above produce solutions to rational equations (mainly, polynomial equations). 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. 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 ‚I. This produces a drop-down menu that includes the following options: Following, we present applications of items 3. Solve poly.., 5. Solve finance, and 1. Solve equation.., in that order. 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. Item 6. MSLV(Multiple equation SoLVer) will be presented later in page 6-10. Notes: 1. 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. 2. 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: A polynomial equation is an equation of the form: anxn + an-1xn-1 + …+ a1x + a0 = 0. For example, solve the equation: 3s4 + 2s3 - s + 1 = 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: ‚I..@@OK@@ Select Solve poly… „O3‚i2‚i0 Enter vector of coefficients ‚i1\‚i1@@OK@@ @SOLVE@ Solve equation The screen will show the solution as follows: 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). Suppose you want to generate the polynomial whose roots are the numbers [1, 5, -2, 4]. To use the calculator for this purpose, follow these steps: ‚I..@@OK@@ Select Solve poly… .„O1‚i5 Enter vector of roots ‚i2\‚i4@@OK@@ @SOLVE@ 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. 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. Assume that the polynomial coefficients are [1,5,-2,4]. Use the following keystrokes: ‚I.. Select Solve poly… „O1‚i5 Enter vector of coefficients ‚i2\‚i4@@OK@@—@SYMB@ 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. Assume that the polynomial roots are [1, 3, -2, 1]. Use the following keystrokes: ‚I..@@OK@@ Select Solve poly… .„O1‚i3 Enter vector of roots ‚i2\‚i1@@OK@@.@SYMB@ Generate symbolic expression ` Return to stack. The expression thus generated is shown in the stack as: To expand the products, you can use the EXPAND command. The resulting expression is: 'X^4+-3*X^3+ -3*X^2+11*X-6'. Financial calculations The calculations in item 5. Solve finance.. 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. This application can also be started by using the keystroke combination „O (associated with the 9 key). Detailed explanations of these types of calculations are presented in Chapter 6 of the calculator’s user’s guide. Solving equations with one unknown through NUM.SLV The calculator's NUM.SLV menu provides item 1. Solve equation.. solve different types of equations in a single variable, including non-linear algebraic and transcendental equations. For example, let's solve the equation: ex-sin(.x/3) = 0. Simply enter the expression as an algebraic object and store it into variable EQ. The required keystrokes in ALG mode are the following: Function STEQ will store its argument into variable EQ, e.g., in ALG mode: In RPN mode, enter the equation between apostrophes and activate command STEQ. Thus, function STEQ can be used as a shortcut to store an expression into variable EQ. Press J to see t...