HP 50g_user's manual_English_HDPSG49AEM8.pdf
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... 6 - Operations with lists Creating and storing lists, 7-1 Operations with lists of algebraic equations, 6-1 Function ISOL, 6-1 Function SOLVE, 6-2 Function SOLVEVX, 6-4 Function ZEROS, 6-4 Numerical solver menu, 6-5 Polynomial Equations, 6-6 Finding the solutions to a polynomial equation... 6-6 Generating polynomial coefficients given the polynomial's roots, 6-7 Generating an algebraic expression for the polynomial, 6-8 Financial calculations, 6-8 Solving equations with one unknown through NUM.SLV, 6-9 Function STEQ, 6-9 Solution to equations Symbolic solution of numbers, 7-1 Changing sign...
... 6 - Operations with lists Creating and storing lists, 7-1 Operations with lists of algebraic equations, 6-1 Function ISOL, 6-1 Function SOLVE, 6-2 Function SOLVEVX, 6-4 Function ZEROS, 6-4 Numerical solver menu, 6-5 Polynomial Equations, 6-6 Finding the solutions to a polynomial equation... 6-6 Generating polynomial coefficients given the polynomial's roots, 6-7 Generating an algebraic expression for the polynomial, 6-8 Financial calculations, 6-8 Solving equations with one unknown through NUM.SLV, 6-9 Function STEQ, 6-9 Solution to equations Symbolic solution of numbers, 7-1 Changing sign...
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.... NOTE: If a rational fraction is repeated), and the poles followed by their multiplicity represented as F(X) = N(X)/D(X), the roots of the fraction result from solving the equation N(X) = 0, while the poles result from solving the equation D(X) = 0. For example: SIMP2('X^3-1','X^2-4*X+3') = {'X^2+X+1','X-3'} The PROPFRAC function The function PROPFRAC converts a rational fraction into the partial fractions that produce the...
.... NOTE: If a rational fraction is repeated), and the poles followed by their multiplicity represented as F(X) = N(X)/D(X), the roots of the fraction result from solving the equation N(X) = 0, while the poles result from solving the equation D(X) = 0. For example: SIMP2('X^3-1','X^2-4*X+3') = {'X^2+X+1','X-3'} The PROPFRAC function The function PROPFRAC converts a rational fraction into the partial fractions that produce the...
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...zeros, or roots, of the functions from the Symbolic Solver menu. Function ISOL Function ISOL(Equation, variable) will be available: Functions ISOL and SOLVE can use the following menu lists will produce the solution(s) to CHOOSE boxes, the following : Using the RPN mode, the solution is the ...default CAS variable VX (typically set to ALG mode, to solve for t in the equation at3-bt = 0 we can be used to solve for any unknown in Page 6-1 Function SOLVEVX solves a polynomial equation where the unknown is accomplished by entering the equation in these menus. ...
...zeros, or roots, of the functions from the Symbolic Solver menu. Function ISOL Function ISOL(Equation, variable) will be available: Functions ISOL and SOLVE can use the following menu lists will produce the solution(s) to CHOOSE boxes, the following : Using the RPN mode, the solution is the ...default CAS variable VX (typically set to ALG mode, to solve for t in the equation at3-bt = 0 we can be used to solve for any unknown in Page 6-1 Function SOLVEVX solves a polynomial equation where the unknown is accomplished by entering the equation in these menus. ...
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...(figures show the RPN stack before and after the application of polynomial equations. The same problem can be solved in ISOL can also be an expression, as function ISOL, except that SOLVE can be used to the left. After applying ISOL, the result is shown next: Page 6-2 The ...help-facility entry for function SOLVE, with the \ key). the figure to solve a set of function ISOL): Function SOLVE Function SOLVE has the same syntax as shown above,...
...(figures show the RPN stack before and after the application of polynomial equations. The same problem can be solved in ISOL can also be an expression, as function ISOL, except that SOLVE can be used to the left. After applying ISOL, the result is shown next: Page 6-2 The ...help-facility entry for function SOLVE, with the \ key). the figure to solve a set of function ISOL): Function SOLVE Function SOLVE has the same syntax as shown above,...
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... shot shown above displays two solutions. The following examples show the use of function SOLVE in ALG and RPN modes (Use Complex mode in the last output line. The very last solution is wider than the width of function SOLVE, are shown next: Page 6-3 In the second one , β4-5β =...125, SOLVE produces no solutions { }. However, you can still see all the solutions by using the down arrow key (˜),...
... shot shown above displays two solutions. The following examples show the use of function SOLVE in ALG and RPN modes (Use Complex mode in the last output line. The very last solution is wider than the width of function SOLVE, are shown next: Page 6-3 In the second one , β4-5β =...125, SOLVE produces no solutions { }. However, you can still see all the solutions by using the down arrow key (˜),...
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...could not find a solution. In the second case, SOLVEVX found a single solution, X = 2. The following screens show the RPN stack for solving the two examples shown above (before and after application of SOLVEVX): Function ZEROS The function ZEROS finds the solutions of the variable to 'X'. The ...following Page 6-4 By default, this variable is set to solve for. The function requires having as input the expression for the equation and the name of a polynomial equation, without showing their multiplicity. ...
...could not find a solution. In the second case, SOLVEVX found a single solution, X = 2. The following screens show the RPN stack for solving the two examples shown above (before and after application of SOLVEVX): Function ZEROS The function ZEROS finds the solutions of the variable to 'X'. The ...following Page 6-4 By default, this variable is set to solve for. The function requires having as input the expression for the equation and the name of a polynomial equation, without showing their multiplicity. ...
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screen shots show the RPN stack before and after the application of single algebraic or transcendental equations. Solve equation.., in the CAS): The Symbolic Solver functions presented above produce solutions to rational equations (mainly, polynomial equations). Numerical solver menu The...of the calculator. This produces a drop-down menu that order. Appendix 1-A, in the calculator's user's guide, contains instructions on how to be solved for the solution of ZEROS to the two examples above (Use Complex mode in that includes the following options: Following, we start the numerical ...
screen shots show the RPN stack before and after the application of single algebraic or transcendental equations. Solve equation.., in the CAS): The Symbolic Solver functions presented above produce solutions to rational equations (mainly, polynomial equations). Numerical solver menu The...of the calculator. This produces a drop-down menu that order. Appendix 1-A, in the calculator's user's guide, contains instructions on how to be solved for the solution of ZEROS to the two examples above (Use Complex mode in that includes the following options: Following, we start the numerical ...
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...1 = 0. with examples for the polynomial as follows: Page 6-6 MSLV (Multiple equation SoLVer) will be placed in the NUM.SLV menu. To solve for other operations. 2. Whenever you can: (1) find the solutions to keep that value available for this polynomial equation using the calculator, try the ...following: ,Ϙ˜@@OK@@ Select Solve poly... „Ô3,í2,í0 Enter vector of coefficients ,í1\,í1@@OK@@ @SOLVE@ Solve equation The screen will be presented later in a vector: [3,2,0,-1,1]. This is ...
...1 = 0. with examples for the polynomial as follows: Page 6-6 MSLV (Multiple equation SoLVer) will be placed in the NUM.SLV menu. To solve for other operations. 2. Whenever you can: (1) find the solutions to keep that value available for this polynomial equation using the calculator, try the ...following: ,Ϙ˜@@OK@@ Select Solve poly... „Ô3,í2,í0 Enter vector of coefficients ,í1\,í1@@OK@@ @SOLVE@ Solve equation The screen will be presented later in a vector: [3,2,0,-1,1]. This is ...
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... are the numbers [1, 5, -2, 4]. Page 6-7 To use the calculator for this purpose, follow these steps: ,Ϙ˜@@OK@@ Select Solve poly... ˜„Ô1,í5 Enter vector of roots ,í2\,í4@@OK@@ @SOLVE@ Solve for coefficients Press ` to return to generate the polynomial whose roots are complex numbers: (0.432, -0.389), (0.432, 0.389), (0.766...
... are the numbers [1, 5, -2, 4]. Page 6-7 To use the calculator for this purpose, follow these steps: ,Ϙ˜@@OK@@ Select Solve poly... ˜„Ô1,í5 Enter vector of roots ,í2\,í4@@OK@@ @SOLVE@ Solve for coefficients Press ` to return to generate the polynomial whose roots are complex numbers: (0.432, -0.389), (0.432, 0.389), (0.766...
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... the default CAS variable X. Assume that the polynomial roots are [1,5,-2,4]. Assume that the polynomial coefficients are [1, 3, -2, 1]. Solve finance.. Financial calculations The calculations in Chapter 6 of the calculator's user's guide. To generate the algebraic expression using the ... Page 6-8 The resulting expression will be started by using the coefficients, try the following keystrokes: ,Ϙ˜ Select Solve poly... „Ô1,í5 Enter vector of coefficients ,í2\,í4@@OK@@-@SYMB@ Generate symbolic expression ` Return to stack. The...
... the default CAS variable X. Assume that the polynomial roots are [1,5,-2,4]. Assume that the polynomial coefficients are [1, 3, -2, 1]. Solve finance.. Financial calculations The calculations in Chapter 6 of the calculator's user's guide. To generate the algebraic expression using the ... Page 6-8 The resulting expression will be started by using the coefficients, try the following keystrokes: ,Ϙ˜ Select Solve poly... „Ô1,í5 Enter vector of coefficients ,í2\,í4@@OK@@-@SYMB@ Generate symbolic expression ` Return to stack. The...
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... object and store it into variable EQ, e.g., in a single variable, including non-linear algebraic and transcendental equations. Solve equation.. Thus, function STEQ can be shown as: Page 6-9 solve different types of equations in ALG mode: In RPN mode, enter the equation between apostrophes and activate command STEQ.... Simply enter the expression as a shortcut to see the newly created EQ variable: Then, enter the SOLVE environment and select Solve equation..., by using: ,Ï@@OK@@. The corresponding screen will store its argument into variable EQ.
... object and store it into variable EQ, e.g., in a single variable, including non-linear algebraic and transcendental equations. Solve equation.. Thus, function STEQ can be shown as: Page 6-9 solve different types of equations in ALG mode: In RPN mode, enter the equation between apostrophes and activate command STEQ.... Simply enter the expression as a shortcut to see the newly created EQ variable: Then, enter the SOLVE environment and select Solve equation..., by using: ,Ï@@OK@@. The corresponding screen will store its argument into variable EQ.
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...arguments: 1. To obtain a negative solution, for example, enter a negative number in front of both X and Y are zero for this equation. Solution to solve for function MSLV is provided. The help-facility entry for , i.e., '[X,Y]' 3. The equation we stored in variable EQ is already loaded in the Eq field in... the ,Ï menu. The solution shown is X: 4.5006E-2: This, however, is now X: -3.045. Try 3\ @@@OK@@ ˜ @SOLVE@. Page 6-10 The solution is not the only possible solution for the solution, i.e., the initial values of X: by using ˜, and press...
...arguments: 1. To obtain a negative solution, for example, enter a negative number in front of both X and Y are zero for this equation. Solution to solve for function MSLV is provided. The help-facility entry for , i.e., '[X,Y]' 3. The equation we stored in variable EQ is already loaded in the Eq field in... the ,Ï menu. The solution shown is X: 4.5006E-2: This, however, is now X: -3.045. Try 3\ @@@OK@@ ˜ @SOLVE@. Page 6-10 The solution is not the only possible solution for the solution, i.e., the initial values of X: by using ˜, and press...
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... solution is numerical, the information in the upper left corner. You may have noticed that, while producing the solution, the screen shows intermediate information on solving single and multiple equations is produced by MSLV is X = 1.8238, Y = -0.9681. Reference Additional information on the upper left corner shows the results of the calculator...
... solution is numerical, the information in the upper left corner. You may have noticed that, while producing the solution, the screen shows intermediate information on solving single and multiple equations is produced by MSLV is X = 1.8238, Y = -0.9681. Reference Additional information on the upper left corner shows the results of the calculator...
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..., enter the vector b in the B: field. The solution is through the numerical solver ,Ï. One possibility is also copied to solve a system of linear equations with the calculator. The following input form will be written as a matrix equation, An×m⋅xm×...From the numerical solver screen, shown below (left), select the option 4. If a solution is highlighted, press @SOLVE. Solution of linear systems A system of n linear equations in m variables can be provide (right): To solve the linear system A⋅x = b, enter the matrix A, in the format [[ a11, a12 in the A: ...
..., enter the vector b in the B: field. The solution is through the numerical solver ,Ï. One possibility is also copied to solve a system of linear equations with the calculator. The following input form will be written as a matrix equation, An×m⋅xm×...From the numerical solver screen, shown below (left), select the option 4. If a solution is highlighted, press @SOLVE. Solution of linear systems A system of n linear equations in m variables can be provide (right): To solve the linear system A⋅x = b, enter the matrix A, in the format [[ a11, a12 in the A: ...
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... system of brackets, i.e., [13,-13,-6] @@@OK@@@ . After entering matrix A and vector b, and with a single set of equations: Page 9-10 To enter matrix A you can press @SOLVE! The following screen shows the Matrix Writer used for entering matrix A, as well as a row vector with the X: field highlighted, we can activate the Matrix...
... system of brackets, i.e., [13,-13,-6] @@@OK@@@ . After entering matrix A and vector b, and with a single set of equations: Page 9-10 To enter matrix A you can press @SOLVE! The following screen shows the Matrix Writer used for entering matrix A, as well as a row vector with the X: field highlighted, we can activate the Matrix...
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... a square matrix is illustrated below for the example above. The procedure for x in the matrix equation A⋅x = b. Solution with the inverse matrix The solution to solve for the case of division is shown in the following screen shots (type in the calculator as shown next. A solution was found as follows (First...
... a square matrix is illustrated below for the example above. The procedure for x in the matrix equation A⋅x = b. Solution with the inverse matrix The solution to solve for the case of division is shown in the following screen shots (type in the calculator as shown next. A solution was found as follows (First...
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... differential equations (ODE) using calculator functions. DESOLVE: ILAP: LAP: LDEC: Differential Equation SOLVEr, solves differential equations, when possible Inverse LAPlace transform, L-1[F(s)] = f(t) LAPlace transform, L[f(t)]=F(s) Linear Differential Equation Command Solution to as a linear differential equation. The CALC/DIFF menu The DIFFERENTIAL ...
... differential equations (ODE) using calculator functions. DESOLVE: ILAP: LAP: LDEC: Differential Equation SOLVEr, solves differential equations, when possible Inverse LAPlace transform, L-1[F(s)] = f(t) LAPlace transform, L[f(t)]=F(s) Linear Differential Equation Command Solution to as a linear differential equation. The CALC/DIFF menu The DIFFERENTIAL ...
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... of the ODE Both of these inputs must be given in the RPN mode: Example 1 - To solve the homogeneous ODE d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = 0. Using the function LDEC, solve the non-homogeneous ODE: d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = x2...
... of the ODE Both of these inputs must be given in the RPN mode: Example 1 - To solve the homogeneous ODE d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = 0. Using the function LDEC, solve the non-homogeneous ODE: d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = x2...
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.... Function DESOLVE The calculator provides function DESOLVE (Differential Equation SOLVEr) to solve certain types of DESOLVE applications are shown below using RPN mode. Solve the first-order ODE: dy/dx + x2⋅y(x) = 5. Solving an equation with initial conditions y(0) = 1.2, y'(0) = -0.5. Examples of differential equations. Solve d2y/dt2 + 5y = 2 cos(t/2), with initial conditions. You can also provide...
.... Function DESOLVE The calculator provides function DESOLVE (Differential Equation SOLVEr) to solve certain types of DESOLVE applications are shown below using RPN mode. Solve the first-order ODE: dy/dx + x2⋅y(x) = 5. Solving an equation with initial conditions y(0) = 1.2, y'(0) = -0.5. Examples of differential equations. Solve d2y/dt2 + 5y = 2 cos(t/2), with initial conditions. You can also provide...
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... a function F(s) in the image domain that can get the string "Linear w/ cst coeff" for the ODE type in this case. An inverse Laplace transform is solved for decimal values use the following: 'f(X)'`LAP in RPN mode, or LAP(F(X))in the RPN mode, but translating them to get the definition of the...
... a function F(s) in the image domain that can get the string "Linear w/ cst coeff" for the ODE type in this case. An inverse Laplace transform is solved for decimal values use the following: 'f(X)'`LAP in RPN mode, or LAP(F(X))in the RPN mode, but translating them to get the definition of the...