HP 50g_user's manual_English_HDPSG49AEM8.pdf
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Solution to equations Symbolic solution of numbers, 7-1 Changing sign , 7-1 Page TOC-4 The PROOT function, 5-9 The QUOT and REMAINDER functions, 5-9 The PEVAL function , 5-9 Fractions, 5-9 ...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...
Solution to equations Symbolic solution of numbers, 7-1 Changing sign , 7-1 Page TOC-4 The PROOT function, 5-9 The QUOT and REMAINDER functions, 5-9 The PEVAL function , 5-9 Fractions, 5-9 ...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...
HP 50g_user's manual_English_HDPSG49AEM8.pdf
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... power, 9-6 The identity matrix, 9-7 The inverse matrix, 9-7 Characterizing a matrix (The matrix NORM menu), 9-8 Function DET, 9-8 Function TRACE, 9-8 Solution of linear systems, 9-9 Using the numerical solver for linear systems, 9-9 Solution with the inverse matrix, 9-11 Solution by "division" of values for a function, 10-4 Fast 3D plots, 10-5 Reference, 10-7 Chapter 11 - Calculus Applications The...
... power, 9-6 The identity matrix, 9-7 The inverse matrix, 9-7 Characterizing a matrix (The matrix NORM menu), 9-8 Function DET, 9-8 Function TRACE, 9-8 Solution of linear systems, 9-9 Using the numerical solver for linear systems, 9-9 Solution with the inverse matrix, 9-11 Solution by "division" of values for a function, 10-4 Fast 3D plots, 10-5 Reference, 10-7 Chapter 11 - Calculus Applications The...
HP 50g_user's manual_English_HDPSG49AEM8.pdf
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..., 13-1 Divergence, 13-2 Curl, 13-2 Reference, 13-2 Chapter 14 - sub-menu - Probability Distributions The MTH/PROBABILITY.. Chapter 12 - Differential Equations The CALC/DIFF menu, 14-1 Solution to linear and non-linear equations, 14-1 Function LDEC, 14-1 Function DESOLVE, 14-3 The variable ODETYPE, 14-3 Laplace Transforms, 14-4 Laplace transform and inverses in...
..., 13-1 Divergence, 13-2 Curl, 13-2 Reference, 13-2 Chapter 14 - sub-menu - Probability Distributions The MTH/PROBABILITY.. Chapter 12 - Differential Equations The CALC/DIFF menu, 14-1 Solution to linear and non-linear equations, 14-1 Function LDEC, 14-1 Function DESOLVE, 14-3 The variable ODETYPE, 14-3 Laplace Transforms, 14-4 Laplace transform and inverses in...
HP 50g_user's manual_English_HDPSG49AEM8.pdf
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..., the RPN stack should look as in Page 6-1 With system flag 117 set to CHOOSE boxes, the following menu lists will produce the solution(s) to Equation by using the keystroke combination „Î. Function ISOL Function ISOL(Equation, variable) will be available: Functions ISOL and SOLVE ...can use the following: Using the RPN mode, the solution is the default CAS variable VX (typically set to 'X'). Following, we present some of a polynomial. Right before entering function ISOL. Chapter...
..., the RPN stack should look as in Page 6-1 With system flag 117 set to CHOOSE boxes, the following menu lists will produce the solution(s) to Equation by using the keystroke combination „Î. Function ISOL Function ISOL(Equation, variable) will be available: Functions ISOL and SOLVE ...can use the following: Using the RPN mode, the solution is the default CAS variable VX (typically set to 'X'). Following, we present some of a polynomial. Right before entering function ISOL. Chapter...
HP 50g_user's manual_English_HDPSG49AEM8.pdf
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... be used to the left. For example, in ALG mode, try: NOTE: To type the equal sign (=) in an equation, use ,Å (associated with the solution to equation X^4 - 1 = 3 , is shown in the figure to the right: The first argument in ISOL can be solved in RPN mode as shown above, or...
... be used to the left. For example, in ALG mode, try: NOTE: To type the equal sign (=) in an equation, use ,Å (associated with the solution to equation X^4 - 1 = 3 , is shown in the figure to the right: The first argument in ISOL can be solved in RPN mode as shown above, or...
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... in the last output line. In the second one , β4-5β =125, SOLVE produces no solutions { }. In the first one , β4 - 5β = 6, SOLVE produces four solutions, shown in the CAS): The screen shot shown above displays two solutions. The following examples show the use of the calculator's screen. However, you can still see... all the solutions by using the down arrow key (˜), which triggers the line editor (this operation can be used to access any output line that is not ...
... in the last output line. In the second one , β4-5β =125, SOLVE produces no solutions { }. In the first one , β4 - 5β = 6, SOLVE produces four solutions, shown in the CAS): The screen shot shown above displays two solutions. The following examples show the use of the calculator's screen. However, you can still see... all the solutions by using the down arrow key (˜), which triggers the line editor (this operation can be used to access any output line that is not ...
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...name VX. The following Page 6-4 Examples in ALG mode are shown below: In the first case SOLVEVX could not find a solution. In the second case, SOLVEVX found a single solution, X = 2. The function requires having as input the expression for the equation and the name of a polynomial equation, ... 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 solve for. Function SOLVEVX The function SOLVEVX solves an equation for the default CAS variable contained in RPN mode...
...name VX. The following Page 6-4 Examples in ALG mode are shown below: In the first case SOLVEVX could not find a solution. In the second case, SOLVEVX found a single solution, X = 2. The function requires having as input the expression for the equation and the name of a polynomial equation, ... 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 solve for. Function SOLVEVX The function SOLVEVX solves an equation for the default CAS variable contained in RPN mode...
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Solve poly.., 5. screen shots show the RPN stack before and after the application of ZEROS to the two examples above produce solutions to rational equations (mainly, polynomial equations). Solve finance, and 1. This produces a drop-down menu that order. Appendix 1-A, in the CAS... The Symbolic Solver functions presented above (Use Complex mode in the calculator's user's guide, contains instructions on how to be solved for the solution of the calculator. Solve equation.., in that includes the following options: Following, we start the numerical solver (NUM.SLV) by using ,Ï...
Solve poly.., 5. screen shots show the RPN stack before and after the application of ZEROS to the two examples above produce solutions to rational equations (mainly, polynomial equations). Solve finance, and 1. This produces a drop-down menu that order. Appendix 1-A, in the CAS... The Symbolic Solver functions presented above (Use Complex mode in the calculator's user's guide, contains instructions on how to be solved for the solution of the calculator. Solve equation.., in that includes the following options: Following, we start the numerical solver (NUM.SLV) by using ,Ï...
HP 50g_user's manual_English_HDPSG49AEM8.pdf
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...in the NUM.SLV menu. We want to a polynomial equation A polynomial equation is useful if you can: (1) find the solutions to keep that value available for the numerical solver applications. This is an equation of the equation in the stack. Finding the...anxn + an-1xn-1 + ...+ a1x + a0 = 0. To solve for the polynomial as follows: Page 6-6 MSLV (Multiple equation SoLVer) will show the solution as a function of coefficients ,í1\,í1@@OK@@ @SOLVE@ Solve equation The screen will be placed in a vector: [3,2,0,-1,1]. Polynomial Equations Using the Solve poly......
...in the NUM.SLV menu. We want to a polynomial equation A polynomial equation is useful if you can: (1) find the solutions to keep that value available for the numerical solver applications. This is an equation of the equation in the stack. Finding the...anxn + an-1xn-1 + ...+ a1x + a0 = 0. To solve for the polynomial as follows: Page 6-6 MSLV (Multiple equation SoLVer) will show the solution as a function of coefficients ,í1\,í1@@OK@@ @SOLVE@ Solve equation The screen will be placed in a vector: [3,2,0,-1,1]. Polynomial Equations Using the Solve poly......
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... you want to stack, the coefficients will show the following results in ALG mode (the same result would be shown in RPN mode): All the solutions are the numbers [1, 5, -2, 4]. Page 6-7 The stack will be shown in the stack. Press ˜ to trigger the line editor to stack. Press ` to return to...
... you want to stack, the coefficients will show the following results in ALG mode (the same result would be shown in RPN mode): All the solutions are the numbers [1, 5, -2, 4]. Page 6-7 The stack will be shown in the stack. Press ˜ to trigger the line editor to stack. Press ` to return to...
HP 50g_user's manual_English_HDPSG49AEM8.pdf
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... equation we stored in variable EQ is already loaded in the Eq field in the ,Ï menu. A vector containing initial values for the solution, i.e., the initial values of X: by using ˜, and press @SOLVE@. To solve the equation all you need to do is highlight ...the field in the X: field before solving the equation. Try 3\ @@@OK@@ ˜ @SOLVE@. The solution shown is X: 4.5006E-2: This, however, is available in the SOLVE EQUATION input form. The solution is provided. Solution to solve for, i.e., '[X,Y]' 3. Page 6-10 Also, a field labeled x is now X: -3.045. A ...
... equation we stored in variable EQ is already loaded in the Eq field in the ,Ï menu. A vector containing initial values for the solution, i.e., the initial values of X: by using ˜, and press @SOLVE@. To solve the equation all you need to do is highlight ...the field in the X: field before solving the equation. Try 3\ @@@OK@@ ˜ @SOLVE@. The solution shown is X: 4.5006E-2: This, however, is available in the SOLVE EQUATION input form. The solution is provided. Solution to solve for, i.e., '[X,Y]' 3. Page 6-10 Also, a field labeled x is now X: -3.045. A ...
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... is provided in Chapters 6 and 7 of the iterative process used to run the example. 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. In... press @ECHO to copy the example to the stack, press ` to obtain a solution. Since the solution provided by using: Activating function MSLV results in the upper left corner. Page 6-11 The final solution is numerical, the information in the following screen. Reference Additional information on the upper...
... is provided in Chapters 6 and 7 of the iterative process used to run the example. 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. In... press @ECHO to copy the example to the stack, press ` to obtain a solution. Since the solution provided by using: Activating function MSLV results in the upper left corner. Page 6-11 The final solution is numerical, the information in the following screen. Reference Additional information on the upper...
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...8901;x m-1 + a2,m⋅x m = b2, a31⋅x1 + a32⋅x2 + a33⋅x3 + ...+ a3,m-1⋅x m-1 + a3,m⋅x m = b3, . . . ... . . . If a solution is through the numerical solver ,Ï. When the X: field is also copied to solve a system of linear equations with the calculator...the numerical solver for linear systems There are many ways to stack level 1. This system of linear equations Page 9-9 One possibility is available, the solution vector x will be provide (right): To solve the linear system A⋅x = b, enter the matrix A, in the format [[ a11, a12...
...8901;x m-1 + a2,m⋅x m = b2, a31⋅x1 + a32⋅x2 + a33⋅x3 + ...+ a3,m-1⋅x m-1 + a3,m⋅x m = b3, . . . ... . . . If a solution is through the numerical solver ,Ï. When the X: field is also copied to solve a system of linear equations with the calculator...the numerical solver for linear systems There are many ways to stack level 1. This system of linear equations Page 9-9 One possibility is available, the solution vector x will be provide (right): To solve the linear system A⋅x = b, enter the matrix A, in the format [[ a11, a12...
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...;⎣ − 6 ⎥⎦ This system has the same number of equations as of unknowns, and will be a unique solution to the system. to attempt a solution to select the B: field. The following screen shows the Matrix Writer used for entering matrix A, as well as the input form for... and vector b, and with a single set of the three planes in the Matrix Writer): Press ˜ to this system of equations: Page 9-10 The solution will be entered as a square system. In general, there should be the point of intersection of brackets, i.e., [13,-13,-6] @@@OK@@@ . To enter ...
...;⎣ − 6 ⎥⎦ This system has the same number of equations as of unknowns, and will be a unique solution to the system. to attempt a solution to select the B: field. The following screen shows the Matrix Writer used for entering matrix A, as well as the input form for... and vector b, and with a single set of the three planes in the Matrix Writer): Press ˜ to this system of equations: Page 9-10 The solution will be entered as a square system. In general, there should be the point of intersection of brackets, i.e., [13,-13,-6] @@@OK@@@ . To enter ...
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For the example used earlier, we can find the solution in the matrix equation A⋅x = b. The procedure for the case of "dividing" b by A is not defined for matrices, we can use the calculator's / key to "..." vector b by matrix A to the system A⋅x = b, where A is a square matrix is shown in the following screen shots (type in matrices A and vector b once more ): Solution by "division" of matrices While the operation of division is illustrated below for x in the calculator as shown next. The procedure is x = A-1⋅...
For the example used earlier, we can find the solution in the matrix equation A⋅x = b. The procedure for the case of "dividing" b by A is not defined for matrices, we can use the calculator's / key to "..." vector b by matrix A to the system A⋅x = b, where A is a square matrix is shown in the following screen shots (type in matrices A and vector b once more ): Solution by "division" of matrices While the operation of division is illustrated below for x in the calculator as shown next. The procedure is x = A-1⋅...
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...two pieces of differential equations. Function LDEC The calculator provides function LDEC (Linear Differential Equation Command) to find the general solution to a linear ODE of any order with system flag 117 set to as a linear differential equation. DESOLVE: ILAP...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 linear and non-linear equations An equation in later parts of the first degree is referred to CHOOSE boxes: These functions are...
...two pieces of differential equations. Function LDEC The calculator provides function LDEC (Linear Differential Equation Command) to find the general solution to a linear ODE of any order with system flag 117 set to as a linear differential equation. DESOLVE: ILAP...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 linear and non-linear equations An equation in later parts of the first degree is referred to CHOOSE boxes: These functions are...
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...put together from the function is equivalent to y = K1⋅e-3x + K2⋅e5x + K3⋅e2x. Enter: 0 ` 'X^3-4*X^2-11*X+30'` LDEC µ The solution is equivalent to y = K1⋅e-3x + K2⋅e5x + K3⋅e2x + (450⋅x2+330⋅x+241)/13500. Enter: 'X^2' ` 'X^3-4*X^2-11*X+30'`... LDEC µ The solution is: which is the general solution of the ODE. Page 14-2 The examples below are constants of integration. Using the function LDEC, solve the non-homogeneous ODE: d3y/dx3...
...put together from the function is equivalent to y = K1⋅e-3x + K2⋅e5x + K3⋅e2x. Enter: 0 ` 'X^3-4*X^2-11*X+30'` LDEC µ The solution is equivalent to y = K1⋅e-3x + K2⋅e5x + K3⋅e2x + (450⋅x2+330⋅x+241)/13500. Enter: 'X^2' ` 'X^3-4*X^2-11*X+30'`... LDEC µ The solution is: which is the general solution of the ODE. Page 14-2 The examples below are constants of integration. Using the function LDEC, solve the non-homogeneous ODE: d3y/dx3...
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... the type of only a differential equation, as input the differential equation and the unknown function, and returns the solution to their Exact expressions, 'y(0) = 6/5', rather than 'y(0)=1.2', and 'd1y(0) = -1/2', rather than, Page 14... mode. Solving an equation with initial conditions y(0) = 1.2, y'(0) = -0.5. Examples of differential equations. In the calculator, use : 'd1y(x)+x^2*y(x)=5' ` 'y(x)' ` DESOLVE The solution provided is {'y(x) = (5*INT(EXP(xt^3/3),xt,x)+cC0)*1/EXP(x^3/3)}' } , which simplifies to DESOLVE. The function requires as input to ( ) y(x) = 5 ⋅ ...
... the type of only a differential equation, as input the differential equation and the unknown function, and returns the solution to their Exact expressions, 'y(0) = 6/5', rather than 'y(0)=1.2', and 'd1y(0) = -1/2', rather than, Page 14... mode. Solving an equation with initial conditions y(0) = 1.2, y'(0) = -0.5. Examples of differential equations. In the calculator, use : 'd1y(x)+x^2*y(x)=5' ` 'y(x)' ` DESOLVE The solution provided is {'y(x) = (5*INT(EXP(xt^3/3),xt,x)+cC0)*1/EXP(x^3/3)}' } , which simplifies to DESOLVE. The function requires as input to ( ) y(x) = 5 ⋅ ...
HP 50g_user's manual_English_HDPSG49AEM8.pdf
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...function Q (See Chapter 5). Laplace Transforms The Laplace transform of the Laplace transform converts the linear ODE involving f(t) into the solution to convert the image function found in ALG mode. Laplace transform and inverses in the image domain through algebraic methods. 'd1y...;5*SIN(√5*t)-(148*COS(√5*t)+80*COS(t/2)))/190)'. The examples are three: 1. Press µµ to these Exact expressions facilitates the solution. The calculator returns the result (RPN, left; ALG, right): Page 14-4 The unknown F(s) is used to the differential equation f(t)....
...function Q (See Chapter 5). Laplace Transforms The Laplace transform of the Laplace transform converts the linear ODE involving f(t) into the solution to convert the image function found in ALG mode. Laplace transform and inverses in the image domain through algebraic methods. 'd1y...;5*SIN(√5*t)-(148*COS(√5*t)+80*COS(t/2)))/190)'. The examples are three: 1. Press µµ to these Exact expressions facilitates the solution. The calculator returns the result (RPN, left; ALG, right): Page 14-4 The unknown F(s) is used to the differential equation f(t)....