Module List

CALC : Math : Programmable 002 : Online User Programmable Root Solver : Calculator

Description : Calculate the roots (zero value points) for the user defined equations.

Discussion : Select the input X variable, the output Z variable, and a guess value. The guess value should be close to the root value. Use the plot pages to graph the variables to help determine the initial guess values. The tool calculates a single root for the selected X variable such that the selected Z variable equals zero, using the Secant method.

The tool also calculates the value, slope and curvature of the selected Z variable with respect to the selected X variable, at the input value of the selected X variable. For example if the selected X variable is xin2, the value of xin2 = 3, and the selected Z variable is zout4. The tool will calculate zout4, dzout4 / dxin2 and d²zout4 / dxin2² at xin2 = 3.

Check that the convergence value is close to or equal to one, and that Z check is close to or equal to zero. False roots can occur at very large numbers because of rounding errors. Check the roots by plotting the values. Some lines do not have roots.

Note : The displayed root value is rounded. The Z check value is calculated from the unrounded root value. If you enter the root value as the value of the selected X variable the Z value will be different from the Z check value because of rounding errors.

Hint : To find the intersection points of two output variables (eg z1 and z2): define z3 = z2 - z1 and find the roots of z3. To find the points where an output variable equals a particular value (eg z1 = 3): define z2 = z1 - 3 and find the roots of z2.

Use the Plot Zs vs X page to plot the value, slope and curvature of the selected Z variable versus the selected X variable.

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CALC : Math : Programmable 004 : Online User Programmable Inflection Point Solver : Calculator

Description : Calculate the inflection points (zero curvature points) for the user defined equations.

Discussion : Select the input X variable, the output Z variable, and a guess value. The guess value should be close to the inflection point. Use the plot pages to graph the variables to help determine the initial guess values. The tool calculates a single inflection point for the selected X variable such that the curvature of the selected Z variable equals zero, using the Secant method.

The tool also calculates the value, slope and curvature of the selected Z variable with respect to the selected X variable, at the input value of the selected X variable. For example if the selected X variable is xin2, the value of xin2 = 3, and the selected Z variable is zout4. The tool will calculate zout4, dzout4 / dxin2 and d²zout4 / dxin2² at xin2 = 3.

Check that the convergence value is close to or equal to one, and that Z check is close to or equal to zero. The curvature is calculated numerically. The curvature can tend to zero for very large numbers because of rounding errors, which can result in phantom inflection point values. Check the inflection points by plotting the values. Some lines do not have a point of inflection (eg straight lines).

Note : The displayed inflection point value is rounded. The Z check value is calculated from the unrounded inflection point value. If you enter the inflection point value as the value of the selected X variable the ddZ or curvature value will be different from the Z check value because of rounding errors.

Hint : To find the points where the curvature is equal for two output variables (eg z1 and z2): define z3 = z2 - z1 and find the inflection points of z3. To find the points where the curvature equals a particular value (eg d²z1 / dx1² = 3): define z2 = z1 - 3 / 2 * x1² and find the inflection points of z2.

Use the Plot Zs vs X page to plot the value, slope and curvature of the selected Z variable versus the selected X variable.

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CALC : Math : Programmable 006 : Online User Programmable Inversion : Calculator

Description : Calculate the value of user defined equations, and plot the inverse.

Discussion : Use the plot Z vs X page to show a plot with the inverted plot. Enter equations defining the output z variables in terms of the input x variables and other output z variables.

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