## Equations in one unknown in Mathcad

The simplest way to find the root of the equation in one unknown in Mathcad is guaranteed by function ed by function ed by function root (). The arguments of function root ( ) are the functional form that governs the equation and the variable name - root (f(x),x) If the equation has several roots, the function guarantees finding a single root, proximate to the assigned initial value for the decision variable. Calculation accuracy can be increased or decreased by assigning the value of the variable TOL, the default value of which is 10-3, the variable is to be found in menu Math, Options (Математика, Опции). The assigned value of TOL also has an influence on calculation accuracy.

In case the equation under analysis in Mathcad takes the form of the polynomial, all its roots can be found with function polyroots (v). The argument of the function is coefficient vector of the polynomial –v, the result comes as vector of polynomial roots. The programme listing shows the example of working out the roots of the equations with functions root ( ) и polyroots ( ) in use.

The other way of finding the solution to equations in Mathcad is the application of a special computing unit, which starts with a key word given and offers to use functions find( ) и minerr ( ).

The unit has the following structure:

The initial value of the desired variable

given

Current equation

Expression with functions find( ) or minerr ( )

Equation roots seeking in Mathcad with the unit given…find ( ) is similar to the same procedure but with function root ( ). The initial value for the desired variable is assigned in Mathcad, after that the solution proximal to the given initial condition is searched for. Unit given…minerr ( ) has a number of essential peculiarities. The solution will be found in any case even in case of its absence. The answer lies in the fact that not the solution to the set of equations is searched for, but the minimal misalignment of equations. The programme listing shows the function, which deliberately has no real roots, but with help of given…minerr ( ) unit the solution is being found, the value of the expression which is mostly proximal to the axis x, and thus guarantees the minimal misalignment. Misalignment (error) value is shown by the system variable ERR.

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