# Non Linear Equation Solver

Description| How it works| Equation of StateThis app can be used to either:

a. find the maximum value of a function f(x) within a given range of x,

b. find the minimum value of a function f(x) within a given range of x, or

c. find multiple real solutions of the equation f(x)=Y within a given range of x.

## Download

.xls file (175 KB) or .zip file (27 KB)## Motivation

Excel comes with a non-linear equation solver - Goal Seek. While Goal Seek works in many cases, it does not provide control on the domain of the function, and only provides one solution. The Solver add-in can also be used as a non-linear equation solver. While it allows the domain to be specified, it too provides only one solution.This app aims to address these limitations by allowing the user to specify the domain in which a solution is to be found and searching for multiple solutions. The tool can also find the maxima and minima of the function in the given range.

## How to use

The use of this app is similar to that of the Function Analysis
app. Key in the function, with the equal to sign, in the cell B5.
For example, to key in the function sin x, key in '=sin(x)'. Key in
the range of the function in the cells B12 and B13 and choose the
type of solution required from the drop down list in B8. Choose
'Minimum' to find the values of x that give the minimum values of
the function, or 'Maximum' to find the values of x that give the
maximum values of the function, or 'Target' to solve f(x)=Y. Key in
the value Y in the cell B9 if B8 is set to 'Target'.

If keyed in correctly, the plot of the function will be seen and the
solutions marked by pink dots. Upto 10 solutions are displayed in
the cells from A20.

The following screenshots show the use of the tool in finding:

a. the maximum value of esin(x) between -3 and 3,

b. the minimum value of esin(x) between -3 and 3,

c. the solutions of esin(x) = 2 between -3 and 3, and

d. the solutions of esin(x) = 0 between -3 and 3.

## Also See:

Linear Equation Solver

Simultaneous Non-linear Equation Solver

Parametric Function Plotter

Coupled ODE Solver