Methods of Advanced Mathematics (C3) Coursework.

The first 200 words of this essay...

Methods of Advanced Mathematics (C3) Coursework.

Task: Candidates will investigate the solution of equations using the following three methods:

* Systematic search for change of sign using one of three methods: decimal search, bisection or linear interpolation.

* Fixed point iteration using the Newton raphson method.

* Fixed point iteration after rearranging the equation f(x) = 0 into the form x = g(x)

Change of Sign

This method is based on how the function has a change of sign either +ve to -ve or -ve to +ve on either side of a route when crossing the x-axis. This method relies on this fact to find the points between the positive and the negative value where there is another change from positive to negative. This can be done until a useful number of decimal places are found.

To investigate this method I plan to use the function f (x) = x^3-5x+1. When I plot this it shows:

From the graph we can see that routes lie on the x-axis between the values -3 and -2, 0 and 1 and 1 and 2. If I consider the function between -3 and -2 I can