Numerical solutions of equations notes

This document contains notes for numerical solutions of equations. It contains just a few quick key points that you should remember especially for FP1 exams.

• Equations of the form f(x) = 0 can be solved using interval bisection.

  If you find an interval in which f(x) changes sign, then the interval must contain a root of the equation f(x) = 0. You then take the mid-point as the first approximation and repeat this process until you get the required accuracy.

• Equations of the form f(x) = 0 can be solved using linear interpolation.
• Equations of the form f(x) = 0 can be solved using the Newton-Raphson process.
• The Newton-Raphson formula is;
  
• The Newton-Raphson process may not always provide a better approximation and may take you further away from the root.