Numerical solution of equations

Numerical Methods

Understand the concept and application of iterative methods for finding solutions of equations.
Familiarise with Newton-Raphson method and how to apply it in solving equations numerically.
Learn about the bisection method and understand how it works to pinpoint roots.
Grasp the regula falsi (false position) method and how it improves upon the bisection method by approximation of roots.
Importance of procedure in change of sign methods to solve equations, and the ability to indicate failure of method visually and algebraically.

Master the usage of error bounds to quantify the quality of results obtained from numerical methods and estimate the ranges within which solutions lie.
Understand the significance of finding upper and lower bounds to pinpoint the error in solutions.
Determine the order of convergence and rate of convergence of a numerical method, particularly Newton-Raphson method
Apply interval bisection technique in establishing error bounds.

Get familiar with polynomial functions and the context under which they can be solved using numerical methods.
Apply numerical methods to find roots of polynomial functions of higher degree.
Implement the Newton-Raphson process in finding roots of polynomial equations.
Understand the theorem on complex roots of polynomial equations and use it in numerical solutions.

Solve systems of non-linear simultaneous equations using numerical methods.
Application of numerical methods in estimating the intersection points of two curves.
Grasp the technicalities behind the graphical interpretation of simultaneous equations and solutions.
Understand the limitations of numerical solutions and when they may fail in the context of solving simultaneous equations.