# Numerical Analysis

## Why Do Is It Even Exist?

Numerical analysis is very interesting, through this mathematicians are capable of approximating almost any solution for any given equation. Some of the main numerical methods are Iterative, Bisection,Secant & Newton’s method...

You can try & solve this equation using a calculator but it would only give you an inaccurate result x^2 - 742x + 2 = 0

It's mainly used by engineers who aim for the fastest & easiest answer of a solution regardless the method used.

## How Can You Apply One Of The Methods?

Iterative Method:

1.Put x in one side& the other side of the equation on the side

2. Denote x (of the highest power) ---> n+1 & other x ---> n

3.Approximate the root of the equation from the graph

4.Let x1= *approximated root* & insert it in the equation

5.Keep repeating the process until you reach the level of accuracy needed !

## Simple Example To Clear The Idea

Consider the function:

x^3 -3x +1=0

x^3 +1=3x

x^3 +1=3x

x=(1/3)(x^3 +1)

x *n+1* = (1/3)(x*n*^3 +1)

I approximated the 1st root to be 0.5-----> x1 = 0.5

x2 = (1/3)(x1^3 +1)=(1/3)(0.53 +1)= 0.375...

x3 = (1/3)(x2^3 +1)=(1/3)(0.3753 +1)= 0.3509…

x4 = (1/3)(x3^3 +1)=(1/3)(0.35093 +1)= 0.3477…

x5 = (1/3)(x4^3 +1)=(1/3)(0.34773 +1)= 0.3473…

## Done By: Rola Daouk

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. ~John Louis von Neumann