# Numerical Analysis

### Finding a Root Of a Function Using Sequence!

## Why Do Is It Even Exist?

__solution for any given equation. Some of the main numerical methods are Iterative, Bisection,Secant & Newton’s method...__

**any**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…

## It' Uses

## Civil EngineeringStructural analysis. Traffic simulations. Environmental simulation. Geographic information system and GPS & So on | ## Chemical EngineeringMolecular modeling. System simulation bio medical engineering & so on | ## Computer & Communication EngineeringNetwork analysis. Signal processing. Electromagnetic fields. |

## Civil Engineering

Structural analysis. Traffic simulations. Environmental simulation. Geographic information system and GPS & So on