Scilab/C4/SolvingNonlinearEquations/English
Title of script: Solving Nonlinear Equations using Numerical Methods
Author: Shamika
Keywords: Nonlinear equation, root, zero



Slide 1  Dear Friends,
Welcome to the spoken tutorial on “Solving Nonlinear Equations using Numerical Methods” 
Slide 2,3 Objectives  At the end of this tutorial, you will learn how to:
The methods we will be studying are
We will also develop Scilab code to solve nonlinear equations. 
Slide 4System Requirements  To record this tutorial, I am using

Slide 5 Prerequisites  Before practising this tutorial, a learner should have
For Scilab, please refer to the Scilab tutorials available on the Spoken Tutorial website. 
Slide 6  For a given function f, we have to find the value of x for which f of x is equal to zero.
This solution x is called root of equation or zero of function f. This process is called root finding or zero finding. 
Slide 7  We begin by studying Bisection Method.

Slide 8  Let us solve this function using Bisection method.
Given function f equal to two sin x minus e to the power of x divided by four minus one in the interval minus five and minus three 
Open Bisection.sci on Scilab Editor 
Open Bisection dot sci on Scilab editor. Let us look at the code for Bisection method. We define the function Bisection with input arguments a b f and tol. 
Highlight as per narration 
Here

Click on Execute and select Save and Execute  Let us solve the problem using this code.

Switch to Scilab console
a=5 Press enter b=3 Press enter 
Switch to Scilab console
Press Enter.
Press Enter. 
deff('[y]=f(x)','y=(2*(sin(x))((%e^x)/4)1') Press enter 
Define the function using deff function.
We type deff open paranthesis open single quote open square bracket y close square bracket equal to f of x close single quote comma open single quote y equal to two asterisk sin of x minus open paranthesis open paranthesis percentage e to the power of x close paranthesis divided by four close paranthesis minus one close single quote close paranthesis 
Press Enter. 
To know more about deff function, type help deff
Press Enter. 
Tol=10^5 Press enter Bisection(a,b,f,Tol) Press enter 
Let tol be equal to 10 to the power of minus five.
Press Enter.
Bisection open paranthesis a comma b comma f comma tol close paranthesis Press Enter. 
The root of the function is shown on the console.  
Slide 12  Let us study Secant's method.

Slide 13  Let us solve this example using Secant method.
The function is f equal to x square minus six.

Open Secant.sci on Scilab Editor  Before we solve the problem, let us look at the code for Secant method.

Highlight as per narration  We define the function secant with input arguments a, b and f.

Highlight as per narration  We find the difference between the value at the current point and the previous point.

Highlight as per narration  Finally we end the function. 
Click on Execute and select Save and Execute  Let me save and execute the code. 
Switch to Scilab console
Type on Scilab console
Press enter 
Switch to Scilab console.
Press Enter. 
a=2
Press enter
Press enter 
Let me define the initial guesses for this example. Type
a equal to 2 Press Enter.
b equal to 3 Press Enter. 
deff('[y]=g(x)','y=(x^2)6')
Press enter 
We define the function using deff function.
Type deff open paranthesis open single quote open square bracket y close square bracket equal to g of x close single quote comma open single quote y equal to open paranthesis x to the power of two close paranthesis minus six close single quote close paranthesis Press Enter. 
Secant(a,b,g)
Press enter 
We call the function by typing
Secant open paranthesis a comma b comma g close paranthesis. Press Enter.

Slide 14  Let us summarize this tutorial.
In this tutorial we have learnt to:

Slide 15 Assignment  Solve this problem on your own using the two methods we learnt today. 
Show Slide 16
Title: About the Spoken Tutorial Project

* Watch the video available at the following link

Show Slide 17
Title: Spoken Tutorial Workshops The Spoken Tutorial Project Team

The Spoken Tutorial Project Team

Show Slide 18
Title: Acknowledgement

* Spoken Tutorial Project is a part of the Talk to a Teacher project

On previous slide  This is Ashwini Patil signing off. Thanks for joining. 