Scilab/C4/Solving-Non-linear-Equations/English-timed

Time	Narration
00:01	Dear Friends, Welcome to the spoken tutorial on “Solving Nonlinear Equations using Numerical Methods”
00:10	At the end of this tutorial, you will learn how to:
00:13	Solve nonlinear equations using numerical methods
00:18	The methods we will be studying are
00:20	Bisection method and
00:22	Secant method
00:23	We will also develop Scilab code to solve nonlinear equations.
00:30	To record this tutorial, I am using
00:32	Ubuntu 12.04 as the operating system and
00:36	Scilab 5.3.3 version
00:40	Before practising this tutorial, a learner should have
00:43	basic knowledge of Scilab and
00:46	nonlinear equations
00:48	For Scilab, please refer to the Scilab tutorials available on the Spoken Tutorial website.
00:55	For a given function f, we have to find the value of x for which f of x is equal to zero.
01:04	This solution x is called root of equation or zero of function f.
01:11	This process is called root finding or zero finding.
01:16	We begin by studying Bisection Method.
01:20	In bisection method we calculate the initial bracket of the root.
01:25	Then we iterate through the bracket and halve its length.
01:31	We repeat this process until we find the solution of the equation.
01:36	Let us solve this function using Bisection method.
01:41	Given
01:42	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
01:54	Open Bisection dot sci on Scilab editor.
02:00	Let us look at the code for Bisection method.
02:03	We define the function Bisection with input arguments a b f and Tol.
02:10	Here a is the lower limit of the interval
02:14	b is the upper limit of the interval
02:16	f is the function to be solved
02:19	and Tol is the tolerance level
02:22	We specify the maximum number of iterations to be equal to hundred.
02:28	We find the midpoint of the interval and iterate till the value calculated is within the specified tolerance range.
02:37	Let us solve the problem using this code.
02:40	Save and execute the file.
02:43	Switch to Scilab console
02:47	Let us define the interval.
02:50	Let a be equal to minus five.
02:52	Press Enter.
02:54	Let b be equal to minus three.
02:56	Press Enter.
02:58	Define the function using deff function.
03:01	We type
03:02	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
03:41	To know more about deff function type help deff
03:46	Press Enter.
03:48	Let tol be equal to 10 to the power of minus five.
03:53	Press Enter.
03:56	To solve the problem, type
03:58	Bisection open paranthesis a comma b comma f comma tol close paranthesis
04:07	Press Enter.
04:09	The root of the function is shown on the console.
04:14	Let us study Secant method.
04:17	In Secant method, the derivative is approximated by finite difference using two successive iteration values.
04:27	Let us solve this example using Secant method.
04:30	The function is f equal to x square minus six.
04:36	The two starting guesses are , p zero equal to two and p one equal to three.
04:44	Before we solve the problem, let us look at the code for Secant method.
04:50	Open Secant dot sci on Scilab editor.
04:54	We define the function secant with input arguments a, b and f.
05:01	a is first starting guess for the root
05:04	b is the second starting guess and
05:07	f is the function to be solved.
05:10	We find the difference between the value at the current point and the previous point.
05:15	We apply Secant method and find the value of the root.
05:21	Finally we end the function.
05:24	Let me save and execute the code.
05:27	Switch to Scilab console.
05:30	Type clc.
05:32	Press Enter
05:34	Let me define the initial guesses for this example.
05:38	Type a equal to 2
05:40	Press Enter.
05:42	Then type b equal to 3
05:44	Press Enter.
05:46	We define the function using deff function.
05:49	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
06:15	Press Enter
06:18	We call the function by typing
06:20	Secant open paranthesis a comma b comma g close paranthesis.
06:27	Press Enter
06:30	The value of the root is shown on the console
06:35	Let us summarize this tutorial.
06:38	In this tutorial we have learnt to:
06:41	Develop Scilab code for different solving methods
06:45	Find the roots of nonlinear equation
06:48	Solve this problem on your own using the two methods we learnt today.
06:55	Watch the video available at the link shown below
06:58	It summarises the Spoken Tutorial project
07:01	If you do not have good bandwidth, you can download and watch it
07:05	The spoken tutorial project Team
07:07	Conducts workshops using spoken tutorials
07:10	Gives certificates to those who pass an online test
07:14	For more details, please write to conatct@spoken-tutorial.org
07:21	Spoken Tutorial Project is a part of the Talk to a Teacher project
07:24	It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
07:32	More information on this mission is available at http://spoken-tutorial.org/NMEICT-Intro
07:39	This is Ashwini Patil signing off.
07:41	Thank you for joining.

Contributors and Content Editors

PoojaMoolya, Pratik kamble, Sandhya.np14