Difference between revisions of "Scilab/C4/Solving-Non-linear-Equations/English-timed"

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| 00:01
|Dear Friends,  
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|Dear Friends, Welcome to the spoken tutorial on '''Solving Nonlinear Equations using Numerical Methods'''.
  
 
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| 00:02
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| 00:10
|Welcome to the spoken tutorial on '''Solving Nonlinear Equations using Numerical Methods'''.
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| 00:10.
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| At the end of this tutorial, you will learn how to   
 
| At the end of this tutorial, you will learn how to   
  
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| 01:41
|| Given:
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|| 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'''
 
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|| '''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'''
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|03:01
 
|03:01
| We type:  
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| We type: '''deff open parenthesis 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 parenthesis open parenthesis percentage e to the power of x close parenthesis divided by four close parenthesis minus one close single quote close parenthesis'''
 
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|-
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| 03:02
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| '''deff open parenthesis 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 parenthesis open parenthesis percentage e to the power of x close parenthesis divided by four close parenthesis minus one close single quote close parenthesis'''
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| Type '''deff open parenthesis 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 parenthesis x to the power of two close parenthesis minus six close single quote close parenthesis '''
 
| Type '''deff open parenthesis 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 parenthesis x to the power of two close parenthesis minus six close single quote close parenthesis '''
  
 
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| 06:15
 
| 06:15
 
 
| Press '''Enter'''.
 
| Press '''Enter'''.
  
 
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| 06:18
 
| 06:18
 
 
| We call the function by typing  
 
| We call the function by typing  
  
 
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|-
 
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|06:20
| 06:20
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| '''Secant open parenthesis a comma b comma g close parenthesis.'''
 
| '''Secant open parenthesis a comma b comma g close parenthesis.'''
  
 
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|-
 
 
| 06:27
 
| 06:27
 
 
| Press '''Enter'''.
 
| Press '''Enter'''.
  
 
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|-
 
 
| 06:30
 
| 06:30
 
 
| The value of the root is shown on the '''console'''.
 
| The value of the root is shown on the '''console'''.
  
 
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|-
 
 
| 06:35
 
| 06:35
 
 
| Let us summarize this tutorial.  
 
| Let us summarize this tutorial.  
  
 
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|-
 
 
| 06:38
 
| 06:38
 
 
| In this tutorial we have learnt to:  
 
| In this tutorial we have learnt to:  
  
 
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| 06:41
 
| 06:41
 
 
|Develop '''Scilab''' code for different solving methods  
 
|Develop '''Scilab''' code for different solving methods  
  
 
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| 06:45
 
| 06:45
 
 
|Find the roots of '''nonlinear equation '''.
 
|Find the roots of '''nonlinear equation '''.
  
 
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|-
 
 
| 06:48
 
| 06:48
 
 
|Solve this problem on your own using the two methods we learnt today.  
 
|Solve this problem on your own using the two methods we learnt today.  
  
 
|-
 
|-
 
|06:55
 
|06:55
 
 
| Watch the video available at the link shown below.  
 
| Watch the video available at the link shown below.  
  
 
|-
 
|-
 
 
| 06:58
 
| 06:58
 
 
| It summarizes the Spoken Tutorial project.  
 
| It summarizes the Spoken Tutorial project.  
  
 
|-
 
|-
 
 
|07:01
 
|07:01
 
 
||If you do not have good bandwidth, you can download and watch it.  
 
||If you do not have good bandwidth, you can download and watch it.  
  
 
|-
 
|-
 
 
|07:05
 
|07:05
 
 
||The spoken tutorial project Team:
 
||The spoken tutorial project Team:
  
 
|-
 
|-
 
 
|07:07
 
|07:07
 
 
||Conducts workshops using spoken tutorials.  
 
||Conducts workshops using spoken tutorials.  
  
 
|-
 
|-
 
 
|07:10
 
|07:10
 
 
||Gives certificates to those who pass an online test.  
 
||Gives certificates to those who pass an online test.  
  
 
|-
 
|-
 
 
|07:14
 
|07:14
 
 
||For more details, please write to conatct@spoken-tutorial.org.  
 
||For more details, please write to conatct@spoken-tutorial.org.  
  
 
|-
 
|-
 
 
|07:21
 
|07:21
 
 
|Spoken Tutorial Project is a part of the Talk to a Teacher project.  
 
|Spoken Tutorial Project is a part of the Talk to a Teacher project.  
  
 
|-
 
|-
 
 
| 07:24
 
| 07:24
 
 
| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.  
 
| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.  
 
|-
 
|-
 
 
| 07:32
 
| 07:32
 
 
|More information on this mission is available at  http://spoken-tutorial.org/NMEICT-Intro.
 
|More information on this mission is available at  http://spoken-tutorial.org/NMEICT-Intro.
  
 
|-
 
|-
 
 
| 07:39
 
| 07:39
 
 
|This is Ashwini Patil, signing off.
 
|This is Ashwini Patil, signing off.
  
 
|-
 
|-
 
 
|07:41
 
|07:41
 
 
| Thank you for joining.
 
| Thank you for joining.

Revision as of 11:33, 10 March 2017

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 practicing 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: 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: deff open parenthesis 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 parenthesis open parenthesis percentage e to the power of x close parenthesis divided by four close parenthesis minus one close single quote close parenthesis
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 parenthesis a comma b comma f comma tol close parenthesis
04:07 Press Enter.
04:09 The root of the function is shown on the console.
04:14 Let us study Secant's method.
04:17 In Secant's 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's 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 parenthesis 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 parenthesis x to the power of two close parenthesis minus six close single quote close parenthesis
06:15 Press Enter.
06:18 We call the function by typing
06:20 Secant open parenthesis a comma b comma g close parenthesis.
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 summarizes 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