Difference between revisions of "Scilab/C4/Integration/English-timed"

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|-
 
|-
 
| 00:02.
 
| 00:02.
−
| Welcome to the Spoken Tutorial on '''“ Composite Numerical Integration” '''
+
| Welcome to the Spoken Tutorial on '''Composite Numerical Integration'''.
  
 
|-
 
|-
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|-
 
|-
 
|00:24
 
|00:24
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|Calculate the '''composite value of the integral'''
+
|Calculate the '''composite value of the integral'''.
  
 
|-
 
|-
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|-
 
|-
 
|00:34
 
|00:34
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| with '''Scilab 5.3.3''' version  
+
| with '''Scilab 5.3.3''' version.
  
 
|-
 
|-
 
|00:38
 
|00:38
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||Before practising this tutorial, a learner should have basic knowledge of  
+
||Before practicing this tutorial, a learner should have basic knowledge of  
  
 
|-
 
|-
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|-
 
|-
 
|00:44
 
|00:44
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| '''Integration using Numerical Methods'''
+
| '''Integration using Numerical Methods'''.
  
 
|-
 
|-
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|-
 
|-
 
| 00:55
 
| 00:55
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| '''Numerical Integration''' is the:
+
| '''Numerical Integration''' is the  
  
 
|-
 
|-
 
| 00:58
 
| 00:58
−
| Study of how the numerical value of an '''integral''' can be found  
+
| study of how the numerical value of an '''integral''' can be found.
  
 
|-
 
|-
 
|01:03
 
|01:03
−
| It is used when exact mathematical integration is not available  
+
| It is used when exact mathematical integration is not available.
  
 
|-
 
|-
 
|01:08
 
|01:08
−
|It approximates a definite '''integral''' from values of the '''integrand'''  
+
|It approximates a '''definite integral''' from values of the '''integrand'''.
  
 
|-
 
|-
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|01:18
 
|01:18
  
−
|This rule is the extension of '''trapezoidal rule'''  
+
|This rule is the extension of '''trapezoidal rule'''.
  
 
|-
 
|-
  
 
| 01:22
 
| 01:22
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|| We divide the interval '''a comma b '''into '''n''' equal intervals  
+
|| We divide the interval '''a comma b ''' into '''n''' equal intervals.
  
 
|-
 
|-
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| 01:29
 
| 01:29
  
−
| Then '''h equal to b minus a divided by n''' is the common length of the intervals  
+
| Then '''h equals to b minus a divided by n''' is the common length of the intervals.
  
 
|-
 
|-
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|01:36
 
|01:36
  
−
| Then '''composite trapezoidal rule''' is given by  
+
| Then '''composite trapezoidal rule''' is given by:
  
 
|-
 
|-
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|02:02
 
|02:02
  
−
| Assume the number of intervals n is equal to ten.  
+
| Assume the number of intervals n is equal to ten (n=10).  
  
 
|-
 
|-
 
|02:09
 
|02:09
−
|Let us look at the code for '''Composite Trapezoidal Rule''' on '''Scilab Editor'''
+
|Let us look at the code for '''Composite Trapezoidal Rule''' on '''Scilab editor'''
  
 
|-
 
|-
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| 02:25
 
| 02:25
−
|| '''a ''' is the lower limit of the integral,
+
|| '''a''' is the lower limit of the integral,
 
   
 
   
 
|-
 
|-
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|02:34
 
|02:34
  
−
| '''linspace''' function is used to create ten equal intervals between zero and one  
+
| '''linspace''' function is used to create ten equal intervals between zero and one.
  
 
|-
 
|-
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| 02:42
 
| 02:42
  
−
|| We find the value of the integral and store it in ''' I one'''
+
|| We find the value of the integral and store it in ''' I one'''.
  
 
|-
 
|-
 
| 02:49
 
| 02:49
−
| Click on '''Execute''' on '''Scilab editor''' and choose '''Save and Execute ''' the code.  
+
| Click on '''Execute''' on '''Scilab editor''' and choose '''Save and execute ''' the code.  
  
 
|-
 
|-
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|-
 
|-
 
| 03:05
 
| 03:05
−
| '''d e f f open paranthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one by open paranthesis two asterisk x plus one close paranthesis close quote close paranthesis'''
+
| '''d e f f open parenthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one by open parenthesis two asterisk x plus one close parenthesis close quote close parenthesis'''
  
 
|-
 
|-
 
| 03:30
 
| 03:30
−
| Press '''Enter '''
+
| Press '''Enter '''.
  
 
|-
 
|-
 
| 03:31
 
| 03:31
−
|  Type '''Trap underscore composite open paranthesis f comma zero comma one comma ten close paranthesis
+
|  Type '''Trap underscore composite open parenthesis f comma zero comma one comma ten close parenthesis'''  
−
'''
+
 
 
|-
 
|-
 
|03:41
 
|03:41
−
| Press '''Enter '''
+
| Press '''Enter '''.
  
 
|-
 
|-
 
|03:43
 
|03:43
−
| The answer is displayed on the '''console '''
+
| The answer is displayed on the '''console '''.
  
 
|-
 
|-
 
| 03:47
 
| 03:47
−
| Next we shall study '''Composite simpson's rule.'''
+
| Next we shall study '''Composite Simpson's rule.'''
  
 
|-
 
|-
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| 03:51
 
| 03:51
  
−
| In this rule, we decompose the interval ''' a comma b''' into '''n is greater than 1'''  subintervals of equal length  
+
| In this rule, we decompose the interval ''' a comma b''' into '''n is greater than 1'''  sub-intervals of equal length.
  
 
|-
 
|-
  
 
| 04:03
 
| 04:03
−
|| Apply '''Simpson's rule''' to each interval  
+
|| Apply '''Simpson's rule''' to each interval.
  
 
|-
 
|-
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| 04:06
 
| 04:06
  
−
| We get the value of the integral to be  
+
| We get the value of the integral to be:
  
 
|-
 
|-
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|04:10
 
|04:10
  
−
| '''h by three multiplied by the sum of f zero, four into f one , two into f two to f n'''
+
| '''h by three multiplied by the sum of f zero, four into f one , two into f two to f n'''.
  
 
|-
 
|-
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| 04:24
 
| 04:24
  
−
|We are given a '''function one by one plus x cube d x in the interval one to two'''
+
|We are given a '''function one by one plus x cube d x in the interval one to two'''.
  
 
|-
 
|-
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| 04:32
 
| 04:32
  
−
| Let the number of intervals be '''twenty '''
+
| Let the number of intervals be '''twenty '''.
  
 
|-
 
|-
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|04:37
 
|04:37
  
−
| Let us look at the code for  '''Composite simpson's rule'''
+
| Let us look at the code for  '''Composite Simpson's rule'''.
  
 
|-
 
|-
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| 05:04
 
| 05:04
  
−
| We find the value of the function with one set and multiply it with two  
+
| We find the value of the function with one set and multiply it with two.
  
 
|-
 
|-
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| 05:10
 
| 05:10
  
−
| With the other set, we find the value and multiply it with four  
+
| With the other set, we find the value and multiply it with four.
  
 
|-
 
|-
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| 05:16
 
| 05:16
  
−
||We sum these values and multiply it with '''h by three and store the final value in I '''
+
||We sum these values and multiply it with '''h by three and store the final value in I '''.
  
 
|-
 
|-
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| 05:24
 
| 05:24
  
−
||Let us execute the code  
+
||Let us execute the code.
  
 
|-
 
|-
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| 05:28
 
| 05:28
  
−
|| Save and execute the file '''Simp underscore composite dot s c i'''
+
|| Save and execute the file '''Simp underscore composite dot s c i'''.
  
 
|-
 
|-
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| 05:42
 
| 05:42
  
−
| Define the function given in the example by typing  
+
| Define the function given in the example by typing:
  
 
|-
 
|-
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|05:45
 
|05:45
  
−
|'''d e f f open paranthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one divided by open paranthesis one plus x cube close paranthesis close quote close paranthesis'''
+
|'''d e f f open parenthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one divided by open parenthesis one plus x cube close parenthesis close quote close parenthesis'''
  
 
|-
 
|-
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|06:12
 
|06:12
  
−
| Press '''Enter '''
+
| Press '''Enter '''.
  
 
|-
 
|-
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| 06:14
 
| 06:14
  
−
| Type '''Simp underscore composite open paranthesis f comma one comma two comma twenty close paranthesis'''
+
| Type '''Simp underscore composite open parenthesis f comma one comma two comma twenty close parenthesis'''
  
 
|-
 
|-
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|06:24
 
|06:24
  
−
||Press '''Enter '''
+
||Press '''Enter '''.
  
 
|-
 
|-
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| 06:35
 
| 06:35
  
−
| It integrates polynomials of degree one or less  
+
| It integrates polynomials of degree one or less,
  
 
|-
 
|-
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|06:40
 
|06:40
  
−
| Divides the interval '''a comma b''' into a ''' subintervals'''of equal width  
+
| divides the interval '''a comma b''' into a ''' sub-intervals'''of equal width.
  
 
|-
 
|-
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|06:49
 
|06:49
  
−
| Finds the midpoint of each interval indicated by '''x i '''
+
| Finds the midpoint of each interval indicated by '''x i '''.
  
 
|-
 
|-
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|06:54
 
|06:54
  
−
| We find the sum of the values of the integral at each midpoint  
+
| We find the sum of the values of the integral at each midpoint.
  
 
|-
 
|-
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|07:00
 
|07:00
  
−
| Let us solve this problem using '''Composite Midpoint Rule'''
+
| Let us solve this problem using '''Composite Midpoint Rule'''.
  
 
|-
 
|-
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|07:05
 
|07:05
  
−
| '''We are given a function one minus x square d x in the interval zero to one point five'''
+
| '''We are given a function one minus x square d x in the interval zero to one point five'''.
  
 
|-
 
|-
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|07:15
 
|07:15
  
−
| We assume '''n''' is equal to '''twenty '''
+
| We assume '''n''' is equal to '''twenty '''.
  
 
|-
 
|-
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|07:18
 
|07:18
  
−
| Let us look at the code for '''Composite Midpoint rule'''
+
| Let us look at the code for '''Composite Midpoint rule'''.
  
 
|-
 
|-
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|07:41
 
|07:41
  
−
| We find the midpoint of each interval  
+
| We find the midpoint of each interval.
  
  
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|07:53
 
|07:53
  
−
| Let us now solve the example  
+
| Let us now solve the example.
  
 
|-
 
|-
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|07:55
 
|07:55
  
−
| Save and execute the file '''mid underscore composite dot s c i'''  
+
| Save and execute the file '''mid underscore composite dot s c i'''.
  
 
|-
 
|-
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|08:04
 
|08:04
  
−
| Let me clear the screen  
+
| Let me clear the screen.
  
 
|-
 
|-
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|08:08
 
|08:08
  
−
| We define the function given in the example by typing  
+
| We define the function given in the example by typing:
  
 
|-
 
|-
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|08:13
 
|08:13
  
−
| '''d e f f open paranthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one minus x square close quote close paranthesis'''
+
| '''d e f f open parenthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one minus x square close quote close parenthesis'''
  
 
|-
 
|-
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|08:37
 
|08:37
  
−
| Press '''Enter'''  
+
| Press '''Enter'''.
  
 
|-
 
|-
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|08:39
 
|08:39
  
−
| Then type '''mid underscore composite open paranthesis f comma zero comma one point five comma twenty close paranthesis'''
+
| Then type '''mid underscore composite open parenthesis f comma zero comma one point five comma twenty close parenthesis'''
  
 
|-
 
|-
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|08:53
 
|08:53
  
−
|Press '''Enter '''
+
|Press '''Enter '''.
  
 
  |-
 
  |-
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|08:54
 
|08:54
  
−
| The answer is displayed on the '''console'''
+
| The answer is displayed on the '''console'''.
  
 
|-
 
|-
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|09:08
 
|09:08
  
−
| Find the value of an '''integral'''  
+
| Find the value of an '''integral'''.
  
  
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|09:11
 
|09:11
  
−
| Watch the video available at the link shown below  
+
| Watch the video available at the link shown below.
  
 
|-
 
|-
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| 09:15
 
| 09:15
  
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| It summarises the Spoken Tutorial project  
+
| It summarizes the Spoken Tutorial project.
  
 
|-
 
|-
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|09:18
 
|09:18
  
−
||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.
  
 
|-
 
|-
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|09:23
 
|09:23
  
−
||The spoken tutorial Team
+
||The spoken tutorial Team:
  
 
|-
 
|-
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|09:29
 
|09:29
  
−
||Gives certificates to those who pass an online test  
+
||Gives certificates to those who pass an online test.
  
 
|-
 
|-
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|09:32
 
|09:32
  
−
||For more details, please write to contact@spoken-tutorial.org  
+
||For more details, please write to contact@spoken-tutorial.org.
  
 
|-
 
|-
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|09:40
 
|09:40
  
−
|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.
  
 
|-
 
|-
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| 09:52
 
| 09:52
  
−
|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.
  
 
|-
 
|-
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| 10:03
 
| 10:03
  
−
|This is Ashwini Patil signing off. Thank you for joining.
+
|This is Ashwini Patil, signing off. Thank you for joining.

Revision as of 16:31, 26 February 2015

Time Narration
00:01 Dear Friends,
00:02. Welcome to the Spoken Tutorial on Composite Numerical Integration.
00:07 At the end of this tutorial, you will learn how to:
00:11 Develop Scilab code for different Composite Numerical Integration algorithms
00:17 Divide the integral into equal intervals
00:21 Apply the algorithm to each interval and
00:24 Calculate the composite value of the integral.
00:28 To record this tutorial, I am using
00:30 Ubuntu 12.04 as the operating system
00:34 with Scilab 5.3.3 version.
00:38 Before practicing this tutorial, a learner should have basic knowledge of
00:42 Scilab and
00:44 Integration using Numerical Methods.
00:47 For Scilab, please refer to the relevant tutorials available on the Spoken Tutorial website.
00:55 Numerical Integration is the
00:58 study of how the numerical value of an integral can be found.
01:03 It is used when exact mathematical integration is not available.
01:08 It approximates a definite integral from values of the integrand.
01:15 Let us study Composite Trapezoidal Rule.
01:18 This rule is the extension of trapezoidal rule.
01:22 We divide the interval a comma b into n equal intervals.
01:29 Then h equals to b minus a divided by n is the common length of the intervals.
01:36 Then composite trapezoidal rule is given by:
01:41 The integral of the function F of x in the interval a to b is approximately equal to h multiplied by the sum of the values of the function at x zero to x n
01:57 Let us solve an example using composite trapezoidal rule.
02:02 Assume the number of intervals n is equal to ten (n=10).
02:09 Let us look at the code for Composite Trapezoidal Rule on Scilab editor
02:16 We first define the function with parameters f , a , b , n.
02:22 f refers to the function we have to solve,
02:25 a is the lower limit of the integral,
02:28 b is the upper limit of the integral and
02:31 n is the number of intervals.
02:34 linspace function is used to create ten equal intervals between zero and one.
02:42 We find the value of the integral and store it in I one.
02:49 Click on Execute on Scilab editor and choose Save and execute the code.
03:02 Define the example function by typing:
03:05 d e f f open parenthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one by open parenthesis two asterisk x plus one close parenthesis close quote close parenthesis
03:30 Press Enter .
03:31 Type Trap underscore composite open parenthesis f comma zero comma one comma ten close parenthesis
03:41 Press Enter .
03:43 The answer is displayed on the console .
03:47 Next we shall study Composite Simpson's rule.
03:51 In this rule, we decompose the interval a comma b into n is greater than 1 sub-intervals of equal length.
04:03 Apply Simpson's rule to each interval.
04:06 We get the value of the integral to be:
04:10 h by three multiplied by the sum of f zero, four into f one , two into f two to f n.
04:19 Let us solve an example using Composite Simpson's rule.
04:24 We are given a function one by one plus x cube d x in the interval one to two.
04:32 Let the number of intervals be twenty .
04:37 Let us look at the code for Composite Simpson's rule.
04:42 We first define the function with parameters f , a , b , n.
04:49 f refers to the function we have to solve,
04:52 a is the lower limit of the integral,
04:56 b is the upper limit of the integral and
04:58 n is the number of intervals.
05:02 We find two sets of points.
05:04 We find the value of the function with one set and multiply it with two.
05:10 With the other set, we find the value and multiply it with four.
05:16 We sum these values and multiply it with h by three and store the final value in I .
05:24 Let us execute the code.
05:28 Save and execute the file Simp underscore composite dot s c i.
05:39 Let me clear the screen first.
05:42 Define the function given in the example by typing:
05:45 d e f f open parenthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one divided by open parenthesis one plus x cube close parenthesis close quote close parenthesis
06:12 Press Enter .
06:14 Type Simp underscore composite open parenthesis f comma one comma two comma twenty close parenthesis
06:24 Press Enter .
06:26 The answer is displayed on the console.
06:31 Let us now look at Composite Midpoint Rule.
06:35 It integrates polynomials of degree one or less,
06:40 divides the interval a comma b into a sub-intervalsof equal width.
06:49 Finds the midpoint of each interval indicated by x i .
06:54 We find the sum of the values of the integral at each midpoint.
07:00 Let us solve this problem using Composite Midpoint Rule.
07:05 We are given a function one minus x square d x in the interval zero to one point five.
07:15 We assume n is equal to twenty .
07:18 Let us look at the code for Composite Midpoint rule.
07:24 We first define the function with parameters f , a , b , n.
07:30 f refers to the function we have to solve,
07:33 a is the lower limit of the integral,
07:36 b is the upper limit of the integral and
07:39 n is the number of intervals.
07:41 We find the midpoint of each interval.


07:45 Find the value of integral at each midpoint and then find the sum and store it in I.
07:53 Let us now solve the example.
07:55 Save and execute the file mid underscore composite dot s c i.
08:04 Let me clear the screen.
08:08 We define the function given in the example by typing:
08:13 d e f f open parenthesis open single quote open square bracket y close square bracket is equal to f of x close quote comma open quote y is equal to one minus x square close quote close parenthesis
08:37 Press Enter.
08:39 Then type mid underscore composite open parenthesis f comma zero comma one point five comma twenty close parenthesis
08:53 Press Enter .
08:54 The answer is displayed on the console.
08:59 Let us summarize this tutorial.
09:02 In this tutorial we have learnt to:
09:04 Develop Scilab code for numerical integration
09:08 Find the value of an integral.


09:11 Watch the video available at the link shown below.
09:15 It summarizes the Spoken Tutorial project.
09:18 If you do not have good bandwidth, you can download and watch it.
09:23 The spoken tutorial Team:
09:25 Conducts workshops using spoken tutorials
09:29 Gives certificates to those who pass an online test.
09:32 For more details, please write to contact@spoken-tutorial.org.
09:40 Spoken Tutorial Project is a part of the Talk to a Teacher project.
09:45 It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
09:52 More information on this mission is available at http://spoken-tutorial.org/NMEICT-Intro.
10:03 This is Ashwini Patil, signing off. Thank you for joining.

Contributors and Content Editors

Gaurav, PoojaMoolya, Sandhya.np14

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