Scilab/C4/Integration/Gujarati - Revision history

PoojaMoolya at 07:38, 1 March 2017

2017-03-01T07:38:59Z

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Jyotisolanki at 06:06, 29 December 2015

2015-12-29T06:06:31Z

Jyotisolanki at 10:55, 10 December 2015

2015-12-10T10:55:05Z

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Jyotisolanki at 07:24, 10 December 2015

2015-12-10T07:24:47Z

Jyotisolanki at 06:00, 10 December 2015

2015-12-10T06:00:08Z

Jyotisolanki: Created page with "{| Border=1 |'''Time''' |'''Narration''' |- | 00:01 |Dear Friends, |- | 00:02. | Welcome to the Spoken Tutorial on '''Composite Numerical Integration'''. |- |00:07 |At th..."

2015-12-10T04:34:19Z

Created page with "{| Border=1 |'''Time''' |'''Narration''' |- | 00:01 |Dear Friends, |- | 00:02. | Welcome to the Spoken Tutorial on '''Composite Numerical Integration'''. |- |00:07 |At th..."

New page

{| Border=1

|'''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-intervals'''of 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.

@@ Line 168: / Line 168: @@
 |-
 | 02:49
-|  '''Execute''' on '''Scilab editor''' પર  '''Execute'''  ને ક્લિક કરો અને કોડ ને  '''Save and execute ''' કરો.
+|   '''Scilab editor''' પર  '''Execute'''  ને ક્લિક કરો અને કોડ ને  '''Save and execute ''' કરો.
 |-
@@ Line 519: / Line 519: @@
 |09:04
-|'''numerical integration''' ના માટે સાઈલેબ કોડ લખ્યા.
+|'''numerical integration''' ના માટે સાઈલેબ કોડ લખતા.
 |-

@@ Line 82: / Line 82: @@
 |01:15
-|Let us study '''Composite Trapezoidal Rule.'''
+| ચાલો '''Composite Trapezoidal Rule.'''  (કમ્પોઝિટ ટ્રેપેઝોઈડલ રુલ ) વિષે શીખીએ.
 |-
@@ Line 88: / Line 88: @@
 |01:18
-|This rule is the extension of '''trapezoidal rule'''.
+| આ રુલ '''trapezoidal rule''' (ટ્રેપેઝોઈડલ રુલ ) વિસ્તરણ છે.
 |-
 | 01:22
-|| We divide the interval '''a comma b ''' into '''n''' equal intervals.
+||  આપણે અંતરાલ '''a comma b ''' into '''n''' સમાન અંતરાલ માં વિભાજીત કરે છે.
 |-
@@ Line 99: / Line 99: @@
 | 01:29
-| Then '''h equals to b minus a divided by n''' is the common length of the intervals.
+|  પછી  '''h equals to b minus a divided by n''' અંતરાલની સામાન્ય લંબાઈ  છે.
 |-
@@ Line 105: / Line 105: @@
 |01:36
-| Then '''composite trapezoidal rule''' is given by:
+|પછી  '''composite trapezoidal rule'''આ પ્રકારે આપેલ છે:
 |-
@@ Line 111: / Line 111: @@
 |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'''
+| a થી  b ના અંતરાલમાં ફંક્શન '''F of x''' નું ઈંટીગ્રલ  આશરે ઇકવલ ટુ  '''h'''  ગુણ્યા '''x zero થી  x n''' સુધી ફંક્શન ની વેલ્યુનો સરવાળો.
 |-
@@ Line 117: / Line 117: @@
 |01:57
-|| Let us solve an example using '''composite trapezoidal rule.'''
+|| ચાલો '''composite trapezoidal rule.'''  નો ઉપયોગ કરીને એક ઉદાહરણને હલ કરીને.
 |-
@@ Line 123: / Line 123: @@
 |02:02
-| Assume the number of intervals n is equal to ten (n=10).
+|  ધારો કે અંતરાલની સંખ્યા '''n is equal to ten (n=10)''' છે.
 |-
 |02:09
-|Let us look at the code for '''Composite Trapezoidal Rule''' on '''Scilab editor'''
+|ચાલો સૈલેબ એડિટર પર  '''Composite Trapezoidal Rule''' ના માટે કોડ જોઈએ.
 |-
 | 02:16
-||We first define the function with parameters '''f , a , b , n.'''
+||   પ્રથમ આપણે પેરામીટરસ  '''f , a , b , n.'''  સાથે  ફંક્શન વ્યાખ્યાયિત કરીએ છીએ.
 |-
 | 02:22
-|'''f '''refers to the function we have to solve,
+|'''f ''' તે ફંક્શનને  સંદર્ભ કરે છે જે આપણને હલ કરવાની છે,
 |-
 | 02:25
-|| '''a''' is the lower limit of the integral,
+|| '''a''' '''integral'''  (ઈંટીગ્રલ) ની લોવર લીમીટ છે,
 |-
@@ Line 146: / Line 146: @@
 |02:28
-||''' b''' is the upper limit of the integral and
+||''' b''' '''integral''' (ઈંટીગ્રલ)  ની અપર લીમીટ છે અને,
 |-
@@ Line 152: / Line 152: @@
 |02:31
-| '''n''' is the number of intervals.
+| '''n''' અંતરાલો ની સંખ્યા છે.
 |-
@@ Line 158: / Line 158: @@
 |02:34
-| '''linspace''' function is used to create ten equal intervals between zero and one.
+| '''linspace''' ફંક્શન ઝીરો અને એક ના વચ્ચે દસ સમાન અંતરાલો ને બનાવવા માટે ઉપયોગ થાય છે.
 |-
@@ Line 164: / Line 164: @@
 | 02:42
-|| We find the value of the integral and store it in ''' I one'''.
+||   આપણે '''integral''' (ઈંટીગ્રલ)  ની વેલ્યુ ને શોધીએ છીએ અને તેને  ''' I one''' માં સંગ્રહિત કરીએ છીએ.
 |-
 | 02:49
-| Click on '''Execute''' on '''Scilab editor''' and choose '''Save and execute ''' the code.
+| Click on '''Execute''' on '''Scilab editor''' પર  '''Execute'''  ને ક્લિક કરો અને કોડ ને  '''Save and execute ''' કરો.
 |-
 |03:02
-|  Define the example function by typing:
+|  આપેલ ટાઈપ કરીને ઉદાહરણ ફંક્શન ને વ્યાખ્યાયિત કરીએ:
 |-
 | 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'''
+| '''d e f f ખુલ્લો કૌંસ એકલ અવતરણ ખુલ્લો છગડીયો કૌંસ  y બંદ છગડીયો કૌંસ is equal to f of x અવતરણ  ને બંદ કરો  comma ખુલ્લો અવતરણ  y is equal to one by  ખુલ્લો કૌંસ  ''' 2 asterisk x plus 1 બંદ કૌંસ બંદ અવતરણ બંદ કૌંસ .
 |-
 | 03:30
-| Press '''Enter '''.
+| એન્ટર દબાવો.
 |-
 | 03:31
-|  Type '''Trap underscore composite open parenthesis f comma zero comma one comma ten close parenthesis'''
+|  ટાઈપ કરો '''Trap underscore composite ખુલ્લો કૌંસ   f comma zero comma one comma ten બંદ કૌંસ '''
 |-
 |03:41
-| Press '''Enter '''.
+| એન્ટર દબાવો.
 |-
 |03:43
-| The answer is displayed on the '''console '''.
+|  કંસોલ પર ઉત્તર  દેખાય છે.
 |-
 | 03:47
-| Next we shall study '''Composite Simpson's rule.'''
+| આગળ આપણે  '''Composite Simpson's rule.''' નો અભ્યાસ કરીશું.
 |-

@@ Line 6: / Line 6: @@
 |-
 | 00:01
-|Dear Friends,
+| નમસ્તે મિત્રો,
 |-
 | 00:02.
-| Welcome to the Spoken Tutorial on '''Composite Numerical Integration'''.
+|  '''Composite Numerical Integration''' પરના આ સ્પોકન ટ્યુટોરિયલમાં તમારું સ્વાગત છે.
 |-
 |00:07
-|At the end of this tutorial, you will learn how to:
+|  આ ટ્યુટોરીયલના અંતમાં આપણે શીખીશું કેવી રીતે:
 |-
 |00:11
-|Develop '''Scilab''' code for different '''Composite Numerical Integration algorithms'''
+| વિવિધ  '''Composite Numerical Integration algorithms'''  ના લીધે સાઈલેબ કોડ કેવી રીતે બનાવે છે
 |-
 | 00:17
-|Divide the '''integral''' into equal '''intervals'''
+| '''integral''' (ઈંટીગ્રલ) ને સમાન અંતરાલે કેવી રીતે વિભાજીત થાય છે.
 |-
 |00:21
-|Apply the algorithm to each '''interval''' and
+|  પ્રત્યેક અંતરાલે અલગોરિધમ ને કેવી રીતે લાગુ કરાય છે.અને
 |-
 |00:24
-|Calculate the '''composite value of the integral'''.
+| ઈંટીગ્રલ ની કોમ્પોઝિટ વેલ્યુ ની ગણના કેવી રીતે કરાય છે.
 |-
 | 00:28
-|To record this tutorial, I am using
+| આ ટ્યુટોરિયલ રિકોર્ડ કરવા માટે હું ઉપયોગ કરી રહી છું,
 |-
 | 00:30
-| '''Ubuntu 12.04''' as the operating system
+|   '''Scilab 5.3.3''' વર્જનના સાથે.
 |-
 |00:34
-| with '''Scilab 5.3.3''' version.
+| '''Ubuntu 12.04''' ઓપરેટીંગ સીસ્ટમ
 |-
 |00:38
-||Before practicing this tutorial, a learner should have basic knowledge of
+|| આ ટ્યુટોરિયલ ના અભ્યાસ પહેલા શીખનારને
 |-
 | 00:42
-|'''Scilab''' and
+|'''Scilab'''  સાઈલેબ અને
 |-
 |00:44
-| '''Integration using Numerical Methods'''.
+| '''Integration using Numerical Methods''' નું સામન્ય જ્ઞાન હોવું જોઈએ.
 |-
@@ Line 60: / Line 60: @@
 | 00:47
-| For '''Scilab''', please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.
+| સાઈલેબ માટે સ્પોકન ટ્યુટોરિયલ વેબ સાઈટ પર ઉપલબ્ધ સંબંધિત ટ્યુટોરિયલ જુઓ.
 |-
 | 00:55
-| '''Numerical Integration''' is the
+| '''Numerical Integration''' છે. કે
 |-
 | 00:58
-| study of how the numerical value of an '''integral''' can be found.
+| '''integral''' (ઈંટીગ્રલ) ની  ન્યુમેરીક્લ વેલ્યુ ને કેવી રીતે મેળવી શકાય છે.
 |-
 |01:03
-| It is used when exact mathematical integration is not available.
+|  આ ઉપયોગ થાય છે જયારે ચોક્કસ મેથેમેટિકલ ઇન્ટીગ્રેશન ઉપલબ્ધ નથી થતું.
 |-
 |01:08
-|It approximates a '''definite integral''' from values of the '''integrand'''.
+| આ  '''integrand''' (ઈંટીગ્રેંડ) ની વેલ્યુ થી  '''definite integral'''  નો અંદાજ લગાડે છે.
 |-