Difference between revisions of "Scilab/C4/ODE-Euler-methods/English-timed"
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PoojaMoolya (Talk | contribs) (Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the Spoken Tutorial on '''“Solving ODEs using Euler Methods” ''' |- | 00.09 | At the …') |
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| − | + | |'''Narration''' | |
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| − | | 00 | + | | 00:01 |
|Dear Friends, | |Dear Friends, | ||
|- | |- | ||
| − | | 00 | + | | 00:02 |
| Welcome to the Spoken Tutorial on '''“Solving ODEs using Euler Methods” ''' | | Welcome to the Spoken Tutorial on '''“Solving ODEs using Euler Methods” ''' | ||
|- | |- | ||
| − | | 00 | + | | 00:09 |
| At the end of this tutorial, you will learn how to: | | At the end of this tutorial, you will learn how to: | ||
|- | |- | ||
| − | |00 | + | |00:12 |
|Solve '''ODEs''' using '''Euler''' and '''Modified Euler methods''' in '''Scilab''' | |Solve '''ODEs''' using '''Euler''' and '''Modified Euler methods''' in '''Scilab''' | ||
|- | |- | ||
| − | |00 | + | |00:18 |
|Develop '''Scilab''' code to solve '''ODEs''' | |Develop '''Scilab''' code to solve '''ODEs''' | ||
|- | |- | ||
| − | | 00 | + | | 00:22 |
|To record this tutorial, I am using | |To record this tutorial, I am using | ||
|- | |- | ||
| − | |00 | + | |00:25 |
|'''Ubuntu 12.04''' as the operating system | |'''Ubuntu 12.04''' as the operating system | ||
|- | |- | ||
| − | | 00 | + | | 00:28 |
|and '''Scilab 5.3.3''' version | |and '''Scilab 5.3.3''' version | ||
|- | |- | ||
| − | | 00 | + | | 00:32 |
| To practise this tutorial, a learner | | To practise this tutorial, a learner | ||
|- | |- | ||
| − | |00 | + | |00:34 |
|should have basic knowledge of '''Scilab''' | |should have basic knowledge of '''Scilab''' | ||
|- | |- | ||
| − | |00 | + | |00:37 |
|and should know how to solve '''ODEs.''' | |and should know how to solve '''ODEs.''' | ||
|- | |- | ||
| − | | 00 | + | | 00:40 |
| To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website. | | To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website. | ||
|- | |- | ||
| − | | 00 | + | | 00:48 |
| In '''Euler method,''' we get an accurately approximate solution of the '''ODE.''' | | In '''Euler method,''' we get an accurately approximate solution of the '''ODE.''' | ||
|- | |- | ||
| − | |00 | + | |00:55 |
|It is used to solve initial value problems where initial values of the '''differential equation''' are given. | |It is used to solve initial value problems where initial values of the '''differential equation''' are given. | ||
|- | |- | ||
| − | |01 | + | |01:03 |
| It can be used to solve '''continuous functions.''' | | It can be used to solve '''continuous functions.''' | ||
|- | |- | ||
| − | |01 | + | |01:08 |
|Let us solve an example using '''Euler method.''' | |Let us solve an example using '''Euler method.''' | ||
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| − | |01 | + | |01:12 |
|We are given an initial value problem - | |We are given an initial value problem - | ||
|- | |- | ||
| − | | 01 | + | | 01:15 |
|'''y dash is equal to minus two t minus y.''' | |'''y dash is equal to minus two t minus y.''' | ||
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|- | |- | ||
| − | | 01 | + | | 01:20 |
||The initial value of y is given as '''minus one''' | ||The initial value of y is given as '''minus one''' | ||
|- | |- | ||
| − | |01 | + | |01:25 |
|| and the '''step length''' is given as '''zero point one.''' | || and the '''step length''' is given as '''zero point one.''' | ||
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|- | |- | ||
| − | |01 | + | |01:29 |
| We have to find the value of '''y''' at time '''t equal to zero point five.''' | | We have to find the value of '''y''' at time '''t equal to zero point five.''' | ||
|- | |- | ||
| − | |01 | + | |01:36 |
|Let us look at the code for '''Euler method.''' | |Let us look at the code for '''Euler method.''' | ||
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|- | |- | ||
| − | |01 | + | |01:39 |
|Open '''Euler underscore o d e dot sci''' on '''Scilab editor.''' | |Open '''Euler underscore o d e dot sci''' on '''Scilab editor.''' | ||
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|- | |- | ||
| − | |01 | + | |01:47 |
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| − | |01 | + | |01:58 |
|'where '''f''' denotes the function to be solved, | |'where '''f''' denotes the function to be solved, | ||
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|- | |- | ||
| − | | 02 | + | | 02:01 |
|'''t init''' is the initial value of time '''t''', | |'''t init''' is the initial value of time '''t''', | ||
|- | |- | ||
| − | |02 | + | |02:05 |
||'''y init''' is the initial value of '''y''' | ||'''y init''' is the initial value of '''y''' | ||
|- | |- | ||
| − | |02 | + | |02:09 |
| '''h''' is the '''step length,''' and '''n''' is the number of '''iterations.''' | | '''h''' is the '''step length,''' and '''n''' is the number of '''iterations.''' | ||
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|- | |- | ||
| − | |02 | + | |02:14 |
| Then we initialize the values of '''t''' and '''y to vectors of zeros. ''' | | Then we initialize the values of '''t''' and '''y to vectors of zeros. ''' | ||
|- | |- | ||
| − | | 02 | + | | 02:21 |
|| We place the initial values of '''t''' and '''y''' in '''t of one''' and '''y of one''' respectively. | || We place the initial values of '''t''' and '''y''' in '''t of one''' and '''y of one''' respectively. | ||
|- | |- | ||
| − | | 02 | + | | 02:29 |
| Then we '''iterate''' from '''one to N''' to find the value of '''y'''. | | Then we '''iterate''' from '''one to N''' to find the value of '''y'''. | ||
|- | |- | ||
| − | |02 | + | |02:33 |
| Here we apply '''Euler method''' to find the value of '''y. ''' | | Here we apply '''Euler method''' to find the value of '''y. ''' | ||
|- | |- | ||
| − | |02 | + | |02:39 |
| Finally we end the '''function. ''' | | Finally we end the '''function. ''' | ||
|- | |- | ||
| − | | 02 | + | | 02:42 |
|Save and execute the file '''Euler underscore o d e dot sci''' | |Save and execute the file '''Euler underscore o d e dot sci''' | ||
|- | |- | ||
| − | | 02 | + | | 02:49 |
|Switch to '''Scilab console''' to solve the example problem. | |Switch to '''Scilab console''' to solve the example problem. | ||
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|- | |- | ||
| − | | 02 | + | | 02:54 |
|We define the ''' function ''' by typing | |We define the ''' function ''' by typing | ||
|- | |- | ||
| − | | 02 | + | | 02:56 |
|'''d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to open paranthesis minus two asterisk t close paranthesis minus y close single quote close paranthesis ''' | |'''d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to open paranthesis minus two asterisk t close paranthesis minus y close single quote close paranthesis ''' | ||
|- | |- | ||
| − | |03 | + | |03:26 |
|Press '''Enter. ''' | |Press '''Enter. ''' | ||
|- | |- | ||
| − | |03 | + | |03:28 |
| Then type '''t init is equal to zero. ''' | | Then type '''t init is equal to zero. ''' | ||
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|- | |- | ||
| − | | 03 | + | | 03:31 |
|Press '''Enter. ''' | |Press '''Enter. ''' | ||
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|- | |- | ||
| − | | 03 | + | | 03:33 |
||Type '''y init is equal to minus one. ''' | ||Type '''y init is equal to minus one. ''' | ||
' | ' | ||
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|- | |- | ||
| − | |03 | + | |03:38 |
||Press '''Enter ''' | ||Press '''Enter ''' | ||
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|- | |- | ||
| − | | 03 | + | | 03:40 |
| Type '''step length h is equal to zero point one. ''' | | Type '''step length h is equal to zero point one. ''' | ||
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|- | |- | ||
| − | | 03 | + | | 03:44 |
| Press '''Enter''' | | Press '''Enter''' | ||
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|- | |- | ||
| − | | 03 | + | | 03:46 |
| The '''step length is zero point one,''' and we have to find the value of '''y''' at '''zero point five.''' | | The '''step length is zero point one,''' and we have to find the value of '''y''' at '''zero point five.''' | ||
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|- | |- | ||
| − | |03 | + | |03:53 |
||So, the number of '''iterations''' should be '''five.''' | ||So, the number of '''iterations''' should be '''five.''' | ||
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|- | |- | ||
| − | |03 | + | |03:59 |
|At each '''iteration,''' the value of '''t''' will be increased by '''zero point one.''' | |At each '''iteration,''' the value of '''t''' will be increased by '''zero point one.''' | ||
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|- | |- | ||
| − | | 04 | + | | 04:05 |
| So type '''capital N is equal to five.''' | | So type '''capital N is equal to five.''' | ||
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|- | |- | ||
| − | | 04 | + | | 04:09 |
|And press '''Enter.''' | |And press '''Enter.''' | ||
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| − | | 04 | + | | 04:11 |
| To '''call''' the '''function,''' type | | To '''call''' the '''function,''' type | ||
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|- | |- | ||
| − | | 04 | + | | 04:14 |
| '''open square bracket t comma y close square bracket equal to Euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis ''' | | '''open square bracket t comma y close square bracket equal to Euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis ''' | ||
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|- | |- | ||
| − | | 04 | + | | 04:33 |
||Press '''Enter.''' | ||Press '''Enter.''' | ||
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|- | |- | ||
| − | | 04 | + | | 04:35 |
||The value of '''y at t equal to zero point five''' is shown. | ||The value of '''y at t equal to zero point five''' is shown. | ||
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|- | |- | ||
| − | | 04 | + | | 04:41 |
||Now let us look at '''Modified Euler method. ''' | ||Now let us look at '''Modified Euler method. ''' | ||
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|- | |- | ||
| − | | 04 | + | | 04:45 |
|It is a '''second order method''' and is a '''stable two step method. ''' | |It is a '''second order method''' and is a '''stable two step method. ''' | ||
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| − | | 04 | + | | 04:51 |
|We find the '''average''' of the '''function''' at the beginning and end of '''time step.''' | |We find the '''average''' of the '''function''' at the beginning and end of '''time step.''' | ||
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|- | |- | ||
| − | |04 | + | |04:56 |
|Let us solve this example using '''Modified Euler method.''' | |Let us solve this example using '''Modified Euler method.''' | ||
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|- | |- | ||
| − | | 05 | + | | 05:02 |
|We are given a '''function y dash is equal to t plus y plus t y. ''' | |We are given a '''function y dash is equal to t plus y plus t y. ''' | ||
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|- | |- | ||
| − | | 05 | + | | 05:08 |
| The initial value of '''y''' is '''one''' | | The initial value of '''y''' is '''one''' | ||
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| − | | 05 | + | | 05:12 |
| and the '''step length''' is '''zero point zero one.''' | | and the '''step length''' is '''zero point zero one.''' | ||
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|- | |- | ||
| − | | 05 | + | | 05:16 |
|We have to find the value of '''y''' at '''time t equal to zero point one ''' using '''Modified Euler's method.''' | |We have to find the value of '''y''' at '''time t equal to zero point one ''' using '''Modified Euler's method.''' | ||
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|- | |- | ||
| − | | 05 | + | | 05:25 |
| Let us look at the code for '''Modified Euler method on Scilab Editor''' | | Let us look at the code for '''Modified Euler method on Scilab Editor''' | ||
|- | |- | ||
| − | | 05 | + | | 05:31 |
|We define the '''function''' with '''arguments f, t init, y init, h and n''' | |We define the '''function''' with '''arguments f, t init, y init, h and n''' | ||
|- | |- | ||
| − | | 05 | + | | 05:39 |
| '''where f''' is the '''function''' to be solved | | '''where f''' is the '''function''' to be solved | ||
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|- | |- | ||
| − | | 05 | + | | 05:42 |
| '''t init''' is the intial '''time''' value, | | '''t init''' is the intial '''time''' value, | ||
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| − | | 05 | + | | 05:45 |
| '''y init''' is the inital value of '''y''' | | '''y init''' is the inital value of '''y''' | ||
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| − | | 05 | + | | 05:49 |
| '''h''' is the '''step length''' and | | '''h''' is the '''step length''' and | ||
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|- | |- | ||
| − | | 05 | + | | 05:51 |
| '''n''' is the number of '''iterations.''' | | '''n''' is the number of '''iterations.''' | ||
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|- | |- | ||
| − | | 05 | + | | 05:54 |
| Then we initialize the '''arrays''' for '''y''' and '''t.''' | | Then we initialize the '''arrays''' for '''y''' and '''t.''' | ||
|- | |- | ||
| − | | 05 | + | | 05:58 |
|We place the initial values of '''t''' and '''y''' in '''t of one''' and '''y of one''' respectively. | |We place the initial values of '''t''' and '''y''' in '''t of one''' and '''y of one''' respectively. | ||
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| − | | 06 | + | | 06:07 |
|We implement '''Modified Euler Method''' here. | |We implement '''Modified Euler Method''' here. | ||
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| − | | 06 | + | | 06:11 |
|Here we find the average value of '''y''' at the beginning and end of '''time step.''' | |Here we find the average value of '''y''' at the beginning and end of '''time step.''' | ||
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| − | | 06 | + | | 06:17 |
|Save and execute the file '''Modi Euler underscore o d e dot sci.''' | |Save and execute the file '''Modi Euler underscore o d e dot sci.''' | ||
|- | |- | ||
| − | | 06 | + | | 06:23 |
|Switch to '''Scilab console.''' | |Switch to '''Scilab console.''' | ||
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| − | | 06 | + | | 06:26 |
|Clear the screen by typing '''c l c.''' | |Clear the screen by typing '''c l c.''' | ||
|- | |- | ||
| − | | 06 | + | | 06:30 |
|Press '''Enter.''' | |Press '''Enter.''' | ||
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| − | | 06 | + | | 06:32 |
|Define the '''function''' by typing '''d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to t plus y plus t asterisk y close single quote close paranthesis''' | |Define the '''function''' by typing '''d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to t plus y plus t asterisk y close single quote close paranthesis''' | ||
|- | |- | ||
| − | | 07 | + | | 07:01 |
|Press '''Enter.''' | |Press '''Enter.''' | ||
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| − | | 07 | + | | 07:03 |
|Then type '''t init equal to zero''', press Enter | |Then type '''t init equal to zero''', press Enter | ||
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| − | | 07 | + | | 07:08 |
|Type '''y init equal to one''' and press '''Enter.''' | |Type '''y init equal to one''' and press '''Enter.''' | ||
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| − | | 07 | + | | 07:12 |
|Then type '''h equal to zero point zero one''' press '''Enter.''' | |Then type '''h equal to zero point zero one''' press '''Enter.''' | ||
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| − | | 07 | + | | 07:19 |
|Type '''capital N equal to ten.''' | |Type '''capital N equal to ten.''' | ||
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| − | | 07 | + | | 07:22 |
|Since the number of '''iterations should be ten to time t equal to zero point one with step length of zero point zero one. ''' | |Since the number of '''iterations should be ten to time t equal to zero point one with step length of zero point zero one. ''' | ||
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| − | | 07 | + | | 07:34 |
|Press '''Enter.''' | |Press '''Enter.''' | ||
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| − | | 07 | + | | 07:36 |
|Then call the '''function modi euler underscore o d e''' by typing.''' | |Then call the '''function modi euler underscore o d e''' by typing.''' | ||
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| − | | 07 | + | | 07:41 |
|'''open square bracket t comma y close square bracket equal to modi euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis''' | |'''open square bracket t comma y close square bracket equal to modi euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis''' | ||
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| − | | 08 | + | | 08:03 |
|Press '''Enter. ''' | |Press '''Enter. ''' | ||
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| − | | 08 | + | | 08:05 |
|The value of '''y at t equal to zero point one''' is shown. | |The value of '''y at t equal to zero point one''' is shown. | ||
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| − | | 08 | + | | 08:10 |
|Let us summarize this tutorial. | |Let us summarize this tutorial. | ||
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| − | | 08 | + | | 08:14 |
|In this tutorial we have learnt to develop Scilab code for '''Euler''' and '''modified Euler methods.''' | |In this tutorial we have learnt to develop Scilab code for '''Euler''' and '''modified Euler methods.''' | ||
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|- | |- | ||
| − | | 08 | + | | 08:21 |
|We have also learnt to solve '''ODEs''' using these methods in '''Scilab.''' | |We have also learnt to solve '''ODEs''' using these methods in '''Scilab.''' | ||
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| Watch the video available at the link shown below | | Watch the video available at the link shown below | ||
|- | |- | ||
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| It summarises the Spoken Tutorial project | | It summarises the Spoken Tutorial project | ||
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||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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||The spoken tutorial project Team | ||The spoken tutorial project Team | ||
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||Conducts workshops using spoken tutorials | ||Conducts workshops using spoken tutorials | ||
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||Gives certificates to those who pass an online test | ||Gives certificates to those who pass an online test | ||
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| − | |08 | + | |08:49 |
||For more details, please write to contact@spoken-tutorial.org | ||For more details, please write to contact@spoken-tutorial.org | ||
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|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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| 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. | ||
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|More information on this mission is available at the link shown below | |More information on this mission is available at the link shown below | ||
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|This is Ashwini Patil signing off. | |This is Ashwini Patil signing off. | ||
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|- | |- | ||
| − | |09 | + | |09:15 |
| Thank you for joining. | | Thank you for joining. | ||
Revision as of 10:30, 11 July 2014
| Time | Narration |
| 00:01 | Dear Friends, |
| 00:02 | Welcome to the Spoken Tutorial on “Solving ODEs using Euler Methods” |
| 00:09 | At the end of this tutorial, you will learn how to: |
| 00:12 | Solve ODEs using Euler and Modified Euler methods in Scilab |
| 00:18 | Develop Scilab code to solve ODEs |
| 00:22 | To record this tutorial, I am using |
| 00:25 | Ubuntu 12.04 as the operating system
|
| 00:28 | and Scilab 5.3.3 version |
| 00:32 | To practise this tutorial, a learner |
| 00:34 | should have basic knowledge of Scilab |
| 00:37 | and should know how to solve ODEs. |
| 00:40 | To learn Scilab, please refer to the relevant tutorials available on the Spoken Tutorial website. |
| 00:48 | In Euler method, we get an accurately approximate solution of the ODE. |
| 00:55 | It is used to solve initial value problems where initial values of the differential equation are given. |
| 01:03 | It can be used to solve continuous functions. |
| 01:08 | Let us solve an example using Euler method. |
| 01:12 | We are given an initial value problem - |
| 01:15 | y dash is equal to minus two t minus y.
|
| 01:20 | The initial value of y is given as minus one |
| 01:25 | and the step length is given as zero point one.
|
| 01:29 | We have to find the value of y at time t equal to zero point five. |
| 01:36 | Let us look at the code for Euler method.
|
| 01:39 | Open Euler underscore o d e dot sci on Scilab editor. |
| 01:47
|
We define the function Euler underscore o d e with arguments f, t init, y init, h and n
|
| 01:58 | 'where f denotes the function to be solved,
|
| 02:01 | t init is the initial value of time t, |
| 02:05 | y init is the initial value of y |
| 02:09 | h is the step length, and n is the number of iterations. |
| 02:14 | Then we initialize the values of t and y to vectors of zeros. |
| 02:21 | We place the initial values of t and y in t of one and y of one respectively. |
| 02:29 | Then we iterate from one to N to find the value of y. |
| 02:33 | Here we apply Euler method to find the value of y. |
| 02:39 | Finally we end the function. |
| 02:42 | Save and execute the file Euler underscore o d e dot sci
|
| 02:49 | Switch to Scilab console to solve the example problem.
|
| 02:54 | We define the function by typing
|
| 02:56 | d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to open paranthesis minus two asterisk t close paranthesis minus y close single quote close paranthesis
|
| 03:26 | Press Enter. |
| 03:28 | Then type t init is equal to zero.
|
| 03:31 | Press Enter.
|
| 03:33 | Type y init is equal to minus one.
'
|
| 03:38 | Press Enter
|
| 03:40 | Type step length h is equal to zero point one.
|
| 03:44 | Press Enter
|
| 03:46 | The step length is zero point one, and we have to find the value of y at zero point five.
|
| 03:53 | So, the number of iterations should be five.
|
| 03:59 | At each iteration, the value of t will be increased by zero point one.
|
| 04:05 | So type capital N is equal to five.
|
| 04:09 | And press Enter.
|
| 04:11 | To call the function, type |
| 04:14 | open square bracket t comma y close square bracket equal to Euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis |
| 04:33 | Press Enter.
|
| 04:35 | The value of y at t equal to zero point five is shown. |
| 04:41 | Now let us look at Modified Euler method. |
| 04:45 | It is a second order method and is a stable two step method.
|
| 04:51 | We find the average of the function at the beginning and end of time step.
|
| 04:56 | Let us solve this example using Modified Euler method.
|
| 05:02 | We are given a function y dash is equal to t plus y plus t y.
|
| 05:08 | The initial value of y is one |
| 05:12 | and the step length is zero point zero one. |
| 05:16 | We have to find the value of y at time t equal to zero point one using Modified Euler's method.
|
| 05:25 | Let us look at the code for Modified Euler method on Scilab Editor |
| 05:31 | We define the function with arguments f, t init, y init, h and n |
| 05:39 | where f is the function to be solved
|
| 05:42 | t init is the intial time value, |
| 05:45 | y init is the inital value of y |
| 05:49 | h is the step length and
|
| 05:51 | n is the number of iterations. |
| 05:54 | Then we initialize the arrays for y and t. |
| 05:58 | We place the initial values of t and y in t of one and y of one respectively. |
| 06:07 | We implement Modified Euler Method here.
|
| 06:11 | Here we find the average value of y at the beginning and end of time step. |
| 06:17 | Save and execute the file Modi Euler underscore o d e dot sci. |
| 06:23 | Switch to Scilab console. |
| 06:26 | Clear the screen by typing c l c. |
| 06:30 | Press Enter.
|
| 06:32 | Define the function by typing d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to t plus y plus t asterisk y close single quote close paranthesis |
| 07:01 | Press Enter.
|
| 07:03 | Then type t init equal to zero, press Enter
|
| 07:08 | Type y init equal to one and press Enter.
|
| 07:12 | Then type h equal to zero point zero one press Enter. |
| 07:19 | Type capital N equal to ten.
|
| 07:22 | Since the number of iterations should be ten to time t equal to zero point one with step length of zero point zero one. |
| 07:34 | Press Enter. |
| 07:36 | Then call the function modi euler underscore o d e by typing. |
| 07:41 | open square bracket t comma y close square bracket equal to modi euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis
|
| 08:03 | Press Enter.
|
| 08:05 | The value of y at t equal to zero point one is shown. |
| 08:10 | Let us summarize this tutorial. |
| 08:14 | In this tutorial we have learnt to develop Scilab code for Euler and modified Euler methods. |
| 08:21 | We have also learnt to solve ODEs using these methods in Scilab.
|
| 08:28 | Watch the video available at the link shown below |
| 08:32 | It summarises the Spoken Tutorial project
|
| 08:35 | If you do not have good bandwidth, you can download and watch it |
| 08:40 | The spoken tutorial project Team |
| 08:42 | Conducts workshops using spoken tutorials
|
| 08:45 | Gives certificates to those who pass an online test
|
| 08:49 | For more details, please write to contact@spoken-tutorial.org
|
| 08:55 | Spoken Tutorial Project is a part of the Talk to a Teacher project
|
| 09:00 | It is supported by the National Mission on Eduction through ICT, MHRD, Government of India. |
| 09:07 | More information on this mission is available at the link shown below |
| 09:13 | This is Ashwini Patil signing off. |
| 09:15 | Thank you for joining. |
