Difference between revisions of "LibreOffice-Suite-Math-6.3/C2/Introduction-to-LibreOffice-Math/English"

From Script | Spoken-Tutorial
Jump to: navigation, search
Line 1: Line 1:
 
Title: Introduction to Libreoffice Math
 
Title: Introduction to Libreoffice Math
  
Keywords: Libreoffice Math, system requirements, Prerequisites, Ubuntu Linux OS, Windows OS,  Formula Editor, Elements dock, markup language, video tutorial.
+
Keywords: Libreoffice Math, system requirements, Prerequisites, Ubuntu Linux OS, Windows OS,  Formula editor, Elements dock, markup language, video tutorial.
  
  
Line 16: Line 16:
 
|| In this tutorial, we will learn about:
 
|| In this tutorial, we will learn about:
 
* '''LibreOffice Math'''
 
* '''LibreOffice Math'''
* System requirements and Prerequisites for using '''Math.'''
+
* System requirements and prerequisites for using '''Math.'''
  
 
|-  
 
|-  
Line 23: Line 23:
 
'''Learning Objectives'''
 
'''Learning Objectives'''
 
|| We will also learn to:
 
|| We will also learn to:
* Use '''Formula Editor '''to write the formulae.
+
* Use '''Formula editor '''to write the formulae.
* Use the '''markup''' language to write a simple formula and
+
* Use the '''markup language''' to write a simple formula and
 
* '''Save '''the file.  
 
* '''Save '''the file.  
 
  
 
|-  
 
|-  
Line 45: Line 44:
 
* The formulae and equations created using '''Math''' can stand alone.
 
* The formulae and equations created using '''Math''' can stand alone.
 
* They can be embedded directly into '''Writer, Calc '''and''' Impress'''.
 
* They can be embedded directly into '''Writer, Calc '''and''' Impress'''.
 
  
 
|-  
 
|-  
Line 52: Line 50:
 
'''OS and Versions'''
 
'''OS and Versions'''
 
|| '''LibreOffice Math''' can run on any of the following '''operating systems''':
 
|| '''LibreOffice Math''' can run on any of the following '''operating systems''':
 
 
 
* '''Microsoft Windows 8''' or higher versions
 
* '''Microsoft Windows 8''' or higher versions
 
* '''GNU/Linux OS '''and
 
* '''GNU/Linux OS '''and
 
* '''Mac OSX'''  
 
* '''Mac OSX'''  
 
  
 
|-  
 
|-  
Line 67: Line 62:
 
* '''Ubuntu Linux OS''' version 18.04 and  
 
* '''Ubuntu Linux OS''' version 18.04 and  
 
* '''LibreOffice Suite''' version 6.3.5
 
* '''LibreOffice Suite''' version 6.3.5
 
  
 
|-  
 
|-  
Line 76: Line 70:
 
https://spoken-tutorial.org/
 
https://spoken-tutorial.org/
 
||
 
||
* By default the latest '''Ubuntu''' '''Linux OS''' has '''LibreOffice Suite''' pre-installed in it.
+
* By default the latest '''Ubuntu Linux OS''' has '''LibreOffice Suite''' pre-installed in it.
 
* To install a specific version, refer to the '''LibreOffice Installation''' series on this website.
 
* To install a specific version, refer to the '''LibreOffice Installation''' series on this website.
 
  
 
|-  
 
|-  
 
|| Narration only
 
|| Narration only
|| Let us learn how to open the '''LibreOffice''' '''Math'''.
+
|| Let us learn how to open the '''LibreOffice Math'''.
 
|-  
 
|-  
 
|| Click on '''Show Applications''' >> search bar type ‘'''Math’ ''' >> Click on '''LibreOffice''' '''Math '''icon.
 
|| Click on '''Show Applications''' >> search bar type ‘'''Math’ ''' >> Click on '''LibreOffice''' '''Math '''icon.
|| In '''Ubuntu''' '''Linux''' '''OS''', click the '''Show Applications''' icon at the bottom left corner.
+
|| In '''Ubuntu Linux OS''', click the '''Show Applications''' icon at the bottom left corner.
  
  
In the '''search''' '''bar '''that appears''' '''type '''Math'''.
+
In the '''search bar '''that appears type '''Math'''.
  
  
Line 104: Line 97:
 
|| Point to the open window
 
|| Point to the open window
 
|| '''Math '''document opens up with '''Untitled 1''' document.
 
|| '''Math '''document opens up with '''Untitled 1''' document.
 
 
  
 
|-  
 
|-  
|| Click on '''Show Applications'''>>search bar type ‘'''Writer’ ''' >> Click on '''LibreOffice''' '''Writer '''icon.
+
|| Click on '''Show Applications'''>>search bar type ‘'''Writer’ ''' >> Click on '''LibreOffice Writer '''icon.
 
|| Now, let us learn to call '''Math '''from the '''Writer document'''.
 
|| Now, let us learn to call '''Math '''from the '''Writer document'''.
  
Line 123: Line 114:
  
 
Point to the '''Math''' interface.
 
Point to the '''Math''' interface.
|| Click on the '''Insert menu''' on the '''menu''' '''bar'''.
+
|| Click on the '''Insert menu''' on the '''Menu bar'''.
  
  
Line 138: Line 129:
 
|| In the '''preview''' area, if we click outside the gray box, the '''Math''' window disappears.
 
|| In the '''preview''' area, if we click outside the gray box, the '''Math''' window disappears.
  
To make it visible again, double click on the gray box in the '''Writer''' window.
+
To make it visible again, double-click on the gray box in the '''Writer''' window.
 
|-  
 
|-  
 
|| Click on close (x)
 
|| Click on close (x)
Line 148: Line 139:
 
|-  
 
|-  
 
|| Cursor in the''' Math''' interface.
 
|| Cursor in the''' Math''' interface.
|| Let us now first familiarize ourselves with the '''LibreOffice''' '''Math '''window.
+
|| Let us now first familiarize ourselves with the '''LibreOffice Math '''window.
 
|-  
 
|-  
 
|| Point to the three areas in the '''window'''.
 
|| Point to the three areas in the '''window'''.
Line 160: Line 151:
 
|-  
 
|-  
 
|| Go to the bottom of the window >> point to the second area.
 
|| Go to the bottom of the window >> point to the second area.
|| The second is the '''Formula Editor''' area at the bottom.
+
|| The second is the '''Formula editor''' area at the bottom.
  
 
Here we type the mathematical formulae in a special '''markup language'''.
 
Here we type the mathematical formulae in a special '''markup language'''.
Line 167: Line 158:
  
 
Click on the '''View menu''' >> '''Elements.'''
 
Click on the '''View menu''' >> '''Elements.'''
|| Third is the '''Elements''' dock on the left.
+
|| Third is the '''Elements dock''' on the left.
  
 
This '''dock''' provides us with a range of mathematical symbols and expressions.
 
This '''dock''' provides us with a range of mathematical symbols and expressions.
  
  
If you don’t see the '''Elements''' dock, click on '''View '''and then choose '''Elements'''.
+
If you don’t see the '''Elements dock''', click on '''View '''and then choose '''Elements'''.
 
|-  
 
|-  
 
|| Go to the top of the '''Elements''' window >> Point to drop-down named '''Category Selector.'''
 
|| Go to the top of the '''Elements''' window >> Point to drop-down named '''Category Selector.'''
Line 187: Line 178:
  
  
As per the selected category, '''Elements''' '''dock''' displays the symbols and operators.
+
As per the selected category, '''Elements dock''' displays the symbols and operators.
 
|-  
 
|-  
 
|| Point to drop-down >> '''Unary or Binary Operators'''.
 
|| Point to drop-down >> '''Unary or Binary Operators'''.
Line 197: Line 188:
 
|| By default '''Unary or Binary Operators''' option is selected in the '''Element categories'''.
 
|| By default '''Unary or Binary Operators''' option is selected in the '''Element categories'''.
  
Below the drop-down, we see basic''' '''mathematical operators.
+
Below the drop-down, we see basic mathematical operators.
  
  
These include '''Addition, Subtraction, Multiplication, Division''' and others.
+
These include addition, subtraction, multiplication, division''' and others.
 
|-  
 
|-  
 
|| Cursor in the interface.
 
|| Cursor in the interface.
|| Let’s now write a simple multiplication formula.
+
|| Let us now write a simple multiplication formula.
 
+
  
 
|-  
 
|-  
 
|| Click on the symbol ‘❒ '''x '''❒’  
 
|| Click on the symbol ‘❒ '''x '''❒’  
  
Go to the '''Formula''' '''editor '''window-> Point to two '''‘<?>’ '''and then '''‘times’ '''.
+
Go to the '''Formula editor '''window-> Point to two '''‘<?>’ '''and then '''‘times’ '''.
  
  
Line 216: Line 206:
  
  
The '''Formula editor '''window''',''' shows''' '''two''' placeholders''' separated by the word '''times'''.
+
The '''Formula editor '''window shows two''' placeholders''' separated by the word '''times'''.
  
  
The''' preview''' area, diaplays two squares separated by the multiplication''' '''sign.
+
The''' preview''' area, displays two squares separated by the multiplication sign.
 
|-  
 
|-  
 
|| Go to '''Formula editor '''window >> double click on first '''‘<?>'''’ >> type 4.
 
|| Go to '''Formula editor '''window >> double click on first '''‘<?>'''’ >> type 4.
Line 238: Line 228:
 
|-  
 
|-  
 
|| Point to the formula.
 
|| Point to the formula.
|| Next let us complete the formula by adding = 12 to it.
+
|| Next let us complete the formula by adding '''= 12''' to it.
 
|-  
 
|-  
 
|| Go to the '''Element '''window >> click on the drop-down -> select '''Relations.'''
 
|| Go to the '''Element '''window >> click on the drop-down -> select '''Relations.'''
Line 254: Line 244:
 
|| Click the first symbol '''squarebox equal squarebox''' denoting '''Is Equal'''.
 
|| Click the first symbol '''squarebox equal squarebox''' denoting '''Is Equal'''.
 
|-  
 
|-  
|| Go to the '''Formula''' '''editor window ''' >> delete first '''‘<?>’ ''' >> double click on second''' ‘<?>’ ''' >> type 12.
+
|| Go to the '''Formula editor window ''' >> delete first '''‘<?>’ ''' >> double click on second''' ‘<?>’ ''' >> type 12.
  
  
Line 261: Line 251:
  
  
|| In the '''Formula editor '''window''', '''delete the first '''placeholder.'''
+
|| In the '''Formula editor '''window, delete the first '''placeholder.'''
  
In the second placeholder, type 12.
+
In the second '''placeholder''', type 12.
  
  
Line 273: Line 263:
 
|| Now, let’s learn how to write a formula in different ways.
 
|| Now, let’s learn how to write a formula in different ways.
 
|-  
 
|-  
|| Point to the symbols in the Elements dock.
+
|| Point to the symbols in the '''Elements dock'''.
 
|| We already know how to use the symbols in the '''Elements dock'''.  
 
|| We already know how to use the symbols in the '''Elements dock'''.  
 
|-  
 
|-  
 
|| Cursor in the Formula editor.
 
|| Cursor in the Formula editor.
|| The second method is to use the context menu in the '''Formula Editor '''window.  
+
|| The second method is to use the context menu in the '''Formula editor '''window.  
 
|-  
 
|-  
|| Right click on the '''Formula editor '''window''' ''' >> Point to the '''categories''' in the '''context menu'''  
+
|| Right click on the '''Formula editor '''window >> Point to the '''categories''' in the '''context menu'''  
  
  
Line 286: Line 276:
  
 
Show the categories.
 
Show the categories.
|| Right click in the '''Formula editor''' to see the context menu.
+
|| Right-click in the '''Formula editor''' to see the context menu.
  
  
The '''context menu '''displays the same categories of symbols as in the''' Elements '''dock.
+
The context menu displays the same categories of symbols as in the''' Elements '''dock.
  
  
You can choose any '''category '''to see the available '''symbols''' under the category.
+
You can choose any '''category '''to see the available symbols under the category.
 
|-  
 
|-  
 
|| Only narration
 
|| Only narration
|| Third method is to directly write the formulae in the''' Formula Editor window.'''
+
|| Third method is to directly write the formulae in the''' Formula editor''' window.
  
 
We will use''' markup language '''that '''Math''' understands.
 
We will use''' markup language '''that '''Math''' understands.
 
|-  
 
|-  
|| Only narration
+
|| Point towards the word '''‘times’'''
 
+
 
+
Point towards the word '''‘times’'''
+
 
+
 
+
 
|| We already saw one simple example of '''markup language'''.
 
|| We already saw one simple example of '''markup language'''.
 
 
  
 
|-  
 
|-  
|| Point to the formula editor.
+
|| Point to the '''Formula editor'''.
  
Select the formula and press the '''Delete key''' on the''' Keyboard'''
+
Select the formula and press the '''Delete key''' on the Keyboard.
  
  
 
Point to the '''preview''' area.
 
Point to the '''preview''' area.
|| Let us delete the formula from the '''formula editor'''.
+
|| Let us delete the formula from the '''Formula editor'''.
  
  
Select the formula and press the '''Delete key '''on the '''Keyboard'''.
+
Select the formula and press the '''Delete key '''on the keyboard.
  
  
Line 325: Line 308:
 
|-  
 
|-  
 
|| Type ‘4 over 4 equals 1’
 
|| Type ‘4 over 4 equals 1’
|| Now let’s write the markup language for 4 divided by 4 equals 1,  
+
|| Now let’s write the '''markup language''' for 4 divided by 4 equals 1,  
  
 
In the''' Formula editor''' type ‘4 over 4 equals 1’.  
 
In the''' Formula editor''' type ‘4 over 4 equals 1’.  
 
|-  
 
|-  
 
|| Point to ‘4 over 4 equals 1’.
 
|| Point to ‘4 over 4 equals 1’.
|| We will learn more about the markup language in the upcoming tutorials.
+
|| We will learn more about the '''markup language''' in the upcoming tutorials.
 
|-  
 
|-  
 
|| Click on '''File''' and Select '''Save'''.
 
|| Click on '''File''' and Select '''Save'''.
Line 365: Line 348:
 
|| In this tutorial, we have learnt about:
 
|| In this tutorial, we have learnt about:
 
* '''LibreOffice Math'''
 
* '''LibreOffice Math'''
* System requirements and Prerequisites for using '''Math'''
+
* System requirements and prerequisites for using '''Math'''
  
  
 
We have also learnt to:
 
We have also learnt to:
 
* Use '''Formula editor''' to write the formulae
 
* Use '''Formula editor''' to write the formulae
* Use the '''markup''' language to write a simple formula and
+
* Use the '''markup language''' to write a simple formula and
 
* '''Save''' the file  
 
* '''Save''' the file  
  
Line 377: Line 360:
  
 
'''Assignment'''
 
'''Assignment'''
|| Here is an assignment for you:* Write the following formulae in the '''Formula Editor'''
+
|| Here is an assignment for you:
 +
* Write the following formulae in the '''Formula editor'''
 
* Check the display of the formulae in the '''Preview''' window.
 
* Check the display of the formulae in the '''Preview''' window.
** a '''Boolean''' '''AND''' b
+
** a '''Boolean AND''' b
 
** 4 is greater than 3
 
** 4 is greater than 3
 
** x is approximately equal to y  
 
** x is approximately equal to y  
Line 391: Line 375:
 
* The video at the following link summarises the Spoken Tutorial project
 
* The video at the following link summarises the Spoken Tutorial project
 
* Please download and watch it
 
* Please download and watch it
 
  
 
|-  
 
|-  
Line 401: Line 384:
 
* We conduct workshops using '''spoken''' '''tutorials''' and give certificates.
 
* We conduct workshops using '''spoken''' '''tutorials''' and give certificates.
 
* For more details, please contact us
 
* For more details, please contact us
 
  
 
|-  
 
|-  
Line 414: Line 396:
 
* The Spoken Tutorial project will ensure an answer
 
* The Spoken Tutorial project will ensure an answer
 
* You will have to register on this website to ask questions
 
* You will have to register on this website to ask questions
 
  
 
|-
 
|-
Line 425: Line 406:
 
* This will help reduce the clutter.
 
* This will help reduce the clutter.
 
* With less clutter, we can use these discussions as instructional material.
 
* With less clutter, we can use these discussions as instructional material.
 
  
 
|-
 
|-
Line 431: Line 411:
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
|| '''Spoken''' '''Tutorial''' project is funded by the Ministry of Education, Govt. of India.
+
|| '''Spoken Tutorial''' project is funded by the Ministry of Education, Govt. of India.
 
|-  
 
|-  
 
|| '''Slide: Thank you'''
 
|| '''Slide: Thank you'''

Revision as of 15:45, 29 June 2022

Title: Introduction to Libreoffice Math

Keywords: Libreoffice Math, system requirements, Prerequisites, Ubuntu Linux OS, Windows OS, Formula editor, Elements dock, markup language, video tutorial.


Visual Cue Narration
Title Slide Welcome to thisis Spoken tutorial on Introduction to LibreOffice Math.
Slide:

Learning Objectives

In this tutorial, we will learn about:
  • LibreOffice Math
  • System requirements and prerequisites for using Math.
Slide:

Learning Objectives

We will also learn to:
  • Use Formula editor to write the formulae.
  • Use the markup language to write a simple formula and
  • Save the file.
Slide:

What is LibreOffice Math?

What is LibreOffice Math?
  • It is a software application designed to create and edit mathematical formulae
  • It is bundled inside LibreOffice Suite, hence it is free and open source software.
Slide:

What is LibreOffice Math?

  • The formulae and equations created using Math can stand alone.
  • They can be embedded directly into Writer, Calc and Impress.
Slide:

OS and Versions

LibreOffice Math can run on any of the following operating systems:
  • Microsoft Windows 8 or higher versions
  • GNU/Linux OS and
  • Mac OSX
Slide:

System Requirements

This tutorial is recorded using,
  • Ubuntu Linux OS version 18.04 and
  • LibreOffice Suite version 6.3.5
Slide:

LibreOffice Installation

https://spoken-tutorial.org/

  • By default the latest Ubuntu Linux OS has LibreOffice Suite pre-installed in it.
  • To install a specific version, refer to the LibreOffice Installation series on this website.
Narration only Let us learn how to open the LibreOffice Math.
Click on Show Applications >> search bar type ‘Math’ >> Click on LibreOffice Math icon. In Ubuntu Linux OS, click the Show Applications icon at the bottom left corner.


In the search bar that appears type Math.


From the displayed list, click on the Libreoffice Math icon.

Click on Start menu >> search bar type Math >> Click on LibreOffice Math icon In Windows OS, click on the Start Menu icon located at the bottom left corner.


In the search bar next to it type Math.


From the displayed list, click on the LibreOffice Math icon.

Point to the open window Math document opens up with Untitled 1 document.
Click on Show Applications>>search bar type ‘Writer’ >> Click on LibreOffice Writer icon. Now, let us learn to call Math from the Writer document.


I have opened the LibreOffice Writer document.

Click on the Insert menu.


Navigate to Object.

Select Formula from the submenu.


Point to the Math interface.

Click on the Insert menu on the Menu bar.


Navigate to Object.

From the submenu select the Formula option.

Math interface opens.

Click outside the gray box.


Double click on the gray box visible in the Writer window.

In the preview area, if we click outside the gray box, the Math window disappears.

To make it visible again, double-click on the gray box in the Writer window.

Click on close (x)

In the Save Document? dialog box click on the Don't Save button.

Let us close the Writer document without saving.

In the Save Document? dialog box click on the Don't Save button.

Cursor in the Math interface. Let us now first familiarize ourselves with the LibreOffice Math window.
Point to the three areas in the window. In the Math window we can see three areas.
Point to the first area on the top of the window. The first is the preview area on the top.


The preview area, displays the equations and formulae in the mathematical form.

Go to the bottom of the window >> point to the second area. The second is the Formula editor area at the bottom.

Here we type the mathematical formulae in a special markup language.

Go to the right of the window >> point to the third area.

Click on the View menu >> Elements.

Third is the Elements dock on the left.

This dock provides us with a range of mathematical symbols and expressions.


If you don’t see the Elements dock, click on View and then choose Elements.

Go to the top of the Elements window >> Point to drop-down named Category Selector.


Click on the drop-down >> Point to the other category option.


Point to the selected category in drop-down >> point to symbols below the drop-down.

On the top of the Elements window, there is a drop-down named Element categories.


This drop down shows a list of mathematical symbols and operators.


As per the selected category, Elements dock displays the symbols and operators.

Point to drop-down >> Unary or Binary Operators.


Point to the drop down.

Point to the respective symbols.

By default Unary or Binary Operators option is selected in the Element categories.

Below the drop-down, we see basic mathematical operators.


These include addition, subtraction, multiplication, division and others.

Cursor in the interface. Let us now write a simple multiplication formula.
Click on the symbol ‘❒ x ❒’

Go to the Formula editor window-> Point to two ‘<?>’ and then ‘times’ .


Go to the Writer gray box area -> Point to two squares and then ‘X’.

Let us click on the symbol squarebox into squarebox denoting multiplication.


The Formula editor window shows two placeholders separated by the word times.


The preview area, displays two squares separated by the multiplication sign.

Go to Formula editor window >> double click on first ‘<?>’ >> type 4.


Double click on second ‘<?>’ >> type 3.

Point to the preview area.

4X3

In the Formula editor, first placeholder is selected.

Type 4 in this placeholder.

Then double click on the second placeholder and type 3.

The preview area shows 4 times 3.

Point to the formula. Next let us complete the formula by adding = 12 to it.
Go to the Element window >> click on the drop-down -> select Relations.

Point to symbols below drop-down.

In the Elements dock, click the Element categories, drop-down and select Relations.


Below the drop-down, notice the various relation elements.

Click on the symbol ‘❒ = ❒’


Click the first symbol squarebox equal squarebox denoting Is Equal.
Go to the Formula editor window >> delete first ‘<?>’ >> double click on second ‘<?>’ >> type 12.


Point to the formula.


In the Formula editor window, delete the first placeholder.

In the second placeholder, type 12.


In the preview area we can see the formula.

‘4 times 3 equals 12’.

Cursor in the interface. Now, let’s learn how to write a formula in different ways.
Point to the symbols in the Elements dock. We already know how to use the symbols in the Elements dock.
Cursor in the Formula editor. The second method is to use the context menu in the Formula editor window.
Right click on the Formula editor window >> Point to the categories in the context menu


Go to one the category >> Point to available symbols


Show the categories.

Right-click in the Formula editor to see the context menu.


The context menu displays the same categories of symbols as in the Elements dock.


You can choose any category to see the available symbols under the category.

Only narration Third method is to directly write the formulae in the Formula editor window.

We will use markup language that Math understands.

Point towards the word ‘times’ We already saw one simple example of markup language.
Point to the Formula editor.

Select the formula and press the Delete key on the Keyboard.


Point to the preview area.

Let us delete the formula from the Formula editor.


Select the formula and press the Delete key on the keyboard.


Notice that the formula is deleted from the preview area also.

Type ‘4 over 4 equals 1’ Now let’s write the markup language for 4 divided by 4 equals 1,

In the Formula editor type ‘4 over 4 equals 1’.

Point to ‘4 over 4 equals 1’. We will learn more about the markup language in the upcoming tutorials.
Click on File and Select Save.


Point to the dialog box.

Type file name as firstmath

Let us now save the file.

Click on File and select Save.


Save dialog box appears.


I will save the file in my Documents folder.


Type the filename as firstmath and click on Save button.


File is saved with the .odf extension.

Narration only: With this we have come to the end of this spoken tutorial.


Let us summarize.

Slide:

Summary

In this tutorial, we have learnt about:
  • LibreOffice Math
  • System requirements and prerequisites for using Math


We have also learnt to:

  • Use Formula editor to write the formulae
  • Use the markup language to write a simple formula and
  • Save the file
Slide:

Assignment

Here is an assignment for you:
  • Write the following formulae in the Formula editor
  • Check the display of the formulae in the Preview window.
    • a Boolean AND b
    • 4 is greater than 3
    • x is approximately equal to y
    • 4 is not equal to 3
Slide:

About Spoken Tutorial Project

  • The video at the following link summarises the Spoken Tutorial project
  • Please download and watch it
Slide:

Spoken tutorial workshops

  • We conduct workshops using spoken tutorials and give certificates.
  • For more details, please contact us
Slide:

Answers for THIS Spoken Tutorial

  • Do you have questions in THIS Spoken Tutorial?
  • Please visit this site
  • Choose the minute and second where you have the question
  • Explain your question briefly
  • The Spoken Tutorial project will ensure an answer
  • You will have to register on this website to ask questions
Slide:

Forum for specific Questions

  • The Spoken Tutorial forum is for specific questions on this tutorial.
  • Please do not post unrelated and general questions on them.
  • This will help reduce the clutter.
  • With less clutter, we can use these discussions as instructional material.
Slide:

Acknowledgement

Spoken Tutorial project is funded by the Ministry of Education, Govt. of India.
Slide: Thank you

Acknowledgement to DesiCrew

This tutorial was originally contributed by DesiCrew Solutions Pvt. Ltd. in 2011

This is Madhuri Ganapathi along with the Spoken Tutorial team from IIT Bombay signing off.

Thank you for watching.

Contributors and Content Editors

Madhurig, Nancyvarkey