Difference between revisions of "LibreOffice-Suite-Math/C3/Set-Operations-Factorials-Cross-reference-equations/English-timed"

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!Narration
 
!Narration
 
|-
 
|-
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|Show Slide Number 1
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|00.00
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+
−
Spoken tutorial on LibreOffice Math
+
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+
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Learning Objectives
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+
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*Write Set operations
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+
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*Write Factorials
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+
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*Cross reference equations by numbering
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|Welcome to the Spoken tutorial on LibreOffice Math.
 
|Welcome to the Spoken tutorial on LibreOffice Math.
  
−
In this tutorial, we will learn how to
+
|-
 +
|00.04
 +
|In this tutorial, we will learn how to
  
−
Write Set operations
+
|-
 +
|00.08
 +
|Write Set operations
  
−
Write Factorials and
 
−
 
−
Cross reference equations by numbering
 
 
|-
 
|-
−
|Open the MathExample1.odt (created in part 2)
+
|00.10
 +
|Write Factorials and Cross reference equations by numbering
 +
|-
 +
|00.16
 
|For this, let us first open our example Writer document that we created in our previous tutorials: MathExample1.odt.
 
|For this, let us first open our example Writer document that we created in our previous tutorials: MathExample1.odt.
 
|-
 
|-
−
|Scroll to last page, go to the end.
+
|00.29
−
 
+
−
Press Control  - Enter to go to a new page
+
−
 
+
−
Type “Set Operations: ” in Writer on this fresh page. Press enter twice.
+
−
 
+
−
Click Insert > Object > Formula
+
 
|Here let us go to the end of the document and press Control Enter to go to a new page.
 
|Here let us go to the end of the document and press Control Enter to go to a new page.
  
−
And type “Set Operations: ” and press the Enter key twice.
+
|-
 +
|00.37
 +
|And type “Set Operations: ” and press ''Enter'' twice.
  
−
Now let us call Math.
 
 
|-
 
|-
−
|Click Format menu > Font size. Increase size to 18 pt.
+
|00.42
−
 
+
|Now let us call Math.
−
Click Format menu > Alignment, choose left option
+
|-
−
 
+
|00.46
−
All pink coloured text goes into Formula Editor Window (FEW in short)
+
−
 
+
−
In FEW, copy and paste:
+
−
 
+
−
A ~=~ lbrace 1, 2, 3, 4, 5 rbrace newline
+
−
 
+
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B ~=~ lbrace 1, 2 rbrace newline
+
−
 
+
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C ~=~ lbrace 4, 5 rbrace newline
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−
 
+
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D ~=~ lbrace 6, 7 rbrace newline newline
+
 
|Before we go ahead, let us increase the font size to 18 point.
 
|Before we go ahead, let us increase the font size to 18 point.
  
−
Change the alignment to the left.
+
|-
 +
|00.51
 +
|Change the alignment to the left.
  
−
Let us now learn how to write Set operations.
+
|-
 +
|00.56
 +
|Let us now learn how to write Set operations.
  
−
Math has separate mark up to represent Sets, which are collections of distinct elements.
+
|-
 +
|01.00
 +
|Math has separate mark up to represent Sets, which are collections of distinct elements.
  
−
Let us write 4 example sets in the Formula Editor window as shown on the screen:
+
|-
 +
|01.07
 +
|Let us write 4 example sets in the Formula Editor window as shown on the screen:
  
−
Set A with 5 elements
+
|-
 +
|01.15
 +
|Set A with 5 elements
  
−
Set B  
+
|-
 +
|01.18
 +
|Set B  
  
−
Set C  
+
|-
 +
|01.20
 +
|Set C  
  
−
And Set D equal to 6, and 7, with 2 elements each.
 
 
|-
 
|-
−
|Point mouse over the four sets in Writer gray box
+
|01.22
−
 
+
|And Set D equal to 6, and 7, with 2 elements each.
−
In FEW, point mouse over above mark up.
+
|-
−
 
+
|01.29
−
In FEW, press enter twice, copy and paste:
+
−
 
+
−
B union C ~=~ lbrace 1, 2, 6, 4, 5 rbrace  newline newline
+
−
 
+
−
In FEW, point mouse over ‘Union’ word
+
−
 
+
−
Point mouse over the last formula in Writer gray box
+
−
 
+
−
In FEW, press enter twice, copy and paste:
+
−
 
+
−
B intersection D ~=~ lbrace 6 rbrace  newline newline
+
−
 
+
−
Point mouse over the last formula in Writer gray box
+
−
 
+
−
In FEW, press enter twice, copy and paste:
+
−
 
+
−
C subset A newline newline
+
−
 
+
−
Point mouse over the subset symbol in the last formula in Writer gray box
+
−
 
+
−
In FEW, point mouse over the last line.
+
−
 
+
−
If elements window not visible, click View >Elements.
+
−
 
+
−
In the Elements window, click the third icon in the Elements window and slowly mouse over on the elements, to show tool tips.
+
−
 
+
−
Click  File > Save.
+
 
|Notice that to write the brackets for sets, we can use the mark up: lbrace and rbrace.
 
|Notice that to write the brackets for sets, we can use the mark up: lbrace and rbrace.
  
−
Now we can write set operations such as unions and intersections.
+
|-
 +
|01.39
 +
|Now we can write set operations such as unions and intersections.
  
−
First let us write a union operation.  
+
|-
 +
|01.45
 +
|First let us write a union operation.  
  
−
The mark up for B union C is the same as we read it;  
+
|-
 +
|01.49
 +
|The mark up for B union C is the same as we read it;  
  
−
and the resulting set is 1, 2, 6, 4, and 5, which includes all the distinct elements in both the sets.
+
|-
 +
|01.55
 +
|and the resulting set is 1, 2, 6, 4, and 5, which includes all the distinct elements in both sets.
  
−
The markup for an intersection operation is again the same as we read it.
+
|-
 +
|02.07
 +
|The markup for an intersection operation is again the same as we read it.
  
−
The intersection includes only the common elements from both the sets.
+
|-
 +
|02.13
 +
|The intersection includes only the common elements from both the sets.
  
−
So the result of B intersection D is 6.
+
|-
 +
|02.20
 +
|So the result of B intersection D is 6.
  
−
And we can also write: set C is a subset of set A, as every element in C is in set A.
+
|-
 +
|02.26
 +
|And we can also write: set C is a subset of set A, as every element in C is in set A.
  
−
The mark up for this is C subset A.
+
|-
 +
|02.39
 +
|The mark up for this is C subset A.
  
−
You can learn to write more set operations, by exploring the Elements window by clicking on the third icon there.  
+
|-
 +
|02.46
 +
|You can learn to write more set operations, by exploring the Elements window by clicking on the third icon there.  
  
−
Go to View> Elements> Set Operations.
+
|-
−
 
+
|02.55
−
Let us save our work now.  
+
|Go to View> Elements> Set Operations.
  
−
Click on File>Save.
 
 
|-
 
|-
−
|Click three times slowly outside right of Writer gray box. Now then click again.
+
|03.03
 +
|Let us save our work now.  
  
−
Press Control  -Enter
+
|-
−
 
+
|03.05
−
Type: “Factorial Function: ” and press enter twice
+
|Click on File>Save.
−
 
+
|-
−
Type fn and press F3
+
|03.10
−
 
+
−
Point mouse over E = mc squared in Writer gray box
+
−
 
+
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Point mouse over (1) on the right in Writer gray box
+
−
 
+
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Double click on E = mc squared in Writer gray box
+
−
 
+
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Click Format menu > Font size. Increase size to 18 pt.
+
−
 
+
−
Click Format menu > Alignment, chooses left option
+
 
|Now let us write Factorial functions.  
 
|Now let us write Factorial functions.  
  
−
We will designate numbers 1 to 3 for the three formulae we are going to write shortly.
+
|-
 +
|03.14
 +
|We will designate numbers 1 to 3 for the three formulae we are going to write shortly.
  
−
These will help to cross reference them anywhere within the Writer document.
+
|-
 +
|03.23
 +
|These will help to cross reference them anywhere within the Writer document.
  
−
Let us go to a new page by clicking three times slowly outside the Writer gray box.
+
|-
 +
|03.29
 +
|Let us go to a new page by clicking three times slowly outside the Writer gray box.
  
−
Press Control  -Enter.
+
|-
 +
|03.37
 +
|Press Control  -Enter.
  
−
Type “Factorial Function: ” and press enter twice.
+
|-
 +
|03.40
 +
|Type “Factorial Function: ” and press enter twice.
  
−
Now, we know how to call Math.
+
|-
 +
|03.45
 +
|Now, we know how to call Math.
  
−
But there is another way to bring up the Math object into the Writer.
+
|-
 +
|03.48
 +
|But there is another way to bring up the Math object into the Writer.
  
−
For this simply write ‘f n’ on the Writer document and press F3.
+
|-
 +
|03.54
 +
|For this simply write ‘f n’ on the Writer document and press F3.
  
−
We are now seeing a new Math object that says E is equal to m c squared;
+
|-
 +
|04.03
 +
|We are now seeing a new Math object that says E is equal to m c squared;
  
−
and along with that, the number one within parentheses, on the right.
+
|-
 +
|04.11
 +
|and along with that, the number one within parentheses, on the right.
  
−
Meaning, we can cross reference this formula with the number 1 anywhere in this document; we will learn the details of how to do this later.
+
|-
 +
|04.18
 +
|Meaning, we can cross reference this formula with the number 1 anywhere in this document; we will learn the details of how to do this later.
  
−
For now, let us double click on the Math object  
+
|-
 +
|04.30
 +
|For now, let us double click on the Math object  
  
−
And do the formatting. Font size 18 and Left Alignment.
 
 
|-
 
|-
−
|In FEW, overwrite existing formula. So press Control + A to select all, then copy and paste:
+
|04.36
−
 
+
|And do the formatting. Font size 18 and Left Alignment.
−
fact 5 = 5 times 4 times 3 times 2 times 1  = 120
+
|-
−
 
+
|04.43
−
In FEW, point mouse over ‘fact’ word in the last line
+
−
 
+
−
Click outside this Writer gray box three times slowly
+
−
 
+
−
Press the down arrow key two or three times to go to the end of this page.
+
−
 
+
−
Type ‘fn’ and press F3
+
−
 
+
−
Double click on E = mc squared in Writer gray box
+
−
 
+
−
Click Format menu > Font size. Increase size to 18 pt.
+
−
 
+
−
Click Format menu > Alignment, chooses left option
+
−
 
+
−
In FEW, overwrite existing formula. So press Control  - A to select all, then copy and paste:
+
−
 
+
−
fact n ~=~ prod from k = 1 to n k newline
+
−
 
+
−
In FEW, point mouse over ‘prod’ word in the last line
+
−
 
+
−
Click outside this second Writer gray box three times slowly
+
−
 
+
−
Press the down arrow key two or three times to go to the end of this page.
+
−
 
+
−
Type ‘fn’ and press F3
+
−
 
+
−
Double click on E = mc squared in Writer gray box
+
−
 
+
−
Click Format menu > Font size. Increase size to 18 pt.
+
−
 
+
−
Click Format menu > Alignment, chooses left option
+
−
 
+
−
In FEW, overwrite existing formula.
+
−
 
+
−
So press Control + A to select all, then copy and paste:
+
−
 
+
−
fact n ~=~ left lbrace binom{1 ~ "if n = 0"}{fact(n-1) `times` n ~ " if n > 0 "} right none newline newline
+
−
 
+
−
Point mouse over this formula in  Writer gray box
+
−
 
+
−
In FEW, point mouse over ‘binom’ word in the last line
+
 
|Okay, let us now write an example for Factorial.  
 
|Okay, let us now write an example for Factorial.  
  
−
The mark up ‘fact’ represents the factorial symbol.
+
|-
 +
|04.48
 +
|The mark up ‘fact’ represents the factorial symbol.
  
−
So let us overwrite the existing formula with ours:  
+
|-
 +
|04.53
 +
|So let us overwrite the existing formula with ours:  
  
−
5 Factorial = 5 into 4 into 3 into 2 into 1 = 120.
+
|-
 +
|04.58
 +
|5 Factorial = 5 into 4 into 3 into 2 into 1 = 120.
  
−
Notice the mark up here.
+
|-
 +
|05.10
 +
|Notice the mark up here.
  
−
Let us write our next formula in a new Math object here.
+
|-
 +
|05.12
 +
|Let us write our next formula in a new Math object here.
  
−
For this, let us first click outside this Writer gray box three times slowly.
+
|-
 +
|05.17
 +
|For this, let us first click outside this Writer gray box three times slowly.
  
−
Press the down arrow key two or three times to go to the end of this page.
+
|-
 +
|05.26
 +
|Press the down arrow key two or three times to go to the end of this page.
  
−
And type ‘f n’ and press F3 to bring up the second Math object.
+
|-
 +
|05.33
 +
|And type ‘f n’ and press F3 to bring up the second Math object.
  
−
Again, we will repeat the formatting  
+
|-
 +
|05.40
 +
|Again, we will repeat the formatting  
  
−
and overwrite the existing formula with the factorial definition:
+
|-
 +
|05.50
 +
|and overwrite the existing formula with the factorial definition:
  
−
N factorial is equal to prod from k = 1 to n of k.
+
|-
 +
|05.55
 +
|N factorial is equal to prod from k = 1 to n of k.
  
−
Notice the mark up ‘prod’ which denotes product, similar to sigma for summation.
+
|-
 +
|06.05
 +
|Notice the mark up ‘prod’ which denotes product, similar to sigma for summation.
  
−
Now, let us introduce a third Math object just like the first two
+
|-
−
 
+
|06.13
−
and rewrite the factorial definition as two conditional formulae as shown on the screen.
+
|Now, let us introduce a third Math object just like the first two
  
−
Notice the mark up ‘binom’, which displays a vertical stack of two elements and helps with better alignment.
 
 
|-
 
|-
−
|Click three times outside Writer gray box, press Control + Enter
+
|06.24
 +
|and rewrite the factorial definition as two conditional formulae as shown on the screen.
  
−
Type: An example of factorial is provided here:
+
|-
−
 
+
|06.33
−
Click Insert menu > Cross reference
+
|Notice the mark up ‘binom’, which displays a vertical stack of two elements and helps with better alignment.
−
 
+
|-
−
In the popup, click on Text in the Type list
+
|06.45
−
 
+
−
Click on first item in the Selection list on the right
+
−
 
+
−
Click Reference in the ‘Insert reference to’ list , click on Insert once and click on close
+
−
 
+
−
Point mouse over (1).
+
−
 
+
−
Click on (1).  
+
−
 
+
−
Point mouse over the formula numbered 1.
+
−
 
+
−
Click File > Save
+
 
|Let us now see how we can cross reference these formulae.
 
|Let us now see how we can cross reference these formulae.
  
−
For this, let us go to a new page
+
|-
 +
|06.50
 +
|For this, let us go to a new page
  
−
and type: An example of factorial is provided here:
+
|-
 +
|06.54
 +
|and type: An example of factorial is provided here:
  
−
Now let us click on the Insert menu, and on Cross reference.  
+
|-
 +
|07.02
 +
|Now let us click on the Insert menu, and on Cross reference.  
  
−
In the new popup, let us select “Text” in the Type list.
+
|-
 +
|07.09
 +
|In the new popup, let us select “Text” in the Type list.
  
−
Then choose the first item in the Selection list denoting the first factorial formula we wrote.
+
|-
 +
|07.15
 +
|Then choose the first item in the Selection list denoting the first factorial formula we wrote.
  
−
Now choose Reference in the ‘Insert reference to’ list and click on Insert once and close.
+
|-
 +
|07.24
 +
|Now choose Reference in the ‘Insert reference tool’ list and click on Insert once and close.
  
−
So the number one in parentheses has appeared next to our text. And we are done.
+
|-
 +
|07.35
 +
|So the number one in parentheses has appeared next to our text. And we are done.
  
−
Let us test it by simply clicking on this number;
+
|-
 +
|07.42
 +
|Let us test it by simply clicking on this number;
  
−
And notice that the cursor has jumped to the location where we wrote the first formula.
+
|-
 +
|07.47
 +
|And notice that the cursor has jumped to the location where we wrote the first formula.
  
−
So this is how we can cross reference Math formulae anywhere within the Writer document.
 
−
 
−
Let us save our work.
 
 
|-
 
|-
−
|Show Slide Number 2
+
|07.54
 +
|So this is how we can cross reference Math formulae anywhere within the Writer document.
  
−
References for Math:
+
|-
−
 
+
|08.01
−
Guide:
+
|Let us save our work.
−
 
+
|-
−
http://www.libreoffice.org/get-help/documentation/
+
|08.05
−
 
+
−
http://help.libreoffice.org/Math/Welcome_to_the_Math_Help
+
 
|Here are some reference links for Math:
 
|Here are some reference links for Math:
  
−
Download guides at libreoffice.org documentation link.
 
−
 
−
You can also visit help.libreoffice.org/Math for more information on Math
 
 
|-
 
|-
−
|Show Slide Number 3
+
|08.10
 +
|Download guides at libreoffice.org documentation link.
  
−
Math mark up assignment:
+
|-
−
 
+
|08.17
−
1. Using the example Sets in this tutorial: check if A union ( B union C) is equal to (A union B) union C
+
|You can also visit the following website ''help.libreoffice.org/''Math for more information on Math
−
 
+
|-
−
2. Write the results of subtraction of set B from set A
+
|08.24
−
 
+
−
3. Cross reference the second and third factorial formulae in the example document in the Writer document
+
 
|And finally, here is an assignment for you. Use the Writer document.
 
|And finally, here is an assignment for you. Use the Writer document.
  
−
1. Using the example Sets in this tutorial: check if A union ( B union C) is equal to (A union B) union C
+
|-
−
 
+
|08.29
−
2. Write the results of A minus B
+
|Using the example Sets in this tutorial: check if A union ( B union C) is equal to (A union B) union C
  
−
3. And cross reference the second and third factorial formulae in the Writer document
 
 
|-
 
|-
−
|Show Slide Number 3
+
|08.44
 +
|Write the results of A minus B
  
−
Summary:
+
|-
−
 
+
|08.47
−
*Write Set operations
+
|And cross reference the second and third factorial formulae in the Writer document
−
 
+
|-
−
*Write Factorials and  
+
|08.54
−
 
+
−
*Cross reference equations by numbering
+
 
|This brings us to the end of this tutorial on Sets, Factorials and Cross Referencing in LibreOffice Math.
 
|This brings us to the end of this tutorial on Sets, Factorials and Cross Referencing in LibreOffice Math.
  
−
To summarize, we learned how to:
+
|-
 +
|09.03
 +
|To summarize, we learned how to:
  
−
Write Set operations
+
|-
 +
|09.06
 +
|Write Set operations
  
−
Write Factorials and  
+
|-
 +
|09.08
 +
|Write Factorials and  
  
−
Cross reference equations by numbering
 
 
|-
 
|-
−
|Acknowledgement Slide
+
|09.11
 +
|Cross reference equations by numbering
 +
|-
 +
|09.15
 
|Spoken Tutorial Project is a part of the Talk to a Teacher project, supported by the National Mission on Education through ICT, MHRD, Government of India.  
 
|Spoken Tutorial Project is a part of the Talk to a Teacher project, supported by the National Mission on Education through ICT, MHRD, Government of India.  
−
This project is co-ordinated by http://spoken-tutorial.org.  
+
|-
−
More information on the same is available at the following link http://spoken-tutorial.org/NMEICT-Intro.  
+
|09.26
−
This script has been contributed by Priya Suresh, Desicrew Solutions, and this is (the name of the narrator and affiliation
+
|This project is co-ordinated by http://spoken-tutorial.org.  
−
and place) signing off. Thanks for joining.
+
|-
 +
|09.31
 +
|More information on the same is available at the following link http://spoken-tutorial.org/NMEICT-Intro.  
 +
|-
 +
|09.35
 +
|This script has been contributed by Priya Suresh, Desicrew Solutions, and this is (Saundarya desicrew solution ) signing off. Thanks for joining.

Revision as of 11:15, 11 February 2013

Visual Cues Narration
00.00 Welcome to the Spoken tutorial on LibreOffice Math.
00.04 In this tutorial, we will learn how to
00.08 Write Set operations
00.10 Write Factorials and Cross reference equations by numbering
00.16 For this, let us first open our example Writer document that we created in our previous tutorials: MathExample1.odt.
00.29 Here let us go to the end of the document and press Control Enter to go to a new page.
00.37 And type “Set Operations: ” and press Enter twice.
00.42 Now let us call Math.
00.46 Before we go ahead, let us increase the font size to 18 point.
00.51 Change the alignment to the left.
00.56 Let us now learn how to write Set operations.
01.00 Math has separate mark up to represent Sets, which are collections of distinct elements.
01.07 Let us write 4 example sets in the Formula Editor window as shown on the screen:
01.15 Set A with 5 elements
01.18 Set B
01.20 Set C
01.22 And Set D equal to 6, and 7, with 2 elements each.
01.29 Notice that to write the brackets for sets, we can use the mark up: lbrace and rbrace.
01.39 Now we can write set operations such as unions and intersections.
01.45 First let us write a union operation.
01.49 The mark up for B union C is the same as we read it;
01.55 and the resulting set is 1, 2, 6, 4, and 5, which includes all the distinct elements in both sets.
02.07 The markup for an intersection operation is again the same as we read it.
02.13 The intersection includes only the common elements from both the sets.
02.20 So the result of B intersection D is 6.
02.26 And we can also write: set C is a subset of set A, as every element in C is in set A.
02.39 The mark up for this is C subset A.
02.46 You can learn to write more set operations, by exploring the Elements window by clicking on the third icon there.
02.55 Go to View> Elements> Set Operations.
03.03 Let us save our work now.
03.05 Click on File>Save.
03.10 Now let us write Factorial functions.
03.14 We will designate numbers 1 to 3 for the three formulae we are going to write shortly.
03.23 These will help to cross reference them anywhere within the Writer document.
03.29 Let us go to a new page by clicking three times slowly outside the Writer gray box.
03.37 Press Control -Enter.
03.40 Type “Factorial Function: ” and press enter twice.
03.45 Now, we know how to call Math.
03.48 But there is another way to bring up the Math object into the Writer.
03.54 For this simply write ‘f n’ on the Writer document and press F3.
04.03 We are now seeing a new Math object that says E is equal to m c squared;
04.11 and along with that, the number one within parentheses, on the right.
04.18 Meaning, we can cross reference this formula with the number 1 anywhere in this document; we will learn the details of how to do this later.
04.30 For now, let us double click on the Math object
04.36 And do the formatting. Font size 18 and Left Alignment.
04.43 Okay, let us now write an example for Factorial.
04.48 The mark up ‘fact’ represents the factorial symbol.
04.53 So let us overwrite the existing formula with ours:
04.58 5 Factorial = 5 into 4 into 3 into 2 into 1 = 120.
05.10 Notice the mark up here.
05.12 Let us write our next formula in a new Math object here.
05.17 For this, let us first click outside this Writer gray box three times slowly.
05.26 Press the down arrow key two or three times to go to the end of this page.
05.33 And type ‘f n’ and press F3 to bring up the second Math object.
05.40 Again, we will repeat the formatting
05.50 and overwrite the existing formula with the factorial definition:
05.55 N factorial is equal to prod from k = 1 to n of k.
06.05 Notice the mark up ‘prod’ which denotes product, similar to sigma for summation.
06.13 Now, let us introduce a third Math object just like the first two
06.24 and rewrite the factorial definition as two conditional formulae as shown on the screen.
06.33 Notice the mark up ‘binom’, which displays a vertical stack of two elements and helps with better alignment.
06.45 Let us now see how we can cross reference these formulae.
06.50 For this, let us go to a new page
06.54 and type: An example of factorial is provided here:
07.02 Now let us click on the Insert menu, and on Cross reference.
07.09 In the new popup, let us select “Text” in the Type list.
07.15 Then choose the first item in the Selection list denoting the first factorial formula we wrote.
07.24 Now choose Reference in the ‘Insert reference tool’ list and click on Insert once and close.
07.35 So the number one in parentheses has appeared next to our text. And we are done.
07.42 Let us test it by simply clicking on this number;
07.47 And notice that the cursor has jumped to the location where we wrote the first formula.
07.54 So this is how we can cross reference Math formulae anywhere within the Writer document.
08.01 Let us save our work.
08.05 Here are some reference links for Math:
08.10 Download guides at libreoffice.org documentation link.
08.17 You can also visit the following website help.libreoffice.org/Math for more information on Math
08.24 And finally, here is an assignment for you. Use the Writer document.
08.29 Using the example Sets in this tutorial: check if A union ( B union C) is equal to (A union B) union C
08.44 Write the results of A minus B
08.47 And cross reference the second and third factorial formulae in the Writer document
08.54 This brings us to the end of this tutorial on Sets, Factorials and Cross Referencing in LibreOffice Math.
09.03 To summarize, we learned how to:
09.06 Write Set operations
09.08 Write Factorials and
09.11 Cross reference equations by numbering
09.15 Spoken Tutorial Project is a part of the Talk to a Teacher project, supported by the National Mission on Education through ICT, MHRD, Government of India.
09.26 This project is co-ordinated by http://spoken-tutorial.org.
09.31 More information on the same is available at the following link http://spoken-tutorial.org/NMEICT-Intro.
09.35 This script has been contributed by Priya Suresh, Desicrew Solutions, and this is (Saundarya desicrew solution ) signing off. Thanks for joining.

Contributors and Content Editors

Jyotisolanki, Krupali, Minal, PoojaMoolya, Pratik kamble, Ranjana, Sandhya.np14, Sneha

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