Difference between revisions of "LibreOffice-Suite-Math/C2/Derivatives-Differential-Equations-Integral-Equations-Logarithms/English-timed"

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||For this, let us first open our example '''Writer document''' that we created in our previous tutorials- 'MathExample1.odt'.
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||For this, let us first open our example '''Writer document''' that we created in our previous tutorials- "MathExample1.odt".
  
 
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||Before we go ahead, let us increase the font-size to 18 point.
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||Before we go ahead, let us increase the font-size to '''18 point'''.
  
 
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||Change the '''alignment''' to the '''Left'''
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||Let us now learn how to write '''Derivatives''' and '''differential equations'''.
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||Let us now learn how to write '''derivatives''' and '''differential equations'''.
  
 
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||We just have to treat them like a fraction and use the '''mark up''' ‘over’.
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||We just have to treat them like a fraction and use the '''mark up''' '''over'''.
  
 
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||For example- to write a '''total derivative''', df by dx, the '''mark up''' is 'df over dx' in the '''Formula Editor Window'''.
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||For example- to write a '''total derivative, df by dx''', the '''mark up''' is "df over dx" in the '''Formula Editor Window'''.
  
 
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||Next, for a '''partial derivative''', we can use the word ‘partial’. And the '''markup''' looks like: "del f over del x".
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||Next, for a '''partial derivative''', we can use the word ‘partial’ and the '''markup''' looks like: '''del f over del x'''.
  
 
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||Notice that we have used various sets of curly brackets to state the order of operation.
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||And the equation looks like as shown on the screen.
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||Now let us see how to write '''Integral equations'''.
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||Now, let us see how to write '''Integral equations'''.
  
 
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||And, let us go to a new page by clicking three times slowly outside the '''Writer gray box'''
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||Now, let us call '''Math''' from the '''Insert Object''' menu;
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||Now, let us call '''Math''' from the '''Insert > Object''' menu;
  
 
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||increase the font size to 18 point  
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||increase the '''Font size''' to '''18 point'''
  
 
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||and change the '''alignment''' to the left.
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||and change the '''Alignment''' to the '''Left'''.
  
 
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||To write an '''integral''' symbol, we just need to use the '''mark up''' “int” in the '''Formula Editor Window'''.
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||To write an '''integral''' symbol, we just need to use the mark-up “int” in the '''Formula Editor Window'''.
  
 
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||So, given a function f of a real variable x and an interval a, b of the real line on the x-axis, the definite integral is written as '''Integral from a to b f of x dx'''.
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||So, given a function 'f' of a real variable 'x' and an interval 'a, b' of the real line on the x-axis, the definite integral is written as '''Integral from a to b f of x dx'''.
  
 
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||We have used the '''mark up''' ‘int’ to denote the '''integral''' symbol.
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||We have used the mark-up ‘int’ to denote the '''integral''' symbol.
  
 
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Revision as of 18:57, 12 January 2016

Time Narration
00:01 Welcome to the Spoken tutorial on LibreOffice Math.
00:05 In this tutorial, we will learn how to write:
  • Derivatives and Differential equations
  • Integral equations and
  • Formulae with Logarithms.
00:17 For this, let us first open our example Writer document that we created in our previous tutorials- "MathExample1.odt".
00:29 Here, let us scroll to the last page of the document and press Control, Enter to go to a new page.
00:37 Now, type: “Derivatives and Differential Equations: ” and press the Enter key twice.
00:45 Now, let us call Math by clicking Insert menu, then Object and then Formula.
00:54 Before we go ahead, let us increase the font-size to 18 point.
01:00 Change the Alignment to the Left
01:03 and add newlines and blank lines in between each of our examples for better readability.
01:11 Let us now learn how to write derivatives and differential equations.
01:19 Math provides a very easy way of writing these formulae or equations.
01:25 We just have to treat them like a fraction and use the mark up over.
01:33 For example- to write a total derivative, df by dx, the mark up is "df over dx" in the Formula Editor Window.
01:50 Next, for a partial derivative, we can use the word ‘partial’ and the markup looks like: del f over del x.
02:02 We have to use the curly brackets when we use the mark-up ‘partial’.
02:08 Notice the 'del' symbol for partial derivatives in the Writer gray box.
02:14 Here is another example: Newton's second law of motion
02:21 which describes the relationship between acceleration and force
02:26 F is equal to m a.
02:30 This can be written as an ordinary differential equation as: F of t is equal to m into d squared x over d t squared.
02:45 Notice that we have used various sets of curly brackets to state the order of operation
02:56 and the equation looks like as shown on the screen.
03:01 Here is another example of a differential equation.
03:05 Newton’s law of cooling.
03:08 If theta of t is the temperature of an object at time t, then we can write a differential equation:
03:18 d of theta over d of t is equal to minus k into theta minus S
03:30 where 'S' is the temperature of the surrounding environment.
03:35 Notice the equation in the Writer gray box.
03:39 Let us save our work now. Go to File and click on Save.
03:45 Now, let us see how to write Integral equations.
03:50 And let us go to a new page by clicking three times slowly, outside the Writer gray box
03:58 and then press Control, Enter.
04:03 Type: “Integral Equations: ”
04:06 and press Enter twice.
04:11 Now, let us call Math from the Insert > Object menu;
04:17 increase the Font size to 18 point
04:22 and change the Alignment to the Left.
04:25 To write an integral symbol, we just need to use the mark-up “int” in the Formula Editor Window.
04:35 So, given a function 'f' of a real variable 'x' and an interval 'a, b' of the real line on the x-axis, the definite integral is written as Integral from a to b f of x dx.
04:58 We have used the mark-up ‘int’ to denote the integral symbol.
05:04 To specify the limits 'a' and 'b', we have used the mark up ‘from’ and ‘to’.
05:13 Notice the formula in the Writer gray box.
05:17 Next, let us write an example double integral formula to calculate the volume of a cuboid.
05:26 And the formula is as shown on the screen.
05:30 As we can see, the mark up for a double integral is ‘i i n t’. Simple..
05:38 Similarly, we can also use a triple integral to find the volume of a cuboid.
05:46 And the mark up for a triple integral is ‘i i i n t’.
05:52 We can also use the subscript mark up to specify Limits of an integral.
06:00 Using the subscript, Math places the character to the bottom right of the integral.
06:06 So, these are the ways we can write integral formulae and equations in Math.
06:13 Now, let us see how to write formulae containing logarithms.
06:19 Let us write these in a fresh Math gray box or Math object.
06:24 Type ‘Logarithms: ‘ and press Enter twice.
06:29 Call Math again;
06:35 and change the font to 18 point
06:39 and align them to the left.
06:42 A simple formula using logarithm is Log 1000 to the base 10 is equal to 3.
06:52 Notice the mark up here.
06:55 Here is another example: Log 64 to the base 2 is equal to 6.
07:03 Let us now write the integral representation of the natural logarithm.
07:10 The natural logarithm of t is equal to the integral of 1 by x dx from 1 to t.
07:20 And the mark up looks like as shown on the screen.
07:25 Let us save our examples.
07:29 Here is an assignment for you:
07:31 Write the following derivative formula:
07:35 d squared y by d x squared is equal to d by dx of ( dy by dx).
07:47 Use scalable brackets.
07:51 Write the following integral:
07:53 Integral with limits 0 to 1 of {square root of x } dx.
08:04 Next, write a double integral as follows:
08:09 Double integral from T of { 2 Sin x – 3 y cubed + 5 } dx dy.
08:23 And using the formula:
08:25 log x to the power of p to the base b is equal to p into log x to the base b
08:35 solve log 1024 to the base 2.
08:41 Format your formulae.
08:43 This brings us to the end of this tutorial on writing Differential and Integral equations and logarithms in LibreOffice Math.
08:52 To summarize, we learned how to write: Derivatives and Differential equations.
08:58 * Integral equations and *Formulae with Logarithms.
09:02 Spoken Tutorial project is a part of the Talk to a Teacher project,
09:06 supported by the National Mission on Education through ICT, MHRD, Government of India.
09:13 This project is coordinated by http://spoken-tutorial.org.
09:18 More information on the same is available at the following link.
09:24 This script has been contributed by Priya Suresh, DesiCrew Solutions. And this is Soundharya, DesiCrew Solutions signing off.

Thanks for joining.

Contributors and Content Editors

Minal, PoojaMoolya, Pratik kamble, Sandhya.np14

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