View source for LibreOffice-Suite-Math/C2/Derivatives-Differential-Equations-Integral-Equations-Logarithms/English-timed

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!Visual Cues
!Narration

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||00:01
||Welcome to the Spoken tutorial on LibreOffice Math.

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||00:05
||In this tutorial, we will learn how to write Derivatives and Differential equations, Integral equations And Formulae with Logarithms

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||00:17
||For this, let us first open our example Writer document that we created in our previous tutorials: MathExample1.odt.

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||00:29
||Here let us scroll to the last page of the document and press Control Enter to go to a new page.

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||00:37
||Now type “Derivatives and Differential Equations: ” and press the Enter key twice.

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||00:45
||Now let us call Math by clicking Insert menu, then Object and then Formula.

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||00:54
||Before we go ahead, let us increase the font size to 18 point.

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||01:00
||Change the alignment to the left

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||01:03
||and add newlines and blank lines in between each of our examples for better readability.

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||01:11
||Let us now learn how to write Derivatives and differential equations.

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||01:19
||Math provides a very easy way of writing these formulae or equations.

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||01:25
||We just have to treat them like a fraction, and use the mark up ‘over’.

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||01:33
||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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||01:50
||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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||02:02
||We have to use the curly brackets when we use the mark up ‘partial’

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||Notice the del symbol for partial derivatives in the Writer gray box.

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||02:14
||Here is another example: Newton's second law of motion

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||02:21
||which describes the relationship between acceleration and force

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||02:26
||F is equal to m a. 

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||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.
 
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||02:45
||Notice that we have used various sets of curly brackets to state the order of operation.

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||02:56
||And the equation looks like as shown on the screen

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||03:01
||Here is another example of a differential equation.

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||03:05
||Newton’s law of cooling.

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||03:08
||If theta of t is the temperature of an object at time t, then we can write a differential equation:

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||d of theta over d of t  is equal to minus k into theta minus S

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||03:30
||where S is the temperature of the surrounding environment.

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||03:35
||Notice the equation in the Writer gray box.

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||03:39
||Let us save our work now. Go to File and click on Save.

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||03:45
||Now let us see how to write Integral equations.

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||03:50
||And let us go to a new page by clicking three times slowly outside the Writer gray box

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||03:58
||And then press Control Enter.

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||04:03
||Type “Integral Equations: ” 

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||04:06
||and press enter twice.

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||04:11
||Now, let us call Math from the Insert Object menu;

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||04:17
||increase the font size to 18 point 

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||04:22
||and change the alignment to the left.

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||04:25
||To write an integral symbol, we just need to use the mark up “int” in the Formula Editor Window.

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||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.

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||04:58
||We have used the mark up ‘int’ to denote the integral symbol.

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||05:04
||To specify the limits a and b, we have used the mark up ‘from’ and ‘to’.

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||05:13
||Notice the formula in the Writer gray box.

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||05:17
||Next let us write an example double integral formula to calculate the volume of a cuboid.

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||05:26
||And the formula is as shown on the screen.

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||05:30
||As we can see, the mark up for a double integral is ‘i i n t’. Simple.

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||05:38
||Similarly, we can also use a triple integral to find the volume of a cuboid.

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||05:46
||And the mark up for a triple integral is ‘i i i n t’.

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||05:52
||We can also use the subscript mark up to specify Limits of an integral. 

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||06:00
||Using the subscript, Math places the character to the bottom right of the integral.

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||06:06
||So these are the ways we can write integral formulae and equations in Math.

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||06:13
||Now let us see how to write formulae containing logarithms.

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||06:19
||Let us write these in a fresh Math gray box or Math object.

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||06:24
||Type ‘Logarithms: ‘ and press Enter twice.

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||06:29
||Call   Math again;

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||06:35
||and change the font to 18 point 

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||06:39
||and align them to the left.

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||06:42
||A simple formula using logarithm is Log 1000 to the base 10 is equal to 3.

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||06:52
||Notice the mark up here.

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||06:55
||Here is another example: Log 64 to the base 2 is equal to 6.

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||07:03
||Let us now write the integral representation of the natural logarithm .

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||07:10
||The natural logarithm of t is equal to the integral of 1 by x dx from 1 to t.

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||07:20
||And the mark up looks like as shown on the screen.

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||07:25
||Let us save our examples.

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||07:29
||Here is an assignment for you:

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||07:31
||Write the following derivative formula:

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||07:35
||d squared y by d x squared is equal to d by dx of ( dy by dx).

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||07:47
||Use scalable brackets.

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||07:51
||Write the following integral:

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||07:53
||Integral with limits 0 to 1 of {square root of x } dx.

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||08:04
||Next, write a double integral as follows:

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||08:09
||Double integral from T of { 2 Sin x – 3 y cubed + 5 } dx dy 

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||08:23
||And using the formula:  

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||08:25
||log x to the power of p to the base b is equal to p into log x to the base b; 

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||08:35
||solve log 1024 to the base 2

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||08:41
||Format your formulae.

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||08:43
||This brings us to the end of this tutorial on writing Differential and Integral equations and logarithms in LibreOffice Math.

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||08:52
||To summarize, we learned how to write:Derivatives and Differential equations

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||08:58
||Integral equations And Formulae with Logarithms

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||09:02
||Spoken Tutorial Project is a part of the Talk to a Teacher project,

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||09:06
||supported by the National Mission on Education through ICT, MHRD, Government of India. 

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||09:13
||This project is co-ordinated by http://spoken-tutorial.org. 

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||09:18
||More information on the same is available at the following link.  

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||09:24
||This tutorial has been contributed by ...............................(Name of the translator and narrator)

And this is -----------------------(name of the recorder) from --------------------------(name of the place)signing off. Thanks for watching.  

Thanks for joining
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