Difference between revisions of "LibreOffice-Suite-Math/C2/Derivatives-Differential-Equations-Integral-Equations-Logarithms/English-timed"
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Revision as of 15:52, 9 July 2014
| 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 co-ordinated by http://spoken-tutorial.org. |
| 09:18 | More information on the same is available at the following link. |
| 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 |
