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

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