LibreOfficeSuiteMath/C2/DerivativesDifferentialEquationsIntegralEquationsLogarithms/English
Visual Cues  Narration 

Show Slide Number 1
Spoken tutorial on LibreOffice Math Learning Objectives

Welcome to the Spoken tutorial on LibreOffice Math.
In this tutorial, we will learn how to write Derivatives and Differential equations Integral equations And Formulae with Logarithms 
Open the MathExample1.odt (created in part 2)  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.
Press Control  Enter to go to a new page Type “Derivatives and Differential Equations: ” in Writer on this fresh page. Press enter twice. Click Insert > Object > Formula 
Here let us scroll to the last page of the document and press Control Enter to go to a new page.
Now type “Derivatives and Differential Equations: ” and press the Enter key twice. Now let us call Math by clicking Insert menu, then Object and then Formula. 
Click Format menu > Font size. Increase size to 18 pt.
Click Format menu > Alignment, choose left option All pink coloured text goes into Formula Editor Window (FEW in short) 
Before we go ahead, let us increase the font size to 18 point.
Change the alignment to the left and add newlines and blank lines in between each of our examples for better readability. Let us now learn how to write Derivatives and differential equations. 
In FEW, copy and paste:
df over dx newline newline In FEW, point mouse over above mark up. In FEW, press enter twice, copy and paste: {partial f} over {partial x} newline newline In FEW, point mouse over curly brackets in the last mark up. Point mouse over del symbol in the last formula in Writer gray box In FEW, press enter twice, copy and paste: F = ma newline newline In FEW, press enter twice, copy and paste: F(t) = m {{d^2}x } over {dt^2 } newline newline In FEW, point mouse over curly brackets in the last line Point mouse the last formula Writer gray box In FEW, press enter twice, copy and paste: {d %theta} over dt ~=~ k(%theta – S) newline newline Point mouse over the last formula in Writer gray box 
Math provides a very easy way of writing these formulae or equations.
We just have to treat them like a fraction, and use the mark up ‘over’. For example, to write a total derivative, df by dx, the mark up is 'df over dx' in the Formula Editor Window. Next, for a partial derivative, we can use the word ‘partial’. And the markup looks like: del f over del x. We have to use curly brackets when we use the mark up ‘partial’ Notice the del symbol for partial derivatives in the Writer gray box. Here is another example: Newton's second law of motion which describes the relationship between acceleration and force F is equal to m a. 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. Notice that we have used various sets of curly brackets to state the order of operation. And the equation looks like as shown on the screen Here is another example of a differential equation. Newton’s law of cooling. If theta of t is the temperature of an object at time t, then we can write a differential equation: d of theta over d of t is equal to minus k into theta minus S where S is the temperature of the surrounding environment. Notice the equation in the Writer gray box. 
Click File > Save.  Let us save our work now. Go to File and click on Save. 
Click three times slowly outside right of Writer gray box. Now then click again.
Press Control Enter Type: “Integral Equations: ” and press enter twice Click Insert > Object > Formula Click Format menu > Font size. Increase size to 18 pt. Click Format menu > Alignment, chooses left option In FEW, copy and paste: int from a to b f(x) dx newline newline In FEW, point mouse over ‘int’ word in the last line And point over ‘from’ and ‘to’ Point mouse over the last formula in Writer gray box In FEW, press enter twice, copy and paste: iint from D p dx dy, "where f(x,y) = p in the region D" newline newline In FEW, point mouse over ‘i i n t’. iiint_cuboid 1 dx dy dz, "where constant function f(x, y, z) = 1" In FEW, point mouse over ‘i i i n t’. In FEW, point mouse over the _ character in the last line Point mouse over the last 3 formulae in Writer gray box 
Now let us see how to write Integral equations.
And let us go to a new page by clicking three times slowly outside the Writer gray box And then press Control Enter. Type “Integral Equations: ” and press enter twice. Now, let us call Math from the Insert Object menu; increase the font size to 18 point and change the alignment to the left. To write an integral symbol, we just need to use the mark up “int” in the Formula Editor Window. So, given a function f of a real variable x and an interval a, b of the real line on the xaxis, the definite integral is written as Integral from a to b f of x dx. We have used the mark up ‘int’ to denote the integral symbol. To specify the limits a and b, we have used the mark up ‘from’ and ‘to’. Notice the formula in the Writer gray box. Next let us write an example double integral formula to calculate the volume of a cuboid. And the formula is as shown on the screen. As we can see, the mark up for a double integral is ‘i i n t’. Simple. Similarly, we can also use a triple integral to find the volume of a cuboid. And the mark up for a triple integral is ‘i i i n t’. We can also use the subscript mark up to specify Limits of the integral. Using the subscript, Math places the character to the bottom right of the integral. So these are the ways we can write integral formulae and equations in Math. 
Click three times outside the gray box and press enter twice.
Type ‘Logarithms: ‘ and press enter twice. Click Insert > Object > Formula Click Format>Font Size. Make it 18pt. Then Click Format>Alignment. Choose Left. In FEW, copy and paste: log_10 1000 = 3 newline newline In FEW, point mouse over above mark up In FEW, press enter twice, copy and paste: log_2 (64) = log_2 (2)^ 6 = 6 log_2 (2) = 6 (1) = 6 newline newline In FEW, press enter twice, copy and paste: ln(t) = int from 1 to t {1 over x} dx Point mouse over last formula in the Writer gray box In FEW, point mouse over mark up in the last line Click File > Save 
Now let us see how to write formulae containing logarithms.
Let us write these in a fresh Math gray box or Math object. Type ‘Logarithms: ‘ and press Enter twice. Call Math again; and change the font to 18 point and align them to the left. A simple formula using logarithm is Log 1000 to the base 10 is equal to 3. Notice the mark up here. Here is another example: Log 64 to the base 2 is equal to 6. Let us now write the integral representation of the natural logarithm . The natural logarithm of t is equal to the integral of 1 by x dx from 1 to t. And the mark up looks like as shown on the screen. Let us save our examples. 
Show Slide Number 2 and 3 (I have split the assignment into 2 slides)
Assignment: 1. Write the following derivative formula: d squared y by d x squared is equal to d by dx of ( dy by dx). Use scalable brackets. 2. Write the following integral: Integral with limits 0 to 1 of {square root of x } dx. 3. Write a double integral as follows: Double integral from T { 2 Sin x – 3 y cubed + 5 } dx dy 4. Using the formula: log x to the power of p to the base b is equal to p into log x to the base b; solve log 1024 to the base 2 Use formatting options provided by Math for better readability 
Here is an assignment for you:
1. Write the following derivative formula: d squared y by d x squared is equal to d by dx of ( dy by dx). Use scalable brackets. 2. Write the following integral: Integral with limits 0 to 1 of {square root of x } dx. Next, write a double integral as follows: Double integral from T of { 2 Sin x – 3 y cubed + 5 } dx dy And using the formula: log x to the power of p to the base b is equal to p into log x to the base b; solve log 1024 to the base 2 Format your formulae. 
Show Slide Number 4
Summary:

This brings us to the end of this tutorial on writing Differential and Integral equations and logarithms in LibreOffice Math.
To summarize, we learned how to write: Derivatives and Differential equations Integral equations And Formulae with Logarithms 
Acknowledgement Slide  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 coordinated by http://spokentutorial.org. More information on the same is available at the following link http://spokentutorial.org/NMEICTIntro. This script has been contributed by Priya Suresh, Desicrew Solutions, Chennai) and this is (the name of the narrator and affiliation and place) signing off. Thanks for joining. 