LibreOffice-Suite-Math-6.3/C2/Calculus-and-Logarithms/English

Title: Calculus and Logarithms

Keywords: LibreOffice Math, LibreOffice Writer, derivatives, partial derivatives, differential equations, integrals, logarithms, font size, key board shortcuts, spoken tutorial, video tutorial.

Visual Cue	Narration
Slide: Title Slide	Welcome to the spoken tutorial on Calculus and Logarithms.
Slide: Learning Objectives	In this tutorial, we will learn how to: Write derivatives and differential equations. Write integrals. Write formulae using logarithms. Customize the shortcuts.
Slide: System Requirements	This tutorial is recorded using: Ubuntu Linux OS version 18.04 and LibreOffice Suite version 6.3.5.
Slide: Prerequisites https:\\spoken-tutorial.org	To follow this tutorial, learner should be familiar with Math interface. If not please access the relevant tutorials on this website.
Slide: Code Files	The files used in the tutorial are provided in the Code files link. Please download and extract the files. Make a copy and use them for practising.
Open the MathExample1.odt	Let us first open the MathExample1.odt file.
Press Ctrl + Enter to go to a new page. Type “Derivatives and Differential Equations: ” Press Enter .	Press Ctrl and Enter, keys to go to a new page. Now type “Derivatives and Differential Equations: ” and press Enter.
Click on the Insert menu >> select the Object. From the sub-menu >> select the Formula option.	Let us call the Math application inside Writer. Click on the Insert menu and select Object. From the sub-menu, select Formula.
Click Format menu >> Font size. Increase size to 18 pt.	Before we go ahead, let us increase the font size to 18 point.
Narration only	Let us now learn how to write derivatives and differential equations. Math provides a very easy way of writing them.
In FEW, copy and paste: Total Derivative: df over dx newline newline	We have to treat the derivatives as fractions and use the markup over. To write a total derivative, df by dx, the markup is 'df over dx'.
In FEW, press Enter twice, copy and paste: {partial f} over {partial x} newline newline. In FEW, point the mouse over curly brackets in the last markup. Point mouse over del symbol in the last formula in Writer gray box	We can use the keyword ‘partial’ for a partial derivative. The keyword ‘partial’ has to be within curly brackets . Notice the del symbol for partial derivatives in the Writer gray box. The partial derivative is del f over del x.
In FEW, press Enter twice, copy and paste: Newton's second law of motion describes the relationship between acceleration and force. newline. F = ma newline newline. Newton's second law of motion which describes the relationship between acceleration “and” force.	Let’s write an example to show Newton’s second law of motion. Observe that “and” appears as inverted V as it is a reserved word. To make it appear as a normal text we have to enclose it within double quotes.
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.	Let us write an ordinary differential equation. F of t is equal to m times d squared x over d t squared. Here we have used curly brackets to state the order of operation.
In FEW, press Enter twice, copy and paste: '''''''''' Newton’s Law of cooling. newline If theta of t is the temperature of an object at time t, newline then we can write a differential equation: newline d of `theta over d of t "is equal to" minus k into theta minus S. newline where S is the temperature of the surrounding environment. newline newline {d %theta} over dt ~=~ -k(%theta – S) newline newline Point mouse over the last formula in Writer gray box.	Let us write the differential equation for Newton’s law of cooling. These lines explain Newton’s law of cooling. Notice the equation in the Writer gray box.
Click Save icon on the standard toolbar.	Let us save the file now.
Slide: Assignment d squared y by d x squared is equal to d by dx of (dy by dx).	Pause the tutorial and do this assignment. Write the markup for following derivative. Use scalable brackets.
Click outside of the Writer gray box. Press Ctrl + Enter.	Now let us see how to write integrals. Let us go to a new page. Click outside the Writer gray box to go to the Writer document. Press Ctrl and Enter keys to go to the new page.
Type: “Integral Equations: ” and press Enter.	Type “Integrals: ” and press Enter.
Click on the Insert menu >> select Object. From the submenu >> select Formula option.	Now let us call the Math application.
Click Format menu >> Font size >> Increase size to 18 pt.	Let’s increase the font size to 18 point .
In FEW, copy and paste: function f of a real variable x "and" newline an interval a, b of the real line on the x-axis, newline the definite integral is written as Integral "from" a "to" b, ` f of x dx newline newline 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	Here is an example of an integral. To write an integral symbol, we need to use the markup “int”. To specify the limits a and b, we have used the markup ‘from’ and ‘to’. Notice the formula in the Writer gray box.
In FEW, press Enter twice, copy and paste: Double Integral newline iint from D p dx dy, `"where f(x,y) = p in the region D" newline newline In FEW, point the mouse over ‘iint’.	Let us write an example of a double integral to calculate the area of a region. The formula is shown on the screen. The markup for a double integral is iint.
Triple Integral newline iiint_cuboid 1 dx dy dz, `"where constant function f(x, y, z) = 1" In FEW, point mouse over ‘iiint’.	Similarly, we can use a triple integral to find the volume of a cuboid. The markup for a triple integral is iiint.
In FEW, point mouse over the _ character in the last line Point mouse over the last 3 formulae in Writer gray box.	We can use the subscript markup to specify the Limits of the integral. Subscript is used to place the character to the bottom right of the integral.
Slide: Assignment Integral with limits 0 to 1 of {square root of x } dx.br/> Double integral from T of { 2 Sin x – 3 y cubed + 5 } dx dy	Pause the tutorial and do this assignment. Write the markup for the following integrals.
	Now let us see how to write formulae containing logarithms. First, let us go to a new page.
Click outside of the Writer gray box. Press Ctrl + Enter.	Click outside the gray box to go back to Writer. Press Ctrl and Enter keys to go to the new page. Let us write the logarithms in a fresh Math object.
Type ‘Logarithms: ‘ and press Enter. Click Insert >> Object >> Formula. Click Format >> >> Font Size. Make it 18pt.	Type ‘Logarithms: ‘ and press Enter . Let us call Math application again. Let’s change the font size to 18 point.
In FEW, copy and paste: log_10 1000 = 3 newline newline In FEW, point mouse over above markup	A simple formula using logarithm is Log 1000 to the base 10 is equal to 3. Notice the markup here.
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	Here is another example: Log 64 to the base 2 is equal to 6. Now let us write the integral representation of natural logarithm using markup. Natural logarithm of t is equal to the integral from 1 to t of 1 by x dx.
Only Narration.	Now let us learn about shortcuts. It is a good practice to add shortcut keys to make our work easier.
Cursor on the interface. Click on Tools >> >> click on Customize. Point towards the Customize dialog box Click on the Keyboard tab	Go to Tools menu and select Customize option. Customize dialog box appears. Click the Keyboard tab to access the options for adding keyboard shortcuts.
Select Math radio button. Go to function list at the bottom of the screen and select Import Formula.	Select the Writer radio button at the extreme right if not selected. In the Function list, scroll down and select Formula.
Click on F7 in the shortcut keys list at the top of the dialog box. Click on Modify button at the right of the dialog box.	In the Shortcut Keys list, let us select F7. Click the Modify button. Your keyboard shortcut will appear in the Keys list. If necessary, continue to add keyboard shortcuts using the above steps.
Click OK at the bottom.	Click the OK button to save your keyboard shortcuts.
Ctrl + S.	Let us now save the changes.
Narration only:	With this we come to the end of this tutorial. Let us summarize.
Slide: Summary	In this tutorial we have learnt how to: Write derivatives and differential equations. Write integrals. Write formulae using logarithms. Customize the shortcuts.
Slide: Assignment log x to the power of p to the base b is equal to p times log x to the base b	Here is an assignment for you Write a markup for the following logarithm. Solve log 1024 to the base 2.
Slide: About Spoken Tutorial Project	The video at the following link summarises the Spoken Tutorial project. Please download and watch it.
Slide: Spoken tutorial workshops	We conduct workshops using spoken tutorials and give certificates. For more details, please contact us.
Slide: Answers for THIS Spoken Tutorial	Please post your time queries in this forum.
Slide: Acknowledgement	The Spoken Tutorial project is funded by the Ministry of Education, Govt. of India.
Slide: Thank you Acknowledgement to DesiCrew	This tutorial was originally contributed by DesiCrew Solutions Pvt. Ltd. in 2011 This is Madhuri Ganapathi along with the Spoken Tutorial team from IIT Bombay. Thank you for watching.

Contributors and Content Editors

Madhurig, Nancyvarkey, Nirmala Venkat