View source for 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, video tutorial.

{| border=1
|| '''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 as 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.
|-
|}