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
For this, let us first open our example Writer document that we created in our previous tutorials: MathExample1.odt.
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.
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.
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 the 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.
Let us save our work now. Go to File and click on Save.
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 x-axis, 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 an 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.
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.
Here is an assignment for you:
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.
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.
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
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