 Welcome back to the session on lipid. In this session, we will learn to type set integration, matrices and equations. The syntax for integration is similar to that of a summation, that is the way in which we specify minimum and maximum values. Limits on the other hand just specify the minimum value. Let us go through these two examples. The command for integration is slash end, which displays the integration sign. This goes from 0 to infinity and then f of x dx. The second example has limit, which displays limits, which goes from x to c and f of x is equal to l. Please do try these examples out. You write a matrix using the environments given below. For example, matrix environment will display a matrix without a border, while P matrix will display with a round bracket, etcetera, etcetera. Let us try out the addition of two matrices. So, we first write dollar and dollar to indicate it is a mathematical mode and then we write slash begin P matrix and we write our content as 1, ampersand means I need to take another column. So, I write 2 slash slash, which denotes I need to take another row 3 and 4. Let us display this. So, we build and run. So, we have a matrix in round brackets 1, 2, 3, 4. Now, let us do some addition of it. So, we write plus, we have another begin matrix and we write 5 and 6 slash slash and 7 and 8 and after that we say equal to. So, we write slash begin P matrix and the answer is 6 and 8 slash slash 10 and 12. So, addition of 1 and 5, which gives 6, 2 and 6, which gives 8, etcetera. Let us build and run. Look how beautifully it is aligned and spaced out. Also, have a look at the size of the round brackets. Let us change from round brackets to box bracket. So, instead of P matrix, we change it to B matrix. Let us build and run. There you go. The matrix is type set using the box brackets. Imagine the effort that it would have taken to accomplish this task ordinarily. Let us go back to our slides. These are mentioned in the equation environment. Only one equation can be written in the environment. These are centered and each equation gets a number. Some examples are given here. Let us write them out. So, we had a section called equations. We write slash begin equation and we say 3 x plus 5 y equal to 2. Let us add another equation. So, we just copy paste it. We align it for better readability and we say 5 x plus 8 y is equal to 3. Let us build and run. So, the equations are centered and they have a number. Let us add one more equation. So, we say slash begin equation and we say x square minus y square equal to x plus y into x minus y. Let us build and run. We have another equation number 3. Well, this is an article document class. As an exercise, just change the document class to a book and add a chapter. Observe the numbering of the equation in that case. Let us switch back to our slides. The align environment is used when you want to write equations on multiple lines or you want to show the steps for solving an equation. An example is shown here. Let us achieve it. So, we write slash begin align and we write our content that is equation 3 x minus 6 equal to 9. We take a new line by writing slash slash and we solve the equation. So, 3 x is equal to 9 plus 6 slash slash. Then finally, we say x is equal to fraction of 9 plus 6 and denominator is 3 and we take a new line again and we say finally, x is 5. Let us build and run. Notice that the equation is centered. Since we are solving it, we would like to align it with respect to the equal to sign. So, we just write ampersand equal to. Ampersand equal to will align the equations keeping the equal to sign in mind. So, we write ampersand equal to. Let us build and run. As you can see, the equation is aligned with respect to the equal to sign. So, one can imagine how the equation is solved. Well, since this is just one equation, we would not like all the steps to be numbered. The no number command tells LaTeX not to number a particular equation step. So, we write slash no number in the remaining 3 lines. Slash no number slash no number and again over here we write slash no number. Let us build and run. So, only the main equation is numbered. This is how we write equations that span multiple lines. Let us go back to our slides. So, with the end of this session, we can now typeset integration limits different types of matrices and equations. Do try out more examples that you might already have in mind or just take up some random examples and try. It is really fun to write mathematics in LaTeX. Thank you. Have a nice day.