 Hello friends, I am Naval Emul working as an assistant professor in mechanical engineering department waltz and institute of technology solar power. In this video, we are going to see sci lab, scalars and vectors part two. Learning outcome at the end of this session, students will be able to perform mathematical functions used in sci lab. Content, relational operations on vectors, logical operations on vectors, built in logical function, elementary mathematical functions, we will see trigonometric functions, inverse trigonometric function, hyperbolic function. Relation operations on vectors, sci lab uses six relation operators for mathematic comparisons of vectors. Relation operations results in a vector of a same size with the answer t when the relation is true and f when relation is false. First operation among six, first is less than the relation operator used as less than sign as shown here less than. Suppose if there are two vectors x, row vector and y as a row vector the relation between x and y that is less than x is less than y it is denoted as x less than y then the output will be f t f f where f is for false and t is for true. We will have a quick where x is equal to I will take a row 2 comma 4 comma 6 comma 8 I will press enter this is row vector y as in 2 comma 4 2 comma 5 comma 7 comma 9 like this then I use enter then x is less than y very simple. So, you get f t t you can see the first element 2 here also 2 it is equal it is not less than it is false then all others are here 5 x is less that is 4 is less than 5 6 is less than 7 and 8 is less than 9 obviously all will be true. So, we can use in the above example like I mean in this example that the second number 3 is less than 4. So, 3 is less than 4 it shows true then all other cases it shows false less than or equal to operator in the same way we can use same vectors you can use the operator less than or equal to sign it shows the output t is true again f is false in the same way we can use greater than relation operator the sign is greater greater sign x and y are defined then x is greater than y you get the output and in the same way greater than or equal to so just we are using greater than symbol first then equal to symbol here. So, x and y are defined variables then if you want to check the relation between two vectors x is greater than y you will get the output again. So, these are very simple calculations you can try on your silap console window. So, here the important thing is whenever you want to find equal to the operator is used as equal to equal to 2 times. So, you need to remember whenever you want to check the relation between two operators we use equal to as equal to and equal to for 2 times. So, here you can see the first element 2 is equal that is why it is showing true rest all is a false next not equal to. So, this negation and equal to sign is for not equal to here x and y x we are using not equal to operator then y here first one shows false then all three shows true because 2 is equal to 2 the output will be opposite that is false rest all as true. Then we will see logical operations on vector logical operator we use the and operator here you need to remember this sign and the operation results in a vector of same size with the answer t when both the expressions are true and f when it is false. So, there are two vectors again x and y. So, here I have taken a command like x is greater than y and x is greater than 2 then show the output. So, it will show f f t that is x x is greater than y that is false actually in the first case itself it is false. So, it goes to false second case is 3 is greater than 4 this is also not possible. So, it shows f second case 7 is greater than 5. So, this is true and it checks that is 7 is greater than 2 that is why it shows true in the same way we can perform and operator and this is the same statement I have explained then logical or operator for or operator we are using this dash sign. So, here x and y are given. So, we are using x this dash and y. So, the output will be f t t t in the same way logical compliment compliment sign is shown here in the figure. So, x and y so that will be opposite to the or if you want to show the output opposite you can use this sign. So, these are three logical operator signs and or and compliment build in logical function. So, build in logical function is is empty this function returns to returns a true value for an empty matrix. Suppose I have given a vector x is equal to 0 3 7 8 and if you want to check whether there is an element inside this vector just type is empty of x you find it is false because there are few elements inside this vector. So, is empty is to check whether the vector is empty or not very simple next function is to find. So, in a vector if you want to find any value suppose x is a vector here we need to find x greater than 5 is real it checks whether the given function is real or not if it is real the output will be true that is true. I will show you the quick calculations for I will clear this window first clc enter I will define a vector a as 0 comma 1 comma 2 comma 3 bracket complete enter and I will check is E M P T Y is empty a. So, it should show false that there is some elements in this and find a greater than enter. So, it will show greater than 1 the values are 2 and 3 and 4. So, it shows the position sorry it shows the position not the values. So, 3 third position is greater than 1 and 4th position is greater than 1. So, in the same way here also here greater than 5 it shows the position. So, 3 means that is a third position seventh element and fourth position that is number 8. So, is real is used then is global is also used if the function is function returns are true value that variable declared is global. Then elementary mathematical functions are used for example, clean the function rounds all small values down to 0. Suppose there are very small values like 0.000 that will be equal to 0 when we use the function clean. For example, let us take a matrix and we do a calculation like a into a matrix or we take a new matrix B that is a into inverse of a that should be a identity matrix. But in Sylab we will get the value like this is 1 the diagonal element is 1 1 1 and other all elements should be 0. But Sylab shows minus 0. Sorry minus 3.053 10 minus 16 it means it is 10 raised to minus 16 this is minus 17. So, in such cases we can use a clean function if you use clean matrix B the all the elements which is smaller it becomes 0. So, clean is used to bring the near low value to 0. Next seal this function rounds a floating point number to the next higher integer. For example, we are using seal for 1.2 space 1.5 space 1.9 minus 1.2 here it will seal seal means it is above. So, it will show the value which is next value which is in whole number like 2 2 2 and it is minus so it will show the below value that is minus 2. So, seal is the pointing showing the higher integer. If we use floor it it shows the lower integer same value it will show 1 1 1 and minus 2 you can try this it is fun when we use these examples like it shows floor value and seal value. We have another example like round this is usually rounds of the nearest integer in a usual way. For example, here it shows 1 the value which are above 0.5 then it shows the next higher integer which is below 5 it shows the below lowest integer we use fix also. So, fix this function around floating point number towards 0. So, that floating number becomes 0 then it shows the only first number that is 1.2 is directly fixed to 1 and 1.9 is also fixed to 1. So, think least down few trigonometry functions used in silo pause the video for few seconds and think. So, we can go trigonometry functions we can do a basic functions like sine cos tan that supports the silo it uses the right angle triangle formula for example, sine 45 just you need to give a function sine and the angle you get the answer in the same way cos angle and for tan or tangent we use a trigonometric function tan. These are the references I have used. Thank you.