 Milka Jagle, working as an assistant professor in Department of Mechanical Engineering, Walchin Institute of Technology, Sulakot. Today, we are going to learn functions used in the SILAM. Let us start. Learning outcome. At the end of this session, students will be able to perform various functions on vectors using SILAM. So, let's see the outline. Elementary mathematical functions, mathematical functions, built-in logical functions, trigonometric functions, hyperbolic functions. So, let's start. So, let us see a few elementary mathematical functions used in the SILAM, which is first is C. C function is used to fix the value to the next higher integer if a floating number is specified in a vector. So, C function is used to round off that value to the next higher integer. So, let's see the examples. These vectors are applicable to only vectors. These elementary mathematical functions are applicable to vectors. So, let's see the example of the SIL function. So, when a vector is defined having few elements such as 1.2, 1.5, 1.9 and minus 1.2, here when we use the SIL function, the number is round off to the next higher integer that is 1.2 is round off 2.2 which is the next higher number of 1.2 and 1.5 is also round off 2.2 and 1.9 and here minus 1.2 is round off to the next higher integer that is minus 1. So, next elementary function is flow. This function is used to round off the number or round off the floating number to the next lower integer. If a number is given, this function is used to round off the number to the lower integer. It is similar to SIL function. Just the difference is SIL is used to round off the number to the next higher integer whereas, flow is used to round off the number to the next lower integer. So, let us see the example. A function flow is used and vector is defined by the elements. So, here 1.2 is round off to 1, 1.5 is round off to 1, 1.9 is round off to 1 whereas, minus 1.2 is round off to minus 2. In the same way, there are few more mathematical functions such as round. This round function is used to round off the number to the nearest integer. If for example, a number is given, it is, it fixes the value or it round off the value to the nearest integer. So, let us see the example of the round function. So, when a vector is defined by few elements, few vector elements, so here 1.2 is round off to 1 because 1 is the nearest integer, 1.5 is round off to 2 because 2 is the nearest integer, 1.9 is round off to 2 and minus 1.2 is round off to minus 1. In the same way, the next function that is fixed function is used to round off the number nearest to 0. So, when a vector is defined by few elements, let us see the example of fixed mathematical function that is 1.2, 1.5, 1.9 and minus 1.2 are the elements specified in a vector. So, 1.2 is round off to 1 which is nearest to the 0, 1.5 is round off to 1, 1.9 is round off to 1 and minus 1.2 is round off to minus 1. So, next elementary function is a sine function. Sine function is used if an integer is positive, it will show as plus 1. If the integer is negative, it will show as minus 1. So, when to find out the sine of a elements, the vector s i g n is used that is 1.2 is shown as 1 because it has a positive sign, 1.5 is shown as 1 because it is also have a positive sign, 1.9 is 1 and minus 1.2 is shown as minus 1 because the negative sign is there because minus 1 is the negative integer. So, mathematical functions applied to scalars are modulo that is this function is used to find out the remainder of division of two numbers. Let us see the example of modulo function modulo of 5 comma 2 that is division of 5 and 2 the remainder of these two numbers is 1. So, the answer here is shown as 1. In the same way, the square root of a number can also be found out by using sqrt function. Let us see an example of this sqrt of 100 that is square root of 100 is shown as 10. So, to find out the square root of a number the function sqrt is used. So, let us see the next the exponential of a number can also be found out by using function exp. Let us see the example. The percent e is used as a function. So, if you see here the value is 2.718 in the same way the natural logarithm of a real number can also be found out. So, let us see an example of that. So, logarithm of 2.35 is 0.854 in the same way the logarithm to the base 10 can also be found out by using function log 10. So, let us see the example log 10 of 1000 comes to 3. So, these are the few additional mathematical functions used. So, built-in logical functions here it returns a true value if the condition is satisfied and it returns a false if the condition is not satisfied. E is empty. It returns a true value if the element if a vector is a empty or it does not contain any elements. So, it returns a false because the vectors are already specified in the vector element that is 0378. So, next built-in function is fine. Here condition is given it shows the position where the condition satisfies condition is given as find x is greater than 5. So, it searches in the vector elements where the value of x is such that it is greater than 5. So, the answer is 3 and 4. On the third and fourth position that is 7 and 8 are the integers whose value is greater than 5. So, here it shows the position or index of the number. It shows the is real function. Is real function shows true value for all the real elements specified in a vector. Trignometric functions. Trignometric functions can also be found out by in the psi lab by using the functions sine of a function cos and tan. Let us see an example of trigonometric functions. The sine 45. Sine of an angle can be found out for the sine and cos 45 and tan 45. So, here the sine cos and tan can found out in the psi lab. So, inverse trigonometric functions can also be found out. So, for that a function a sine is used for trigonometric sine of a function is sine function is used and for inverse trigonometric a sine function is used a sine a cos and a tan. So, let us see an example a sine 0.5 gives the answer as 0.5239 and a cos 0.5 shows the answer as 1.047 and the tan inverse trigonometric functions of a can be found out by using a tan of 0.5. As you see the results are specified. So, in the similar way hyperbolic functions can also be found out. So, the function which is used to find out the hyperbolic function is s i n h c o s h cos and tan inverse hyper inverse of sine hyperbolic function of sine hyperbolic cos and hyperbolic tan can be found out. So, let us see the example of hyperbolic functions. So, hyperbolic of sine of 45 if the answer comes as you see here hyperbolic cos of 45 hyperbolic tan of 45 is specified here. So, statistical functions, statistical functions plays an important role in finding out the computational solutions. So, these are the references a book modeling and simulation in psi lab psi cos by Stephen Campbell. Next book psi lab by Hema Ramachandran and Naya. Thank you.