This Lab is about an introduction to matlab.

The objective of this lab is to learn about

• Basic mathematical and logical operator in matlab
• Working with Matrix and vector
• Use of conditional ‘if’
• Use of for and while loop

Practice script

 %Basic matrix operation
 a=[1 2 3;4 5 6;7 8 9]
 b=[3 2 1;6 5 4;9 8 7]
 c=a+b
 d=a*b
 n=5
 e=a+n*c

%Use of if, while and for
%while 1 %Try not to use while 1 in matlab. It is not a good idea.
total=0
for i=0:1:5
mark= input('What is the mark ')

if mark >=90 
 point=5;
elseif mark>=80 
 point=4;
elseif mark>=70 
 point=3;
elseif mark>=60 
 point=2;
elseif mark>=50 
 point=1;
else
 point=0;
end % end of if
total=total+point;
end %end of for loop

total=total/6

%end % end for while loop

MATLAB intro

Task #1

Write a program to use fixed point iteration to solve the equation f(x)=e^(-x) – x where inputs will be the initial guess, maximum number of iterations and maximum error (es). If the approximation error (ea) is less than es your program should stop continuing any iterations.

Task #2

Write a program to use Newton Raphson Method to solve the equation f(x)=e^(-x) – x where inputs will be the initial guess, maximum number of iterations and maximum error (es). If the approximation error (ea) is less than es your program should stop continuing any iterations.

Task #2b

Modify your code in 2a to solve for a quadratic equation.

Task #3

Write a program to use  Secant Method to solve the equation f(x)=e^(-x) – x where inputs will be the initial guess, maximum number of iterations and maximum error (es). If the approximation error (ea) is less than es your program should stop continuing any iterations.

Task #1

Write a program to find root of an equation in the form ax^2+bx+c, where a,b,c, will be taken as input. You have to take input the number of iteration and the termination criterion.

Use bisection method to find the root where the upper limit and lower limit will be taken as input.

Task #2

Write a program to find root of an equation in the form ax^2+bx+c, where a,b,c, will be taken as input. You have to take input the number of iteration and the termination criterion.

Use False Position method to find the root where the upper limit and lower limit will be taken as input.

Task #1

Write a program to find an estimate of any value of cos(x). You should take input the value of x in degree, the maximum number of iteration, and the minimum error requirement

Sample code

#include<stdio.h>
#include<math.h>
int fact(int n)
{
 if (n==1){return 1;}
 return n*fact(n-1);
}
int main()
{
 int i,j, iter, sign=1;
 double x, es,ea, previous=1, approx=1, curr_approx;
 scanf("%lf", &x);
 x=(x/180)*3.141592654;
 //printf("%lf\n", x);
 scanf("%d", &iter);
 scanf("%lf", &es);
 for (i=1;i<iter;i++)
 {
 j=i*2;
 curr_approx=(pow(x,j)/(fact(j)));
 if (sign%2==1)
 {
 approx=approx-curr_approx;
 }
 else {approx=approx+curr_approx;}

ea=fabs(((approx-previous)/approx)*100);
 previous=approx;
 sign++;
 printf("\n %lf\t %lf", approx, ea);
 if (ea<es) break;

}

printf("\n%lf", approx);
}

Task #2

Write a program to find an estimate of any value of sin(x). You should take input the value of x in degree, the maximum number of iteration, and the minimum error requirement

Sample code

#include<stdio.h>
#include<math.h>
int fact(int n)
{
 if (n==1){return 1;}
 return n*fact(n-1);
}
int main()
{
 int i,j, iter, sign=0;
 double x, es,ea, previous=0, approx=0, curr_approx;
 scanf("%lf", &x);
 x=(x/180)*3.141592654;
 //printf("%lf\n", x);
 scanf("%d", &iter);
 scanf("%lf", &es);
 for (i=1;i<iter;i++)
 {
 j=(i*2)-1;
 curr_approx=(pow(x,j)/(fact(j)));
 if (sign%2==1)
 {
 approx=approx-curr_approx;
 }
 else {approx=approx+curr_approx;}

ea=fabs(((approx-previous)/approx)*100);
 previous=approx;
 sign++;
 printf("\n %lf\t %lf", approx, ea);
 if (ea<es) break;

}

printf("\n%lf", approx);
}

Assignment

There is no assignment for this lab.