Pract: Write a program to find mean & median for direct series.

#include<stdio.h>
#include<conio.h>
void main()
{
int n,i,j;
float a[10],mean,median,sum=0.0,temp;
clrscr();
printf(“Enter total no. of element: “);
scanf(“%d”,&n);
printf(“Enter %d elements:”,n);
for(i=0;i<n;i++)
scanf(“%f”,&a[i]);
for(i=0;i<n;i++)
sum=sum+a[i];
mean=sum/n;
printf(“\nMean value= %f”,mean);
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
{
if(a[i]<a[j])
{
temp=a[i];
a[i]=a[j];
a[j]=temp;
}
}
}
printf(“\nAfter Sorting: “);
for(i=0;i<n;i++)
printf(“%f\t”,a[i]);
if((n%2)!=0)
median=a[n/2];
else
median=(a[(n/2)-1]+a[n/2])/2;
printf(“\nMedian value= %f”,median);

getch();
}

Pract: Develop a C program to solve linear equation using Gauss Elimination method

#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<ctype.h>

void main()
{
int i,j,k,n=0,m,l,b;
int p,q;
float a[10][10],x[10],t,sum,temp;
clrscr();

printf(“\nSolution of system of equations using Gauss-Elimination Method\n”);
printf(“\nx1 + x2 + x3 = C1\nx1 + x2 + x3 = C2\nx1 + x2 + x3 = C3\n…..\n”);

printf(“\nEnter no. of equations:”);
scanf(“%d”,&n);
printf(“\nEnter Co-efficients of x1,x2,x3 & C\n”);
for(i=1;i<=n;i++)
{
b=1;
for(j=1;j<=(n+1);j++)
{
if(j!=4)
{
printf(“Enter Co-efficient of x%d:”,b++);
fflush(stdin);
scanf(“%f”,&a[i][j]);
}
else
{
printf(“Enter C%d:”,b++);
fflush(stdin);
scanf(“%f”,&a[i][j]);
}
}
}
printf(“\nThe Matrix is:\n”);
for(i=1;i<=n;i++)
{
for(j=1;j<=(n+1);j++)
{
if(j!=4)
printf(“%7.2f\t”,a[i][j]);
else
printf(“|%7.2f”,a[i][j]);
}
printf(“\n”);
}
for(i=1;i<=(n-1);i++)
{
/*m=fabs(a[i][i]);
p=i;
for(l=(i+1);l<=n;l++)
{
if((fabs(a[l][i]))>m)
{
m=fabs(a[l][i]);
p=l;
}
}
if(p!=i)
{
for(q=i;q<=(n+1);q++)
{
temp=a[i][q];
a[i][q]=a[p][q];
a[p][q]=temp;
}
}*/
for(j=(i+1);j<=n;j++)
{
t=(a[j][i])/(a[i][i]);
for(k=i;k<=(n+1);k++)
a[j][k]=a[j][k]-(t*a[i][k]);
}
}
x[n]=(a[n][n+1]/a[n][n]);
for(i=(n-1);i>=1;i–)
{
sum=0;
for(j=(i+1);j<=n;j++)
sum=sum+(a[i][j]*x[j]);

x[i]=(a[i][n+1]-sum)/a[i][i];
}
printf(“\nSolution of the Equations”);
for(i=1;i<=n;i++)
printf(“\nX%d=%5.2f”,i,x[i]);
getch();
}

 

Pract: Develop a C program to implement Simpsons 3/8th Rule.

#include<stdio.h>
void main()
{
int i,n;
float x[20], y[20], h, sum, integral, s2, s3;
clrscr();
printf(“Enter number of intervals: “);
scanf(“%d”,&n);
printf(“Enter size(height) of interval: “);
scanf(“%f”,&h);
printf(“Enter %d pair of (x,y)\n”,n+1);

for(i=1; i<=(n+1); i++) {
printf(“x[%d]= “,i);
scanf(“%f”,&x[i]);

printf(“y[%d]= “,i);
scanf(“%f”,&y[i]);
}
sum = y[1]+y[n+1];
s2 = s3 = 0.0;
for(i=2; i<=(n-1); i+=3) {
s3 = s3+y[i]+y[i+1];
}
for(i=4; i<=(n-2); i+=3) {
s2 = s2+y[i];
}
integral = (3.0*h/8.0)*(sum+2*s2+3*s3);
printf(“\nValue of Integral = %.4f\n”,integral);
getch();
}

 

Pract: Develop a C program to implement Simpsons 1/3rd Rule.

#include<stdio.h>
void main()
{
int i,n;
float x[20], y[20], h, sum, integral, s2, s4;
clrscr();
printf(“Enter number of intervals: “);
scanf(“%d”,&n);
printf(“Enter size(height) of interval: “);
scanf(“%f”,&h);
printf(“Enter %d pair of (x,y)\n”,n+1);

for(i=1; i<=(n+1); i++) {
printf(“x[%d]= “,i);
scanf(“%f”,&x[i]);

printf(“y[%d]= “,i);
scanf(“%f”,&y[i]);
}
sum = y[1]+y[n+1];
s2 = s4 = 0.0;
for(i=2; i<=n; i+=2) {
s4 = s4+y[i];
}
for(i=3; i<=(n-1); i+=2) {
s2 = s2+y[i];
}
integral = (h/3.0)*(sum+2*s2+4*s4);
printf(“\nValue of Integral = %.4f\n”,integral);
getch();
}

 

Pract: Develop a C program to compute derivatives of a tabulated function at a specified value using the Newton interpolation approach. (Newton’s Divided Interpolation Formula)

#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
float x[10],y[10][10],sum,p,u,temp;
int i,n,j,k=0,f,m;
float fact(int);
clrscr();
printf(“Enter total number of values: “);
scanf(“%d”,&n);
for(i=0; i<n; i++)
{
printf(“enter the value of x[%d]: “,i+1);
scanf(“%f”,&x[i]);
printf(“enter the value of y[%d]: “,i+1);
scanf(“%f”,&y[k][i]);
}
printf(“\nEnter X for finding y(x): “);
scanf(“%f”,&p);

for(i=1;i<n;i++)
{
k=i;
for(j=0;j<n-i;j++)
{
y[i][j]=(y[i-1][j+1]-y[i-1][j])/(x[k]-x[j]);
k++;
}
}
printf(“\n_____________________________________________________”);
printf(“\n  x(i)\t   y(i)\t    y1(i)    y2(i)    y3(i)    y4(i)”);
printf(“\n_____________________________________________________\n”);
for(i=0;i<n;i++)
{
printf(“\n %.3f”,x[i]);
for(j=0;j<n-i;j++)
{
printf(”   “);
printf(” %.3f”,y[j][i]);
}
printf(“\n”);
}

i=0;
do
{
if(x[i]<p && p<x[i+1])
k=1;
else
i++;
}while(k != 1);
f=i;

sum=0;
for(i=0;i<n-1;i++)
{
k=f;
temp=1;
for(j=0;j<i;j++)
{
temp = temp * (p – x[k]);
k++;
}
sum = sum + temp*(y[i][f]);
}
printf(“\n f(%.2f) = %f”,p,sum);
getch();
}