The document contains programs and outputs from 7 experiments involving numerical methods: 1) A program to calculate the area and perimeter of a rectangle and area and circumference of a circle. 2) A program to determine if a character entered is a capital letter, small letter, digit or symbol. 3) A menu-driven program with options to calculate factorial, check if prime, and check if even/odd. 4) A program to sort an array using bubble sort. 5) A program to find roots of an equation using Newton-Raphson method. 6) A program to solve a differential equation using the Runge-Kutta method. 7) A program

1. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
1 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
Experiment No. 1
Aim:-Write a C-Program to calculate the area & Perimeter of the rectangle and the area &
circumference of the circle. The length and breadth of a rectangle and radius of a circle are
input through keyboard.
/* Program for finding area & circumference */
#include<stdio.h>
#include<conio.h>
#define pi 3.14
int main()
{
float r,l,b,area,perimeter,circum,areac;
printf("enter the radius of circletlength breadth of rectanglen");
scanf("%f %f %f",&r,&l,&b);
circum=2*pi*r;
areac=pi*r*r;
area=l*b;
perimeter=2*l+2*b;
printf("Area and circumference of circle is =%ft%fnnn",areac,circum);
printf("Area and Perimeter of rectangle is =%ft%f",area,perimeter);
getch();
}

2. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
2 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
/* Output */
enter the radius of circle length breadth of rectangle
5
3
4
Area and circumference of circle is =78.500000 31.400000
Area and Perimeter of rectangle is =12.000000 14.000000

3. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
3 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
Experiment No. 2
Aim:-Write a C-Program to determine whether the character entered through a keyboard is a
capital letter ,a small case letter, a digit or a special symbol.
/* Program to whether the character entered through a keyboard is a capital letter ,a small case
letter, a digit or a special symbol.*/
#include<stdio.h>
#include<conio.h>
int main()
{
char ch;
printf("Enter any charactern");
scanf("%c",&ch);
if(ch>=65 && ch<=91)
printf("Entered character is capital case letter");
else if(ch>=97 && ch<=123)
printf("Entered character is small case letter");
else if(ch>=48 && ch<=57)
printf("Entered character is Digit");
else
printf("Entered character is special symbol");
getch();
}
/* Output */
Enter any character

4. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
4 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
p
Entered character is small case letter
Experiment No. 3
Aim:-Write a program which has the following options:
a) Factorial of a number
b) Prime or not
c) Odd or Even
/* Menu Driven Program*/
#include<stdio.h>
#include<conio.h>
int main()
{
int ch,fact=1,num,i;
printf("Enter any numbernn");
scanf("%d",&num);
printf("nEnter your chice from 1 to 3nn");
printf("Factorial of a number.............1nn");
printf("Prime or not......................2nn");
printf("Odd or even.......................3nn");
scanf("%d",&ch);
switch(ch)
{
case 1:
for(i=1;i<=num;i++)
fact= fact*i;
printf("factorial of given number is = %d",fact);
break;
case 2:

5. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
5 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
for(i=2;i<num;i++)
{
if(num%i==0)
{
printf("Entered number is not
primen");
break;
}
}
if(num==i)
printf("number is primen");
break;
case 3:
if(num%2==0)
printf("Enter number is even");
else
printf("Enter number is Odd");
break;
default:
printf("Out of range");
break;
getch();
}
}
/* Output */
Enter any number
5

6. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
6 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
Enter your chice from 1 to 3
Factorial of a number.............1
Prime or not......................2
Odd or even.......................3
1
factorial of given number is = 120
Enter any number
5
Enter your chice from 1 to 3
Factorial of a number.............1
Prime or not......................2
Odd or even.......................3
2
number is prime
Enter any number
5
Enter your chice from 1 to 3
Factorial of a number.............1
Prime or not......................2
Odd or even.......................3

7. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
7 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
3
Enter number is Odd
Experiment No. 4
Aim:-Write a C-Program to sort an array using bubble sort technique.
/*Program to sort an array using bubble sort*/
#include<stdio.h>
#include<conio.h>
int main()
{
int i,j,num,a[10],temp;
printf("enter total number to store in arrayn");
scanf("%d",&num);
printf("enter nummbersn");
for(i=0;i<num;i++)
scanf("%d",&a[i]);
for(i=0;i<num;i++)
{
for(j=0;j<num-i;j++)
{
if(a[j]>a[j+1])
{
temp=a[j];
a[j]=a[j+1];
a[j+1]=temp;
}
}
}
printf("stored array using bubble sortn ");
for(i=0;i<num;i++)
printf("%dt",a[i]);

8. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
8 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
getch();
}
/* Output */
enter total number to store in array
7
enter nummbers
12
15
6
8
3
9
5
stored array using bubble sort
3 5 6 8 9 12 15

9. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
9 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
Experiment No. 5
Aim:-Write a program to find the roots of an equation using Newton Raphson Method.
/* Program for Newton Raphson Method*/
#include<stdio.h>
#include<conio.h>
#include<math.h>
float f(float x)
{
return x*log10(x) - 1.2;
}
float df (float x)
{
return log10(x) + 0.43429;
}
int main()
{
int itr, maxmitr;
float h, x0, x1, allerr;
printf("nEnter x0, allowed error and maximum iterationsn");
scanf("%f %f %d", &x0, &allerr, &maxmitr);
for (itr=1; itr<=maxmitr; itr++)
{
h=f(x0)/df(x0);
x1=x0-h;
printf(" At Iteration no. %3d, x = %9.6fn", itr, x1);
if (fabs(h) < allerr)
{

10. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
10 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
printf("After %3d iterations, root = %8.6fn", itr, x1);
return 0;
}
x0=x1;
}
printf(" The required solution does not converge or iterations are
insufficientn");
getch();
}
/* Output */
Enter x0, allowed error and maximum iterations
2
4
4
At Iteration no. 1, x = 2.813170
After 1 iterations, root = 2.813170

11. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
11 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
Experiment No. 6
Aim:-Write a program to find the solution of differential equation by Runge Kutta Equation.
#include<stdio.h>
#include<conio.h>
#include<math.h>
float f(float x,float y);
int main()
{
float x0,y0,m1,m2,m3,m4,m,y,x,h,xn;
printf("Enter x0,y0,xn,h:");
scanf("%f %f %f %f",&x0,&y0,&xn,&h);
x=x0;
y=y0;
printf("nnXttYn");
while(x<xn)
{
m1=f(x0,y0);
m2=f((x0+h/2.0),(y0+m1*h/2.0));
m3=f((x0+h/2.0),(y0+m2*h/2.0));
m4=f((x0+h),(y0+m3*h));
m=((m1+2*m2+2*m3+m4)/6);
y=y+m*h;
x=x+h;
printf("%ft%fn",x,y);
}

12. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
12 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
}
float f(float x,float y)
{
float m;
m=(x-y)/(x+y);
return m;
getch();
}
/* Output */
Enter x0,y0,xn,h:3
4
5
6
X Y
9.000000 4.909602

13. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
13 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
Experiment No. 7
Aim:-Write a program to practice one of the numerical Integration Method.
/* SIMPSON'S 1/3 RULE Integration method*/
#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
float x[10],y[10],sum=0,h,temp;
int i,n,j,k=0;
float fact(int);
clrscr();
printf("nhow many record you will be enter: ");
scanf("%d",&n);
for(i=0; i<n; i++)
{
printf("nnenter the value of x%d: ",i);
scanf("%f",&x[i]);
printf("nnenter the value of f(x%d): ",i);
scanf("%f",&y[i]);
}
h=x[1]-x[0];
n=n-1;
sum = sum + y[0];
for(i=1;i<n;i++)

14. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
14 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
{
if(k==0)
{
sum = sum + 4 * y[i];
k=1;
}
else
{
sum = sum + 2 * y[i];
k=0;
}
}
sum = sum + y[i];
sum = sum * (h/3);
printf("nn I = %f ",sum);
getch();
}
/* Output */
how many record you will be enter: 5
enter the value of x0: 0
enter the value of f(x0): 1
enter the value of x1: 0.25
enter the value of f(x1): 0.8

15. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
15 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi
enter the value of x2: 0.5
enter the value of f(x2): 0.6667
enter the value of x3: 0.75
enter the value of f(x3): 0.5714
enter the value of x4: 1
enter the value of f(x4): 0.5
I = 0.693250

16. Shri Rawatpura Sarkar Institute of Technology-II New Raipur (C.G.)
16 DepartmentofMechanicalEngineering–4th
Sem.PreparebyMsSwagitaDwivedi