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Title: simplest with best research
Description: These notes were made after a lot of research by me. I made these notes very simple and understandable. Please share these asap.
Description: These notes were made after a lot of research by me. I made these notes very simple and understandable. Please share these asap.
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NUMERICAL ANALYSIS AND
STATISTICAL TECHNIQUES LAB
ETMA -252
SUBMITTED TO
URFI SIR
SUBMITTED BY
VISHAL SINGH
MAE- IV SEMESTER
00320903613
INDEX
S
...
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Name of the Experiment
Page
No
...
3
To write a program in C language for finding Sum and
Average of ‘n’ integer numbers
...
7
To write a program in C language for finding sum of
series of function Sin(x) up to 5th term
...
Date
10
To write a program in C language for finding value of
function at given value of argument on the basis of given
data by using Newton’s Divided Difference method
...
16
To write a program in C language for calculating value of
integration within given limits and number of intervals by
Trapezoidal Rule
...
22
To write a program in C language for solving
simultaneous equation in ‘n’ variables by using Gauss
Elimination Method
...
29
To write a program in C language for solving given
differential equation by Runge-Kutta Method
...
01y) and find the amount
of radioactive material left given initial amount and final
time by Modified Euler Method
...
35
38
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |i
Experiment 1
Aim
To write a program in C language for finding the largest number out of three integers
...
h>
#include
Theory
Variables
Variables are memory location in computer's memory to store data
...
Variable names are just the symbolic
representation of a memory location
...
, count etc
...
Integer (int) values are
whole numbers (like 10 or -10)
...
(Like 1
...
123)
...
If you declare a character
variable you must always put the character between single quotes (like so ‘A’)
...
Constants
Constants are the terms that can't be changed during the execution of a program
...
5,
"Programming is easy
...
In C, constants can be classified as:
Integer constants
Integer constants are the numeric constants (constant associated with number) without any
fractional part or exponential part
...
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |3
Floating-point constants
Floating point constants are the numeric constants that has either fractional form or exponent
form
...
0, 0
...
22E-5
Character constants
Character constants are the constant which use single quotation around characters
...
String constants
String constants are the constants which are enclosed in a pair of double -quote marks
...
//prints string with newline
Enumeration constants
Keyword enum is used to declare enumeration types
...
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |4
Experiment 3
Aim
To write a program in C language for finding Sum and Average of ‘n’ integer numbers
...
h>
#include
00;
printf("\n Enter the number of data \n");
scanf("%d",&n);
printf("\n enter the data\n");
for(i=1;i<=n;i++)
{
scanf("%f",&x);
sum=sum+x;
}
avg=sum/n;
printf("\n Sum of %d numbers = %f",n,sum);
printf("\n Average of %d numbers = %f",n,avg);
getch();
return 0;
}
Output
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |6
Experiment 4
Aim
To write a program in C language for finding the Roots of given Quadratic Equation
Flowchart
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |7
Program
#include
h>
#include
5))/2*a;
x2=(-b-pow(d,0
...
5))/2*a;
printf("\n Roots are \n x1=%f-%fi",x1,x2);
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |8
printf("\n x2=%f+%fi",x1,x2);
}
}
getch();
return 0;
}
Output
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |9
Experiment 5
Aim
To write a program in C language for finding sum of series of function Sin(x) up to 5th term
...
h>
#include
h>
int main()
{
int fact(int);
int i;
float x,s;
s=0
...
Flowchart
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |13
Program
#include
h>
int main()
{
int n,i,j;
float x[100],fx[100],xp,fxd[100],fxdj,t,fact,fxp;
printf("\n Enter the number of known points\n");
scanf("%d",&n);
printf("\n Enter the points with their value\n");
for(i=0;i
printf("\n Enter the %dst term \n",i+1);
scanf("%f%f",&x[i],&fx[i]);
}
printf("\n Enter the point at which value of function is required\n");
scanf("%f",&xp);
for(i=0;i
fxd[i]=fx[i];;
}
fxp=fx[0];
fact=1
...
Flowchart
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |16
Program
#include
h>
int main()
{
int n,i,j;
float x[100],fx[100],xp,N,D,fxp;
printf("\n How many data inputs are to be entered\n");
scanf("%d",&n);
printf("\n Enter the value of\n \tx[i]\tfx[i]");
for(i=0;i
printf("\n %d \t",i+1);
scanf("%f%f",&x[i],&fx[i]);
}
fxp=0
...
0;
for(j=0;j
if(i==j)
continue;
N=N*(xp-x[j]);
D=D*(x[i]-x[j]);
}
fxp=fxp+(N/D)*fx[i];
}
printf("\n The value of function at x=%0
...
4f",xp,fxp);
getch();
return 0;
}
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |17
Output
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |18
Experiment 8
Aim
To write a program in C language for calculating value of integration within given limits and number of intervals
by Trapezoidal Rule
...
h>
#include
h>
int main()
{
int n,i;
float x[100],fx[100],a,b,h,S;
printf("\n Enter the initial & final limit\n");
scanf("%f%f",&a,&b);
printf("\n Enter the number of intervals \n");
scanf("%d",&n);
h=(b-a)/n;
for(i=0;i<=n;i++)
{
x[i]=a+i*h;
fx[i]=sin(x[i]);
printf("\n x=%f\t fx=%f",x[i],fx[i]);
}
S=fx[0]+fx[n];
for(i=0;i
S=S+(2
...
5*h*S;
printf("\n The value of integration=%f",S);
getch();
}
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |20
Output
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |21
Experiment 9
Aim
To write a program in C language for calculating the value of integration within given limits and number of
intervals by Simpson’s 1/3rd and 3/8th Rule
...
h>
#include
0*fx[i];
}
for(i=2;i
s=s+2
...
0/3
...
0/8
...
Flowchart
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |25
Program
#include
h>
int main()
{
int i,j,k,n;
float a[21][21],b[20],c,x[20],S;
printf("Enter the number of unknowns [n<=20]\n");
scanf("%d",&n);
printf("Enter the coefficient matrix A \n");
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
scanf("%f",&a[i][j]);
}
printf("\n");
}
printf("Enter the matrix B \n");
for(i=1;i<=n;i++)
{
scanf("%f",&b[i]);
printf("\n");
}
for(i=1;i
for(j=i+1;j<=n;j++)
{
c=a[j][i];
b[j]=b[j]-(b[i]*(c/a[i][i]));
for(k=1;k<=n;k++)
{
a[j][k]=a[j][k]-(a[i][k]*(c/a[i][i]));
}
}
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |26
}
for(i=1;i<=n;i++)
{
a[i][n+1]=b[i];
}
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
printf("%f\t",a[i][j]);
}
printf(" | %f\n",a[i][n+1]);
}
for(i=0;i<=n;i++)
{
x[i]=0
...
Flowchart
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |29
Program
#include
h>
int main()
{
int i,j,k,n;
float a[21][21],b[20],x[20],temp,Sum;
printf("Enter the number of unknowns [n<=20]\n");
scanf("%d",&n);
printf("Enter the coefficient matrix A \n");
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
scanf("%f",&a[i][j]);
}
printf("\n");
}
printf("Enter the matrix B \n");
for(i=1;i<=n;i++)
{
scanf("%f",&a[i][n+1]);
printf("\n");
}
printf("Enter the Initial Approximation \n");
for(i=1;i<=n;i++)
{
printf("x[%d] = ",i);
scanf("%f",&x[i]);
printf("\n");
}
for(k=1;k<=5;k++)
{
printf("\n %d Iteration : ",k);
for(i=1;i<=n;i++)
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |30
{
Sum=0;
for(j=1;j<=n;j++)
{
if(i!=j)
{
temp=x[j]*a[i][j];
Sum=Sum+temp;
}
}
x[i]=a[i][n+1]-Sum;
x[i]=x[i]/a[i][i];
printf("x[%d] = %0
...
Flowchart
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |32
Program
#include
h>
int main()
{
int n=0;
float k1,k2,k3,k4,x,y,S,h;
float f(float x,float y);
printf("Enter the initial approximation of x and y \n");
scanf("%f %f",&x,&y);
printf("\n");
h=0
...
01y) and find the amount of
radioactive material left given initial amount and final time by Modified Euler Method
...
h>
#include
2f \t Radioactive substance=%f \n",x,y);
n++;
}while(n
...
01*y);
}
Output
V i s h a l S i n g h ( 0 0 3 2 0 9 0 3 6 1 3 ) |37
Experiment 14
Aim
To write a program in C language for solving a linear or transcendental equation by Newton-Raphson Method
...
h>
#include
h>
int main()
{
int i;
float x1,x2,f1,f2;
printf("Enter the intitial approxiamtion\n");
scanf("%f",&x1);
x2=x1;
for(i=0;;i++)
{
x1=x2;
f1=pow(x1,2)-9;
f2=(2*x1);
x2=x1-(f1/f2);
if(abs(x2-x1)<0
Title: simplest with best research
Description: These notes were made after a lot of research by me. I made these notes very simple and understandable. Please share these asap.
Description: These notes were made after a lot of research by me. I made these notes very simple and understandable. Please share these asap.