Program No(1)

8/2/2019 Program No(1)

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*********************************************************************

Program No:1

Program using Newtons Backward Interpolation Formula

*********************************************************************

#include

#include

#define Err 0.000005

long Fact(int x);

main()

{

int i,j,m;

float P,Z,P1,Poly,Diff,X[20],Y[20];

printf(" ***************************************\n");

printf(" Newton's Backward Interpolation formula.\n");

printf(" ***************************************\n");

printf(" Enter the number of points.");scanf("%d",&m);

printf(" Enter the number to be searched.");

scanf("%f",&Z);

printf(" Enter the points.\n");

for(i=1;i


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printf("\t X\t\t Y\n");

printf(" ***************************************\n");

for(i=1;i


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Output

***************************************

Newton's Backward Interpolation formula.

***************************************

Enter the number of points.5

Enter the number to be searched.1975

Enter the points.

X[1]=1941

Y[1]=46

X[2]=1951

Y[2]=65

X[3]=1961

Y[3]=81

X[4]=1971

Y[4]=93

X[5]=1981Y[5]=101

***************************************

Newton's Backward Interpolation formula.

***************************************

***************************************

X Y

***************************************

1941.0000 46.00001951.0000 65.0000

1961.0000 81.0000

1971.0000 93.0000

1981.0000 101.0000

**************************************

Value of F(1975.00) : 96.646400

**************************************


4/38

*********************************************************************

Program No:2

Program using trapezoidal rule to find the integral value when function is given

*********************************************************************

#include

#include

float F(float x);

main()

{

int i;

float a,b,h,N,Trap,Int1;

printf(" *********************************************************\n");

printf(" Program to find integral value using trapezoidal rule.\n");

printf(" when function is given. \n");

printf(" *********************************************************\n");

printf(" Enter the lower limit of integral.");scanf("%f",&a);

printf(" Enter the upper limit of integral.");

scanf("%f",&b);

printf(" Enter the divided point.");

scanf("%f",&h);

N=(b-a)/h;

Int1=0;

Trap=0;

for(i=1;i


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Output

***********************************************************

Program to find integral value using trapezoidal rule.

when function is given.

*********************************************************

Enter the lower limit of integral.0

Enter the upper limit of integral.1

Enter the divided point.0.5

*********************************************************

Program to find integral value using trapezoidal rule.


*********************************************************

Lower limit : 0.00

Upper limit : 1.00

Divided Point : 0.50

Function : 1/(1+x)Integral Value : 0.731370


6/38

*********************************************************************

Program No:3

Program using Newtons Divided Difference Formula

*********************************************************************

#include

#include

main()

{

int i,j,k,m;

float Z,Factor,Diff,Dr,Poly,X[20],Y[20];

printf(" *******************************************\n");

printf(" Newton's Divided Difference formula.\n");

printf(" *******************************************\n");

printf(" Enter the number of points.");

scanf("%d",&m);printf(" Enter the number to be searched.");

scanf("%f",&Z);


for(i=1;i


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for(i=1;i


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Output

*******************************************

Newton's Divided Difference formula.

*******************************************


Enter the number to be searched.301

Enter the points.

X[1]=300

Y[1]=2.4771

X[2]=304

Y[2]=2.4829

X[3]=305

Y[3]=2.4843

X[4]=307

Y[4]=2.4871

*****************************************

La Granges' Inverse Interpolation formula.

***************************************

Y X

***************************************

2.4771 300.0000

2.4829 304.0000

2.4843 305.0000

2.4871 307.0000

**************************************

Value of X when Y=301.00 : 2.477100

**************************************


9/38

*********************************************************************

Program No: 4

Program to implement Simpsons 1/3rd

rule .

*********************************************************************

#include

#include

main()

{

float x[10],y[10],sum=0,h,temp;

int i,n,j,k=0;

float fact(int);

printf("\nhow many record you will be enter: ");

scanf("%d",&n);

for(i=0; i


10/38

Output

-------------------------------------------------------------------------------------------------------

how many record you will be enter: 5

enter the value of x0: 1

enter the value of f(x0): 1

enter the value of x1: 1.5

enter the value of f(x1): .666



enter the value of x3: 2.5




I = 1.099500

-------------------------------------------------------------------------------------------------------


11/38

*********************************************************************

Program No:5

Program to fit an exponential function by the method of least squares

*********************************************************************

#include

#include

main()

{

int N,i;

float A[20],B[20],SumX,SumY,SumXX,SumXY,A0,A1,P;

printf("Program to fit an exponential function\n");

printf("=======================================\n\n\n");

printf("Enter the No. of points :");

scanf("%d",&N);

printf("Enter the points :\n");

for(i=1;i


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Output

----------------------------------------------

Program to fit an exponential function

----------------------------------------------

Enter the No. of points :5

Enter the points :

0

0.1

0.5

0.45

1.0

2.15

1.5

9.15

2

40.35

-------------------------------------------------------------------------------------------------------PROGRAM TO FIT AN EXPONENTIAL FUNCTION

-------------------------------------------------------------------------------------------------------

No. of points : 5

The entered points are:

x y

===============

0.00 0.10

0.50 0.451.00 2.15

1.50 9.15

2.00 40.35

The constants P and A1 which best fit an exponential function are:

P= 0.1015

A1= 3.0025

The exponential function is : Y=0.1015*e^3.0025X


13/38

*********************************************************************

Program No:6

Program to fit a straight line

*********************************************************************

#include

#include

main()

{

int i,j,n;

float a[10],b[10],sumx,sumy,sumxx,sumxy,A0,A1;

printf(" ************************************\n");

printf(" Program for fitting a straight line.\n");

printf(" ************************************\n");

printf(" Enter the number of data elements.");

scanf("%d",&n);

printf(" Enter the values for a and b.\n");

for(i=1;i


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Output

************************************

Program for fitting a straight line.

************************************

Enter the number of data elements.6

Enter the values for a and b.

A[1] =2

B[1] =7.32

A[2] =4

B[2] =8.24

A[3] =6

B[3] =9.2

A[4] =8

B[4] =10.19

A[5] =10

B[5] =11.01

A[6] =12

B[6] =12.05*****************************************

Program for fitting a straight line.

*****************************************

Points are ....

A B

2.0000 7.3200

4.0000 8.2400

6.0000 9.2000

8.0000 10.1900

10.0000 11.0100

12.0000 12.0500******************************************

The calculated value of A0 : 6.3733


******************************************

Equation of the straight line : (A0+A1*X)

6.3733 + 0.4707 X

******************************************


15/38

*********************************************************************

Program No:7

Program using Newtons Forward Interpolation formula Formula

*********************************************************************

#include

#include

#define Err 0.000005

long Fact(int x);

main()

{

int i,j,m;

float P,Z,P1,Poly,Diff,X[20],Y[20];

printf(" ***************************************\n");

printf(" Newton's Forward Interpolation formula.\n");

printf(" ***************************************\n");

printf(" Enter the number of points.");scanf("%d",&m);

printf(" Enter the number to be searched.");

scanf("%f",&Z);


for(i=1;i


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for(i=1;i


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Output

***************************************

Newton's Forward Interpolation formula.

***************************************


Enter the number to be searched.1.7

Enter the points.

X[1]=1.6

Y[1]=0.625

X[2]=1.8

Y[2]=0.5556

X[3]=2.0

Y[3]=0.5

X[4]=2.2

Y[4]=0.4555

***************************************

Newton's Forward Interpolation formula.

***************************************

*****************************

X Y

*****************************

1.6000 0.62501.8000 0.5556

2.0000 0.5000

2.2000 0.4555

*****************************

Value of F(1.70) : 0.588406

*****************************


18/38

*********************************************************************

Program No:8

Program using Gauss Elimination method(solution of linear squares)

*********************************************************************

#include

#include

main()

{

int i,j,k,N;

float X[10],A[10][10],B[10][10];

printf(" *********************************************************\n");

printf(" Gaussian Elimination Method(Solution of linear systems).\n");

printf(" *********************************************************\n");

printf(" Enter the order of system N.");

scanf("%d",&N);

printf(" Enter the argmented matrix.\n\t");

for(i=1;i


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for(i=1;i


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Output

*********************************************************

Gaussian Elimination Method(Solution of linear systems).

*********************************************************

Enter the order of system N.3

Enter the argmented matrix.

2

1

1

10

3

2

3

18

1

49

16

*********************************************************

Gaussian Elimination Method(Solution of linear systems).

*********************************************************

The argmented matrix.

2.000000 1.000000 1.000000 10.000000

3.000000 2.000000 3.000000 18.000000

1.000000 4.000000 9.000000 16.000000

Roots are...

x1 = 7.0000

x2 = -9.0000

x3 = 5.0000


21/38

*********************************************************************

Program No:9

Program using LaGranges Inverse Interpolation Formula

*********************************************************************

#include

#include

main()

{

int i,j,m;

float Z,L,Poly,X[20],Y[20];

printf(" *******************************************\n");

printf(" La Granges' Inverse Interpolation formula.\n");

printf(" *******************************************\n");

printf(" Enter the number of points.");

scanf("%d",&m);

printf(" Enter the number to be searched.");scanf("%f",&Z);


for(i=1;i


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Output

*******************************************


*******************************************


Enter the number to be searched.2.6

Enter the points.

X[1]=1

Y[1]=0

X[2]=3

Y[2]=1

X[3]=55

Y[3]=3

*****************************************


*****************************************

***************************************Y X

***************************************

0.0000 1.0000

1.0000 3.0000

3.0000 55.0000

**************************************

Value of X when Y=2.60 : 39.479996

**************************************


23/38

*********************************************************************

Program No:10

Program to find the root of the equation x3-2x-5 by Newtons Rapsons method

*********************************************************************

#include

#include

#define ERR 0.000005

#define F(X) ( pow(X,3)-(2*X)-5)

#define dF(X) (3*pow(X,2)-2)

main()

{

float X,X1;

printf("---------------------------------------------------------------------------------\n");

printf(" PROGRAM TO FIND THE ROOTS USING NEWTON RAPSON

METHOD \n");

printf("-------------------------------------------------------------------------------------\n");printf("\n\n");

printf("The given equation is x^3-2x-5 \n");

printf("\n\n");

printf("Enter the initial approximation: ");

scanf("%f",&X);

printf("\nThe approximations are:\n");

X1=X-((F(X))/(dF(X)));

while( fabs(X1-X)>ERR)

{

X=X1;printf("%3.5f\n",X);

X1=X-((F(X))/(dF(X)));

}

printf("\nThe root is %3.5f",X);

printf("\n-------------------------------------------------------------------------------------");

}


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Output

-------------------------------------------------------------------------------------------------------

PROGRAM TO FIND THE ROOTS USING NEWTON RAPSON METHOD

-------------------------------------------------------------------------------------------------------

The given equation is x^3-2x-5

Enter the initial approximation: 3

The approximations are:

2.36000

2.12720

2.09514

2.09455

The root is 2.09455

-------------------------------------------------------------------------------------------------------


25/38

*********************************************************************

Program No : 11

Program for power function

*********************************************************************

#include

main()

{

int count,n;

float x,y;

printf("Enter the values of x&n:");

scanf("%f%d",&x,&n);

y=1.0;

count=1;

while(count


26/38

*********************************************************************

Program No:12

Program to fit a power function

*********************************************************************

#include

#include

main()

{

int i,n;

float a[10],b[10],sumx,sumy,sumxx,sumxy,A0,A1;

printf(" ************************************\n");

printf(" Program to fit a power function.\n");

printf(" ************************************\n");


scanf("%d",&n);

printf(" Enter the values for a and b.\n");

for(i=1;i


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Output

************************************

Program to fit a power function.

************************************

Enter the number of data elements.6

Enter the values for a and b.

A[1] =2

B[1] =43

A[2] =4

B[2] =25

A[3] =7

B[3] =18

A[4] =10

B[4] =13

A[5] =20

B[5] =8A[6] =40

B[6] =5

*****************************************

Program to fit a power fuction.

*****************************************

Points are ....

A B

2.0000 43.0000

4.0000 25.0000

7.0000 18.0000

10.0000 13.000020.0000 8.0000

40.0000 5.0000

******************************************


The calculated value of A1 : -0.7183

******************************************

Power function : (A0*X^A1)

4.2452*X^-0.7183

******************************************


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*********************************************************************

Program No: 13

Programto implement Cramers rule.

*********************************************************************

#include

double finddet(double a1,double a2, double a3,double b1, double b2,double b3,double c1, double c2, double c3);

main()

{

double a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2, d3,det, detx, dety, detz;

printf("\n a1?");

scanf("%lf",&a1);

printf("\n b1?");

scanf("%lf",&b1);

printf("\n c1?");

scanf("%lf",&c1);

printf("\n d1?");

scanf("%lf",&d1);

printf("\n a2?");

scanf("%lf",&a2);

printf("\n b2?");

scanf("%lf",&b2);

printf("\n c2?");

scanf("%lf",&c2);

printf("\n d2?");

scanf("%lf",&d2);

printf("\n a3?");scanf("%lf",&a3);

printf("\n b3?");scanf("%lf",&b3);

printf("\n c3?");

scanf("%lf",&c3);

printf("\n d3?");

scanf("%lf",&d3);

det=finddet(a1,a2,a3,b1,b2,b3,c1,c2,c3);

detx=finddet(d1,d2,d3,b1,b2,b3,c1,c2,c3);

dety=finddet(a1,a2,a3,d1,d2,d3,c1,c2,c3);detz=finddet(a1,a2,a3,b1,b2,b3,d1,d2,d3);

if(d1==0 && d2==0 && d3==0 && det==0)

printf("\n Infinite Solutions\n ");

else if(d1==0 && d2==0 && d3==0 && det!=0)

printf("\n x=0\n y=0, \n z=0\n ");

else if(det!=0)

printf("\n x=%lf\n y=%lf\n z=%lf\n", (detx/det), (dety/det), (detz/det));

else if(det==0 && detx==0 && dety==0 && detz==0)

printf("\n Infinite Solutions\n ");

elseprintf("No Solution\n ");

}


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double finddet(double a1,double a2, double a3,double b1, double b2,double b3,

double

c1, double c2, double c3)

{

return ((a1*b2*c3)-(a1*b3*c2)-(a2*b1*c3)+(a3*b1*c2)+(a2*b3*c1)-(a3*b2*c1));

}


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Output

-------------------------------------------------------------------------------------------------------

a1?1

b1?1

c1?1

d1?7

a2?2

b2?3

c2?2

d2?17

a3?4

b3?9

c3?1

d3?37

x=2.000000

y=3.000000

z=2.000000

------------------------------------------------------------------------------------------------------


31/38

*********************************************************************

Program No:14

Program to fit a quadratic equation

*********************************************************************

#include

#include

main()

{

int i,j,k,n;

float x[10],y[10],a[10][10];

float sumx,sumx2,sumx3,sumx4,sumy,sumxy,sumxyz;

printf(" ************************************\n");

printf(" Program to fit a quadratic equation.\n");

printf(" ************************************\n");


scanf("%d",&n);printf(" Enter the values for arrays x and y.\n");

for(i=1;i


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printf(" *****************************************\n");

printf(" Points are ....\n");

printf(" X Y\n");

for(i=1;i


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34/38

*********************************************************************

Program No:15

Program to find the roots of the equation x3-2x-5 using regular falsi method

*********************************************************************

#include

#include

#define ERR 0.000005

#define F(X) (pow(X,3)-(2*X)-5)

main()

{

float A,B,mid;

printf("---------------------------------------------------------------\n");

printf(" PROGRAM TO FIND THE ROOT USING REGULAR FALSING

METHOD \n");

printf("-----------------------------------------------------------------------------------\n");printf("\n\n");

printf("The given equation is x^3-2x-5 \n");

printf("\n");

printf("Enter the values of A & B: ");

scanf("%f%f",&A,&B);

printf("\nThe approximations are:\n");

if((F(A)0) || (F(A)>0 && F(B) ERR )){

if(F(mid)


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Output

-------------------------------------------------------------------------------------------------------

PROGRAM TO FIND THE ROOT USING REGULAR FALSING METHOD

-------------------------------------------------------------------------------------------------------

The given equation is x^3-2x-5

Enter the values of A & B: 2 3

The approximations are:

2.08126

2.08964

2.09274

2.09388

2.09431

2.09446

2.094522.09454

2.09455

2.09455

2.09455

2.09455

The root is 2.09455

-------------------------------------------------------------------------------------------------------


36/38

*********************************************************************

Program No : 16

Program using Simpsons 3/8 rule to find the integral value when function is given

*********************************************************************

#include

#include

float F(float x);

main()

{

int i,N,S;

float a,b,h,Int1,Int2,Simp;

printf(" *********************************************************\n");

printf(" Program using Simpson's 3/8th rule to find integral value \n");

printf(" when function is given. \n");

printf(" *********************************************************\n");printf(" Enter the lower limit of integral.");

scanf("%f",&a);

printf(" Enter the upper limit of integral.");

scanf("%f",&b);

printf(" Enter the divided point.");

scanf("%f",&h);

N=(b-a)/h;

Int1=0;

Int2=0;

Simp=0;

S=(int)N;if (S%2==0) {

i=1;

do{

if (i%3==0)

Int2=Int2+F(a+i*h);

else

Int1=Int1+F(a+i*h);

i=i+1;

}while(i


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}

float F(float x)

{

return (1/(1+x));

}


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Output

*********************************************************

Program using Simpson's 3/8th rule to find integral value


*********************************************************

Enter the lower limit of integral.0

Enter the upper limit of integral.1

Enter the divided point.0.5

*********************************************************

Program to find integral value using Simpson's 3/8th rule.


*********************************************************

Lower limit : 0.00

Upper limit : 1.00

Divided Point : 0.50Function : 1/x+1

Integral Value : 0.656250

Documents

Program No(1)