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

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

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

    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.

    when function is given.

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

    Lower limit : 0.00

    Upper limit : 1.00

    Divided Point : 0.50

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

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

    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);

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

    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 of points.4

    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

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

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

    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

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    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 x2: 2

    enter the value of f(x2): .5

    enter the value of x3: 2.5

    enter the value of f(x3): .4

    enter the value of x4: 3

    enter the value of f(x4): .333

    I = 1.099500

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

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

    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

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

    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

    The calculated value of A1 : 0.4707

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

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

    6.3733 + 0.4707 X

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

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

    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);

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

    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 of points.4

    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

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

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

    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

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

    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);

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

    for(i=1;i

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    Output

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

    La Granges' Inverse Interpolation formula.

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

    Enter the number of points.3

    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

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

    La Granges' Inverse Interpolation formula.

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

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

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

    0.0000 1.0000

    1.0000 3.0000

    3.0000 55.0000

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

    Value of X when Y=2.60 : 39.479996

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

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

    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

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

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

    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

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

    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");

    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 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 A0 : 4.2452

    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

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

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

    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");

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

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

    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

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

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

    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

    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 Simpson's 3/8th rule.

    when function is given.

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

    Lower limit : 0.00

    Upper limit : 1.00

    Divided Point : 0.50Function : 1/x+1

    Integral Value : 0.656250