Maths project of Newton Forward Interpolation.

3. INTRODUCTION:
INTER-POLATION: It is a process of finding an approximate value of function at some point ,
within the range (Xo,Xn) , but not in the set of data points .
EXTRA-POLATION: It is a process of finding an approximate value of function at some point
outside the range .
NEWTON`S FORWARD INTERPOLATION : Forward Interpolation is used to interpolate the values
of y nearer to the beginning value of the given table .
Formula:

4. FORWARD DIFFERENCE TABLE

17. Some other methods to obtain value of a
function at a given point
 When the arguments are equispaced, Stirling’s formula can be used.
 When the arguments are not equispaced,we can use the following
methods:
(i) Lagrange’s interpolation
(ii) Newton’s Divided difference

18. APPLICATIONS AND USES:
Application:
A spring is an elastic object used to store
mechanical energy. In case of mechanical spring
there is a spring load and deflection graph. The
deflection is in millimeters and the load is
measured in newton. The deflection is plotted on
the x-axis and the corresponding load in newton on
y-axis. Often we have to find the values between
the two sets of values (load vs. deflection). Hence
interpolation is the technique used to find the
unknown values. The graph is usually plotted in
excel.
Uses: Interpolation is used to scale image
and to convert the sampling rate of digital
signals .