2. • Calculus is the mathematics of change. Because engineers
must continuously deal with systems and processes that
change, calculus is an essential tool of engineering.
• Standing in the heart of calculus are the mathematical concepts
of differentiation and integration
• Numerical differentiation is the process of finding the
numerical value of the derivative of a given function at a given
point.
3. For some particular value of x from the given data (xi,yi), i=1, 2,
3…..n where y=f(x) i explicitly, the interpolation to be used depends on
the particular value of x which derivatives are required.
•If the values of x are not equally spaced, we represent the function by
difference formula and the derivatives are obtained.
•If the values of x are equally spaced, the derivatives are calculated by
using Newton’s Forward interpolation formula or backward interpolation
formula.
4. Principle:
First fit a polynomial for the given difference data interpolation using
Newton ’s divided difference interpolation formula and compute the
derivatives for a given x.
10. erivatives using Finite difference
Example 2.
Find the first two derivatives of y at x=54 from the following data
x 50 51 52 53 54
y 3.6840 3.7083 3.7325 3.7563 3.7798
12. erivatives using Finite difference
Example 1
Find first and second derivatives of the function at the point x=1.2
from the following data
x 1 2 3 4 5
y 0 1 5 6 8
The difference table
