Joseph-Louis Lagrange ( . . - . .
) Learning Objectives After studying this chapter, students will be able to understand z the finite differences z how to find the polynomial using finite differences z how to find the relations between the operators z how to find the missing terms z how to interpolate the values of a given series using Newton’s interpolation formulae z how to apply the Lagrange’s interpolation formula . Finite Differences Consider the arguments x x x x n and the entries y y y y n . y ( ) be a function of x . Let us assume that the values of x are in increasing order and equally spaced with a space length h .
Then the values of x may be taken to be x x h x nh and the function assumes the values ), ( ), ( ), , ( nh + Here we study some of the finite differences of the function y ( ) . . . Forward Difference Operator, Backward Difference Operator and Shifting Operator Forward Difference Operator (∆ ): Let y = f ( x ) be a given function of x .
Let y y y n be the values of at x = x x x x n ¼ respectively. Then … are called the first (forward) differences of the function y . They are denoted by y n ,..., − respectively. XII Std - Business Maths & Stat EM Chapter - - Numerical Methods (i.e) ,..., In general, D y + , , , ,...
The symbol D is called the forward difference operator and pronounced as delta . The forward difference operator ∆ can also be defined as D f x