This unit deals with the definition of transcendental function and explains the Bisection Method, Secant and Regula-Falsi Methods and Newton Raphson Method. It also explains Muller method, Chebyshev method and describes the multipoint iteration methods to find roots of the equations.

This unit defines rate of convergence of an iterative method and explains rate of convergence of Secant and Regula-Falsi Methods, and Newton-
Raphson Method. It also explains rate of convergence of Muller method and Chebyshev method.

This unit defines iteration function and explains high order Methods. It also explains acceleration of the convergence and efficiency of a method and helps in analyzing system of non-linear equations.

This unit defines change of sign occurrence and explains Descartes' Rule of Signs and Shum's theorem. It also explains Birge-Vieta method and Bairstowmethod and helps in analyzing Graffe's Root Squaring method.

There are two main uses of .interpolation or 'interpolating polynomials. The first use is in reconstructing the function f(x) when it is not given explicitly and only the value of f(x) and / or its certain order derivatives at it set of points, called nodes; tabular points or arguments are known. The second use is to replace the function f(x) by and interpolating polynomial P(x) so that many commo ......

The Hermite interpolating polynomial interpolates not only the function f(x) but also its (certain order) derivatives at a given set of tabular points.

The commonly used classes of approximating functions include polynomials,trigonometric function, exponential functions and rational functions. However, from application view point, the polynomial functions are mostly used, although in special cases, the trigonometric, rational and other functions are also used.

There are several methods available to find the derivative of a function f(x) in closed form. However, when f(x) is a complicated function or when it is given in a tabular form, we use numerical methods.

There are several methods available to find the derivative of a function f(x) or to evaluate the definite integral in closed form.
However, when f(x) is a complicated function or when it is given in a tabular form, we use numerical methods.

Numerical difference equations play a important role in numerical analysis. Here, we give a brief in detailed topics are covered about difference equations, numerical methods, single step methods and its stability on various grounds and finally about multi-step methods.

This unit explains Initial Value Problem and linear second order differential equations. It also explains non-linear second order differential equations. and describes finite difference methods.

Pages: 13

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