UNIT 1

Approximation & Error analysis:

Approximations and round of errors, Truncation errors and Taylor

Series.

Roots of Non-linear Equations:

Determination of roots of polynomials and transcendental equations by

Bisection, Secant and Bairstow’s method, Newton-Raphson method, Successive substitution method etc  .

UNIT 2

Linear Algebraic Equation

: Solutions of linear simultaneous linear algebraic equations by Gauss

Elimination and Gauss-Siedel iteration methods Successive substitution method and Decomposition

methods.

UNIT 3

Curve fitting & Numerical Differentiation:

Curve fitting – linear and nonlinear regression analysis;

Backward, Forward and Central difference relations and their uses in numerical differentiation and

integration, Application of difference relations in the solution of differential equations.

UNIT 4

Introduction to numerical integration

Numerical Integration and Area under a Curve:

and Area

; Trapezoidal method, Simpson’s 1/3 method, Simpson’s 3/8 method and

under a Curve

Newton’s method for integration.

UNIT 5

Ordinary Differential Equation:

Numerical solution of ordinary differential equations by Euler, Modified

Euler, Runga-Kutta and Predictor-Corrector method.

Partial Differential Equation:

Elliptic equation & parabolic equation & their solution techniques. Finite

Element Method: – General approach, application in one dimension. Computer programming using C/ C++

on these topics.