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Course Overview

Introduction and Objectives: In today’s world the practical problems are quite complex and it may not be possible to find their analytical solutions. Hence we have to resort to oriented numerical methods for solving them. Numerical analysis provides knowledge of various techniques to get mathematical entities involved in solving the problems.

BLOCK 1: Computer Arithmetic and Solution of Linear and Non-linear Equations

Unit 1 : Computer Arithmetic

Floating–Point Arithmetic and Errors, Rounding and Chopping of a Number and Associated Errors, Floating Point Representation of Numbers, Truncation errors and Taylor’s Series

Unit 2 : Solution of Linear Algebraic Equations

Preliminaries, Direct Methods, Gauss Elimination Method (Basic), Gauss Elimination Method (Row Interchanges: Pivotal condensation),Iterative Methods, Gauss Jacobi Iterative Method, The Gauss-Seidel Iteration Method, Comparison of Direct and Iterative Methods

Unit 3 : Solution of Non-linear Equations

Non Linear Equations, Solution of Non Linear Equations, Successive Substitution Method(Fixed point method), Bisection Method ,Newton-Raphson Method, Regula-falsi Method, Secant Method

BLOCK 2 : Interpolation

Unit 1 : Operator

What is Interpolation, Some Operators and their Properties, Interrelation between operators, Applications of operators on some functions

Unit 2 : Interpolation with Equal Intervals

Difference Table, Interpolation Methods, Newton Forward Difference Formula, Newton Backward Difference Formula, Central Difference Formula, Stirling’s Formula, Bessle’s Formula

Unit 3 : Interpolation with Unequal Intervals

Lagrange’s Method, Divided Difference Method, Divided Difference Table, Newton’s Divided Difference Method

BLOCK 3: Differentiation, Integration and Differential Equations

Unit 1 : Numerical Differentiation

Differentiation by Forward/Backward Difference Formula, Differentiation by Central Difference Formula

Unit 2 : Numerical Integration

Methodology’s of Numerical Integration, Rectangular Rule, Trapezoidal Rule, Simpsons (1/3) Rule

Unit 3 : Ordinary Differential Equation

Initial Value and Boundary Value Problem, Euler’s Method, Improved Euler’s Method, Runge Kutta (R-K) Methods (of Order 2 and 4)

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