BCS-054:Computer Oriented Numerical Techniques

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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)